Guillaume Daudin
email: guillaume.daudin@ofce.sciences-po.fr

Sandrine Levasseur
email: sandrine.levasseur@ofce.sciences-po.fr

MEASURING THE EFFECT OF INTERNATIONAL RELOCATIONS ON FRENCH ECONOMY

). A heated debate already took place in the early 1990s, culminating with the reports of Arthuis and Devedjian in 1993 2 . Recently, the new enlargement of the European Union to Central and Eastern European countries (CEECs hereafter) and the suppression of quotas on textile imports, especially from China, have resumed fears about international relocations, which are assumed causing both employment losses and deindustrialisation of the French economy.

the divergence between skilled and unskilled wages 4 . Hence, international relocations are seen as exercising downward pressures on unskilled wages. In France, it is the growing unemployment of the unskilled labour force over the two last decades 5 that is perceived by many citizens as resulting from French enterprises realising an increasing share of their activities in (or with) countries where labour costs are lower. However, this distinction is currently narrowing, as the public debate in the United States has been recently framed in terms of job losses and some French cases have received a huge amount of attention in the media and political circles about the possible adverse effects of international relocations on existing regulations. In the case of MetalEurope, the public was shocked to learn that an industrial firm was able to convince its workers of lengthening the 35-hour work week without any wage compensation, otherwise international relocation would occur. The current right-wing government is using the same argument to increase the support for structural reforms on the labour market.

While the debate is heated again, the underlying empirical data used by protagonists are mainly anecdotic evidence of very rough measures 6 . The goal of the present annex is to discuss and provide some empirical insights on the subject. First, we propose data on job losses in industrial sectors, corrected by temporary employment (interim) and domestic outsourcing. Second, we draw a review of empirical studies measuring the effects of international openness (including international relocations) on French employment.

Development of industrial French employment over 1970-2002

What sectors are suspected of having suffered from international relocations?

Three types of development are needed to isolate the sectors that might have suffered from international relocations: for a given sector, imports and the trade deficit must grow faster than domestic demand while its share in the total employment must decrease. In the INSEE classification, five sectors correspond to that description from 1978 to 2002: clothing 4 For a comparison between developed OECD countries, see ?. Both the United Kingdom and the United States emerge as countries where the wage inequalities between skilled and unskilled workers were widening over 1979-1994, contrasting strongly with France. 5 The unemployment rate for males with low education (and then assumed "unskilled") rose from 5.4 % in 1981 to 13.5 % in 1994. By contrast, the unemployment rate for males with high education (and then assumed "skilled") increased from 3 % in 1981 to "only" 5.9 % in 1994. The gap for female unemployment rates by education level is even larger: see Strauss-Kahn (2003). 6 For example, Direction Générale du Trésor et de la Politique Économique (2004) simply states that 3,4 % of all jobs in 2002 (796 000) are potentially threatened by service international relocations. and leather products, fuel production, household equipment, electric and electronic equipment, and textile [START_REF][END_REF] . Leaving aside fuel production, the rise of imports in these "unskilled labour" from trade with developing countries is impressive, as can be seen in Figure 3. 7 Drumetz (2004).

A first measure of industrial job losses

Here, we will not explore deeper the trade data. Our focus will be on the employment data. A change in the INSEE classification of manufacturing makes it difficult to measure the job losses in these sectors from 1970 to 2002. To do that, we have to use an OECD database, STAN.

In France, while the growth rate of total employment was 18 % over 1970-2002, industrial employment declined by 30 % ( As a result of the so-called "desindustrialisation" of the French economy, the share of manufacturing employment in total employment decreased from 25.5 % in 1970 to 15.2 % in 2002, that is by 10 percent points in three decades (Table 3). The "textiles and leather" sectors moved from 4.3% of total French jobs in the 1970s to less than 1% now. This development in manufacturing sectors sharply contrasts with the one in service sectors. 1,7 1,7 1,6 1,6 1,6 1,5 1,3 1 Sources: OECD, STAN.

,3 -24% -18% CHEMICAL, RUBBER, PLASTICS & FUEL PRODUCTS 2,6 2,6 2,6 2,5 2,3 2,1 1,9 1,9 -29% -24% OTHER NON-METALLIC MINERAL PRODUCTS 1,5 1,5 1,2 1,0 0,9 0,8 0,7 0,7 -55% -32% BASIC METALS & FABRICATED METAL PRODUCTS 4,0 4,0 3,6 3,0 2,8 2,4 2,3 2,2 -45% -25% MACHINERY & EQUIPMENT 4,1 4,1 4,2 3,9 3,6 3,2 3,1 2,9 -28% -24% TRANSPORT EQUIPMENT 2,5 2,5 2,6 2,3 1,9 1,6 1,6 1,5 -38% -32% MANUFACTURING NEC; RECYCLING 1,1 1,1 1,2 1,1 1,0 0,9 0,

A better measure of job losses

At least a part of the industrial job losses is due to changes in the employment structure of industry, with the rise of temporary employment (interim) and of domestic outsourcing. Then, from a statistical viewpoint, an increasing number of jobs are classified in services sectors.

A first breakdown of temporary workers by sectors gives interesting insights. Temporary employment developed strongly in France, especially during the second part of 1990s characterised by a strong economic recovery: the number of temporary workers has increased from 232,000 in 1990 to 290,700 in 1996 to reach 554,900 in 2003, after culminating to 604,300 in 2000. Moreover, over this period, between 45 and 55 % of temporary workers were working in manufacturing sectors and 20 % in construction. The temporary rate -that is the share of temporary employment in total employment -was, on average, 6.9 % for all manufacturing sectors in 2003 against 4.0 % in 1995 (when evaluated in full-time equivalents as in Table 4). Sectors with the largest temporary rate are the automobile industry (11 % in 2003), chemical sectors (8.5 %) and electric and electronic components (7 %). The wearing apparels and leather products sectors, in which international relocations are suspected quite large, have the lowest temporary rate (1.8 % in 2003).

As reported in Table 4, the use of temporary rates allows the calculation that the manufacturing sector (including energy), instead of losing 169,400 jobs between 1995 and 2003, lose "only" 57,300 jobs. The picture of French desindustrialisation is then overevaluated by 115,000 jobs when temporary employment is not taken into account. Even job losses in the textile and leather sectors, with small temporary rates, are over-evaluated by 2,200 jobs over 1995-2002: they would be "only" 91,60011 . Surely, while the sector of household equipment recorded also substantial job losses (-13,660 jobs over 1995-2002), other sectors intensive in low-skilled labour and currently suspected of international relocations have created jobs: mechanical equipment (+6,700 jobs), electronic and electric equipment or components (+22,500 jobs), metal products (+24,700 jobs). Note that French employment in automobile sectors has gained near 28,900 jobs between 1995 and 2003 (with more than 1,000 jobs between 2002 and 2003) at a time where international relocations in CEECs was perceived as growing fast. However, the resort to temporary workers is largely linked to the general dynamism of the economy as illustrated by the end of 1990s. Moreover, no data is available to measure temporary employment before 1995.

To get a longer-term view, we have to look into outsourcing of services in generalincluding temporary workers. Many activities previously realised by employees of industrial firms are currently realised by services firms: cleaning, logistic, retail, R&D activities etc. 14 This results in an artificial decrease of the employment share of manufacturing. The importance of this phenomenon is confirmed by the rise of the ratio between the value added of different sectors and the value of intermediate consumption from the business services (see Table 5). The growth of externalisation was particularly impressive in the 1990s, reaching up 50% in some sectors. In first approximation, such a bias in favour of services can be corrected by measuring the development of employment in the business services sector. According to the INSEE, it has increased from 1,500,000 in 1980 to 3,100,000 in 2002 15 . By weighting these figures with the share of intermediate consumption of business services by industrial sectors in the production of the business sector as a proxy of a number of jobs externalised by industrial sectors, we find that the total employment losses of the manufacturing sector are overvalued by 315,000 jobs over 1980-2002 (or 193,000 over 1995-2002), or 22,5% of the total (1,400,000 from 1980 to 2002). This is probably an under-valuation of the effect of outsourcing, as the rise of temporary employment by itself, simply between 1995 and 2002 was 115,000: that suggests that only 78,000 jobs were outsourced beside temporary employment. However, the national accounts do not give a readily way of dispatching the jobs of the business service sector in its consuming sectors, as the Input-Output table only exist in terms of consumption, not value-added or jobs; the only possible conclusion is that the "true" manufacturing job losses from 1980 to 2000 were probably less than 77,5% of the directly measured ones, or less than 1,085,000 This is still a sizeable number. It is certain that not all losses were linked to international relocation -or even, more generally, to trade. Technical progress and shifts in demands are other obvious suspects. The next part will present the studies that try to compare the responsibility of these different effects.

Existing studies

First, it must be underlined that it is not possible to measure the effects of international relocation per se. The data available are very recent, and they do not allow to isolate the whole phenomenon. The European Monitoring Centre on Change (EMCC) -which analyses the causes of enterprises restructurings in Europe since 2002 -indicates, international relocations account for a small part of (actual or planned) employment losses: 6.3 % for France and 9 % for Europe as a whole. By contrast, internal restructuring and bankruptcy (and closure) are the main sources of employment losses (more than 85 % for both France and Europe) 16 . Of course, one would like to know how many bankruptcies are caused by international competition… which brings the subject of the study of the whole effect of international trade.

Second, North-North trade has different effects than North-South trade, and we would like to isolate the latter. However, that is difficult as part of the evolution of North-north trade is caused by North-South trade between third parties.

Hence, most of the studies we present try to measure the effect of international trade, as a whole, on French employment:, even if we will try to isolate what they have to say on the effect of North-South trade whenever possible. Three types of studies exist and will be studied in turn:

(1) studies on the job content of trade

(2) econometric studies

(3) general equilibrium models

To our knowledge, no study is based on micro-data survey over a long time period -in contrast with what exists for Germany17 . Furthermore, most studies focus on the effect of trade on employment rather than wages because of the notion that the French labour market is regulated in such a way that competitive pressures should have quantity effects rather than price effects.

Job content of trade

The "job content of trade" is by far the most widely used method for evaluating the impact of international trade on French employment. The basic idea is that exports constitute additional production for the domestic economy, and hence induce job creation, while imports are substitutes to domestic production and hence induce job losses. The difference between "job creation" and "job losses" is then attributed to international trade. Empirical estimates consist thus in computing the average "job content" -i.e. labour requirement of production in the domestic country -of both exports and imports. For exports, most of studies not only consider direct employment embodied in production but also indirect employment embodied in the production of intermediate inputs.

For imports, the usual assumption is that of a substitution between domestic and foreign production in value -i.e. one euro of imports substitutes to one euro of domestic production -rather than in volume18 -i.e. a pair of foreign shoes substitutes to a pair of domestic shoes. The assumption of substitution in value is not really restrictive as long as international trade of France is predominantly oriented towards developed countries: in that case, the unitary price and quality of goods imported from abroad and produced domestically is roughly similar. As, in 1997, developed countries account for 79 % of French imports (75 % of French exports), with figures reaching 90 % in many sectors, the value hypothesis is not too much of a problem the measure the global effect of international trade. However, the value hypothesis is much more a problem when one tries to measure the effect of French trade with developing countries. Due to price differentials, substitution in volume is much more plausible. In so far as we are looking primarily into these effects, we should favour this latter hypothesis.

There are other difficulties. The results are strongly influenced by the sign of the trade balance. As a result, trade balance disequilibria are sometimes corrected to compute only the structural effect of external trade on domestic employment. When this is the case, estimates are based on theoretical balanced trade flows. Finally, the counterfactual situation used for comparison is "autarky". The definition of autarky is very restrictive: it is assumed to have no impact on the nature of goods produced, prices, wages, productivity and consumption. To sum up, while this method has the advantage of simplicity, its drawbacks are numerous: lack of strong theoretical grounds, problems related to the counterfactual situation, assumption of on French labour is positive in the long-run, temporary job losses can occur following an "openness" shock with developing countries, as in 198720 .

Only three studies compute the specific effect of trade with developing countries -with different definitions of these countries. They suggest this trade caused 150,000 to 330,000 job losses. However, these results need to be confirmed by more robust methods. This can be done either in a empirical way or a theoretical way.

Theoretical models

It is possible to build models taking into account all the different effects that make a simple job content evaluation unreliable. We know of two examples in the case of France,

shown in Table 7. It is worth mentioning that, despite the differences in methods, both studies find similar orders of magnitude for the effect of trade with developing countries on unemployment: a rise of at least 150,000 and probably at most 300,000.

Econometric studies

Another approach is mainly empirical22 . Three main factors can explain employment changes -either the decrease of the share of industrial production in total employment or of the share of unskilled workers in total employment -in developed countries: technical progress; changes in demand and international trade. Econometrical studies presented in Table 8 try to isolate the true impact of international trade, including outsourcing activities, on employment. To analyse the different causes, the assumptions are that technological progress explains the shifts of labour demand towards skilled workers within industries; changes in domestic demand explain the shifts of labour demand towards skilled workers between industries; and finally, international trade is assumed to be detrimental to unskilled workers as soon as France imports from developing countries, where labour costs are lower. Controlling for internal factors allows for more accurate estimates of the true impact of external factors on French employment. France , 1977-1993.

Econometric study per sector

Role of international vertical specialization (defined as the share of imported inputs in production) in the decline of unskilled workers (in total manufacturing employment)

Share of imported inputs in production: from 9 % (in 1977) to 14 % (in 1993) Shift away from unskilled labour : 0.65-0.7 percentage points/year (0.5-0.6 for manufacturing sectors) Contribution of international vertical specialisation in the decline of unskilled workers in manufacturing employment : 11-15 % over 1977-1985 and 25 % over 1985-1993. No break in the data. FMI method (Rowthorn & Ramaswamy (1999)): 10 % for France (15 % for the average OECD countries) New method (correction of autocorrelation): 1,9 % for France (3.4 % for the average OECD countries) Bazen and Cardebat (2001) show that the effect of trade with low-cost partners (proxied by the changes of relative import prices) changed in the late 1980s: from job-destroying influence to a wage-depressing one. However, they do not provide enough elements to estimate the total effect of trade on the unskilled share of employment and relative wages. Strauss-Kahn (2003) tests econometrically to which extent international vertical specialization explains the decline in the relative demand for unskilled labour in the French manufacturing sector over 1977-1993. Vertical specialization is the completion of the different production stages of a good in different countries. Strauss-Khan measures it as the value of directly imported inputs embodied in goods produced, using data from input-output tables. As she uses French statistical aggregates, she has to divide workers in the French manufacturing sector following occupation rather than education. This produces a division between skilled and unskilled workers that is roughly equivalent to the US white-collar/blue collar division. She finds that, while international vertical specialisation has increased from 9 % in 1977 to 14 % in 1993, its contribution to the observed decline in the relative demand of unskilled workers was relatively low. Nevertheless, this contribution increases over the time sample, from 11-15 % in 1977-1985 to 25 % in 1985-1993 23 .

The Fontagné and Lorenzi report 24 has given a lot of publicity to the results of Boulhol (2004). He tests econometrically to which extent (industrial) imports from emerging countries contribute to "desindustrialisation" (that is, changes of industrial employment in total employment) for 16 OECD countries over 1970-2002. Moreover, he is interested in testing if the acceleration of imports from emerging countries observed since 1987 has changed the value of estimated parameters. Following Rowthorn and Ramaswamy (1999), the dependent variable is the variation of the share of industrial production in total employment. The explanatory variables are GDP per capita, the square of GDP per capita, industrial imports from emerging countries in percentage of GDP, investment in percentage of GDP, the trade balance for industrial goods and the rate of externalisation by firms measured as the share of inputs in production. In a first application of this method, he shows that the imports from emerging countries contribute to 15 % of the decline in industrial employment for OECD sample, and to only 10 % for France. Correcting for autocorrelation yields even smaller estimates: respectively 3,4 % and 1,9 %. Moreover, the coefficient of imports is constant between the pre-1987 period and the post-1987 period. However, due to the acceleration of imports from developing countries in 1987, the losses of industrial employment caused by imports are larger after 1987 than before 1987. Finally, he concludes that the decline of industrial employment in France is mainly due to internal factors, e.g. the low rate of investment in France compared to the United States.

Rowther and Ramaswamy (1999) explain 150,000 manufacturing job losses by trade with developing countries. If Boulhol is right, these losses only numbered 30,000. This is the lowest estimation we have found so far. Without going into the precise examination of the econometrics, it is possible that part of the decline in French investment is due to international relocation outsourcing.

Conclusion

One difficulty in drawing conclusions from this review is that few estimates are based on recent data. Most of studies do not cover the ten last years. That makes drawing robust 23 This result is consistent with Goux & Maurin (2000) who find that around 2/3 of the decline of the unskilled labour is due to changes in the industry composition of domestic demand for goods and services and that international trade (and technical progress) have played only a minor role. 24 Fontagné & Lorenzi (2005).

conclusions and extracting insights for future developments of the French labour markets difficult. Estimation of the job losses due to trade with developing countries vary between 150,000 and 300,000, with an outlier at only 30,000. That represents only between 10 and 20% of the total industrial job losses since thirty years (between 15 and 30% if one excludes domestic outsourcing and temporary employment).

However, trade with a group of countries cannot be taken in isolation: trade between the developed and developing countries in general can have an impact on trade between France and other developed countries and should hence be taken into account. The review suggests that most French employment developments were not related to international trade as a whole -including international relocations and trade with developing countries -but had domestic causes: low investment, skill-biased technological process and demand shifts.

Hence, technical progress and internal factors explain the bulk of the decrease in industrial production and employment that frightens the public so much. This does not mean that trade cannot have a temporarily negative effect on employment, as happened in the late 1980s. It does not mean either than some categories do not suffer particularly because of trade, as did unskilled workers. Nevertheless, if we assume that the contribution of international trade to French employment developments over the 1980-95 period is representative of effects of a growing openness to trade, the following prospective features emerge: first, even the temporary adverse effect in the future of deeper integration with CEECs, including vertical foreign direct investment, will be limited since both European Association Agreements and foreign direct investment liberalisation in the 1990s have already induced most of adjustments. However, stronger trade flows with emerging countries (China, India, etc.) will have probably an adverse impact on French labour market in the next few years, especially for unskilled workers in specific sectors. The traditional sectors, like textiles, are already much reduced compared to what they were in the 1970s, and they will probably not disappear completely as some niche markets can be developed: other sectors may be threatened. There will be individual, sectoral and territorial net losses that warrant cushioning from the community, maybe as a redistribution of part of the sizeable gains offered by trade for consumers.

Figure

  Figure 1: French manufactured imports from 'emerging industrial' countries as a percentage of French GDP 8

Figure

  Figure 3: French selected imports from 'emerging industrial' countries as a percentage of French GDP

Bibliography

  ARTHUIS, J., 1993: Rapport d'information sur l'incidence économique et fiscale des délocalisations hors du territoire national des activités industrielles et de service, Sénat. 231 p.

French manufactured exports to 'emerging industrial' countries as a percentage of French GDP

	3,0
																			Tunisia, Morocco Af Nord+afnda
																			Turkey+Bulgaria+Romania
																			CEEC (EU-25)
																			Emerging Asia
	67	69	71	73	75	77	79	81	83	85	87	89	91	93	95		97	99	01
	0,5 1,0 1,5 2,0 2,5 3,0 Figure 2: 0,0																		Tunisia, Morocco Turkey+Bulgaria+Romania CEEC (EU-25) Emerging Asia
		67	69	71	73	75	77	79	81	83	85	87	89	91	93	95	97	99	01

8 All figures are courtesy of Catherine Mathieu.

Table 2

 2

	). Put differently, the French economy

Table 2 : French employment by sectors (thousand of engaged)

 2

		1970 1975 1980 1985 1990 1995 2000 2002	1970-2002	1985-2002	1970-2002	1985-2002
	GRAND TOTAL	21,

051 21,563 22,191 21,845 22,851 22,682 24,308 24,887 +18% +14% +3,837 3,042 AGRICULTURE, HUNTING, FORESTRY & FISHING 2,946 2,301 1,948 1,634 1,348 1,112 1,034 1,015 -66% -38% -1,931 -620 TOTAL MANUFACTURING 5,365 5,501 5,231 4,610 4,396 3,874 3,811 3,789 -29% -18% -1,576 -821

	FOOD PRODUCTS, BEVERAGES & TOBACCO	613 613 621 626 613 597 632 641 +4% +2% +27 +15
	TEXTILES, TEXTILE PRODUCTS, LEATHER & FOOTWEAR	904 808 680 545 444 333 260 234 -74% -57% -670 -310
	WOOD & PRODUCTS OF WOOD & CORK	144 144 140 112 114 100	90	91 -37% -19% -53	-21
	PULP, PAPER, PAPER PRODUCTS, PRINTING & PUBLISHING	355 363 357 344 366 332 326 320 -10% -7% -35	-24
	CHEMICAL, RUBBER, PLASTICS & FUEL PRODUCTS	555 600 587 539 529 475 461 466 -16% -13% -88	-73
	OTHER NON-METALLIC MINERAL PRODUCTS	320 299 272 219 210 184 171 170 -47% -22% -151 -49
	BASIC METALS & FABRICATED METAL PRODUCTS	848 874 795 649 633 547 553 553 -35% -15% -295 -96
	MACHINERY & EQUIPMENT	864 964 931 843 818 735 742 731 -15% -13% -133 -113
	TRANSPORT EQUIPMENT	521 575 572 499 440 373 379 385 -26% -23% -136 -114
	MANUFACTURING NEC; RECYCLING 240 261 275 234 230 199 199 199 -17% -15% -41	-36
	ELECTRICITY

, GAS & WATER SUPPLY 153 159 175 198 192 191 192 192 +25% -3% +38 -6 CONSTRUCTION 2,070 1,970 1,917 1,590 1,663 1,433 1,430 1,493 -28% -6% -578 -97 WHOLESALE

	& RETAIL TRADE; RESTAURANTS & HOTELS	3,281 3,409 3,587 3,628 3,913 3,819 4,142 4,312 +31% +19% +1,031 +685
	TRANSPORT & STORAGE & COMMUNICATION	1,115 1,179 1,256 1,291 1,328 1,334 1,480 1,545 +39% +20% +430 +254
	FINANCE, INSURANCE, REAL ESTATE & BUSINESS SERVICES	1,574 1,934 2,283 2,497 3,097 3,275 3,995 4,193 +166% +68% +2,619 +1,696
	COMMUNITY SOCIAL & PERSONAL SERVICES	4,546 5,110 5,792 6,399 6,913 7,644 8,224 8,350 +84% +30% +3,804 +1,951

TOTAL SERVICES 10,517 11,632 12,919 13,814 15,251 16,073 17,841 18,400 +75% +33% +7,883 +4,586 Source

: OECD, STAN.

Table 3 : French employment by sectors (in % of total employment)

 3

		1970	1975	1980	1985	1990	1995	2000	2002	1970-2002	1985-2002
	AGRICULTURE, HUNTING, FORESTRY & FISHING	14,0	14,0	8,8	7,5	5,9	4,9	4,3	4,1	-71% -46%
	TOTAL MANUFACTURING	25,5	25,5	23,6	21,1	19,2	17,1	15,7	15,2	-40% -28%
	FOOD PRODUCTS, BEVERAGES & TOBACCO	2,9	2,9	2,8	2,9	2,7	2,6	2,6	2,6	-12% -10%
	TEXTILES, TEXTILE PRODUCTS, LEATHER & FOOTWEAR	4,3	4,3	3,1	2,5	1,9	1,5	1,1	0,9	-78% -62%
	WOOD & PRODUCTS OF WOOD & CORK	0,7	0,7	0,6	0,5	0,5	0,4	0,4	0,4	-47% -29%
	PULP, PAPER, PAPER PRODUCTS, PRINTING &
	PUBLISHING

Table 4 : Over-evaluation of industrial employment losses (

 4 salary employment, full-time equivalent, in thousands)

					Temporary	Total employment	Over-
			Employment		rate	(including temporary	evaluati
					(in %) 12		workers)		on
		1995	2002	1995-2002	1995 2002 1995	2002	1995-2002	1995-2002
	Food industries	501.7	540	38.3	4.2	7.2	523.7 581.6 57.9	-19.6
	Consumption goods	723.4 635.8	-87.6	2.7	5.0	743.6 669.0 -74.5 -13.1
	Wearing & leather products	185.5 116.9	-68.6	0.8	1.7	187.0 118.9 -68.1	-0.5
	Printing & publishing	214.8	210	-4.8	1.5	2.5	218.0 215.5	-2.5	-2.3
	Chemicals & chemical products 112.3 116.2	3.9	4.9	9.1	118.1 127.9	9.8	-5.9
	Household equipment	210.8 192.7	-18.1	4.4	6.8	220.4 206.8 -13.7	-4.4
	Automobile industry	250.6 260.7	10.1	5.5 11.0 265.2 293.0 27.8	-17.7
	Good equipment	724.4 732.3	7.9	4.7	6.4	760.2 782.2 22.0	-14.1
	Ship, aircraft & railroad equipment 116.3 117.8	1.5	2.9	5.9	119.8 125.2	5.4	-3.9
	Mechanical equipment	414.6 413.4	-1.2	5.4	7.1	438.3 445.0	6.7	-7.9
	Electric & electronic equipment 193.5 201.1	7.6	4.3	5.2	202.2 212.1	9.9	-2.3
	Intermediate industries	1365.1 1332.1	-33.0	4.4	7.7 1427.3 1443.5 16.2	-49.2
	Mineral products	173.5 159.8	-13.7	3.6	6.5	180.0 170.8	-9.2	-4.5
	Textile industry	127.4 102.2	-25.2	2.3	4.4	130.3 106.9 -23.5	-1.7
	Wood and paper	180.6	167	-13.6	3.8	7.2	187.6 180.0	-7.6	-6.0
	Chemicals, rubber & plastics	306	308.5	2.5	5.0	9.6	322.0 341.2 19.1	-16.6
	Basic metals & metal products	408.1	419	10.9	5.1	9.9	430.1 454.8 24.8	-13.9
	Electric & electronic components 169.5 175.6	6.1	4.3	7.5	177.2 189.8 12.6	-6.5
	INDUSTRIE (excluding energy) 3 565.2 3 500.9 -64.3	4.2	7.1 3720.0 3769.4 49.3 -113.6
	Energy	235	213.4	-21.6	1.5	2.6	238.7 219.1 -19.6	-2.0
	Energy producing materials	46.3	31.4	-14.9	1.7	3.8	47.1	32.6	-14.5	-0.4
	Electricity, gas & water	188.7 182.0	-6.7	1.5	2.4	191.6 186.4	-5.1	-1.6
	INDUSTRIE (including energy) 3 800.2 3 714.3 -85.9	4.0	6.9 3958.7 3988.5 29.8 -115.7

Source: INSEE and DARES databases, and authors' computation 13 .

Table 5 : Intermediate consumption of business services by manufacturing sectors

 5

		(in % of value added)
		1980	1990	1995	2000	2002 Changes between
							1995 and 2002
	Food industries	14,1	28,3	34,9	46,0	42,1	21%
	Consumption goods	..	..	33,8	46,9	45,4	34%
	Wearing & leather products	..	..	23,2	31,6	32,2	39%
	Printing & publishing	..	..	25,9	36,0	34,1	32%
	Chemicals & chemical products	24,4	38,6	47,7	61,6	59,3	24%
	Household equipment	29,1	63,7	35,8	50,9	47,6	33%
	Automobile industry	11,9	28,8	49,8	54,0	46,8	-6%
	Equipment goods	21,0	33,4	37,8	47,2	47,1	25%
	Ship, aircraft & railroad equipment	24,0	42,5	37,4	54,0	47,4	27%
	Mechanical equipment	26,2	41,6	34,7	40,8	43,2	24%
	Electric & electronic equipment	14.8	23,8	42,6	52,9	52,8	24%
	Intermediate industries	15,6	11,9	20,8	27,1	28,0	34%
	Mineral products	13.5	17,8	15,4	19,8	19,2	25%
	Textile industry	..	..	26,1	31,6	30,9	18%
	Wood and paper	..	..	10,1	11,7	12,3	22%
	Chemicals, rubber & plastics	11.1	9,5	31,8	40,4	41,8	31%
	Basic metals & metal products	..	..	12,8	18,4	18,1	41%
	Electric & electronic components	..	..	30,9	40,7	48,1	56%
	INDUSTRIE (excluding energy)	..	..	30,8	39,7	39,0	26%
	Energy	..	..	23,6	24,9	26,9	14%

Source: INSEE national accounts.

Table 7 : Studies using models

 7

	Source	Data	Methodology	Estimation	Results
			Macroeconomic model for general	Role of trade with
	Mathieu & Sterdyniak	France	equilibrium effects. Alternative	developing Asia on the	+0.5/+0.6 points of
	(1994)	1973-1991	scenario: developing Asia growth at the	development of	unemployment
			same speed than the OECD	unemployment
	Jean (1999), p. 154-155 21	France 1977-1993	Computable General Equilibrium Model taking into account North-South trade, technical progress and qualification development in the population	Role of the increase of French trade from 1977 to 1993 on unemployment	+ 2 points of unemployment Trade with the South : < +1 point

Table 8 : Studies using an econometric method

 8

	Source	Data	Methodology	Estimation	Results
	Bazen & Cardebat (2001)	France 1985, 1989 and 1992	Econometric study per sector	Role of international trade (measured as relative import prices) on relative unskilled employment	1985-1989: Trade => Decline in relative unskilled employment, not wages 1989-1992: Trade => Decline in relative unskilled wages, not employment
	Strauss-Kahn (2003)

Exactly: FP Electroménager; FQ Matériel électrique; Fr Fournitures électriques; Fm Electronique grand public; Gh Articles en plastique; Gi Articles en caoutchouc; DA Fils et tissus; DB Vêtements de confection; DC Vêtements de bonneterie; DE Cuirs; EA Ouvrages en bois; FL Composants électroniques.

To a higher level of disaggregation, a few manufacturing sectors show an increase of employment over 1987-2002 (figures not reported in Table2): "pharmaceuticals (+11.5 %), "offices, computing and accounting" (+11.4 %), "rubber and plastic products" (10.1 %), "building and repairing of ships and boats" (+3.7 %).

This figure derives from 68,100 job losses in sectors of wearing and leather products, plus 23,500 in textile industry.

Interim workers divided by total salaries workers (including interim workers, both in full time equivalents).

See also[START_REF] Fontagné | Désindustrialisation et délocalisations[END_REF], p. 36,[START_REF] Gonzales | L'incidence du recours à l'intérim sur la mesure de la productivité du travail des branches industrielles[END_REF] and[START_REF] Mihoubi | Intérim, travail externalisé et mesure de la productivité du travail dans l'industrie[END_REF].

Note that growing externalisation by sectors not belonging to manufacturing sectors (e.g. construction) contributes also to the bias in favour of employment in services sectors (or "tertiarisation" of the French economy).

See also[START_REF] Mihoubi | Intérim, travail externalisé et mesure de la productivité du travail dans l'industrie[END_REF].

European Monitoring Centre on Change (2005).

[START_REF] Marin | A Nation of Poets and Thinkers. Less so with Eastern Enlargement? Austria and Germany[END_REF].

This opposition between value and volume is different from the usual one which takes into account the evolution of prices through time.

See, for instance,[START_REF] Messerlin | The Impact of Trade and Capital Movements on Labour: Evidence on the French Case[END_REF] or[START_REF] Jean | The Impact of Globalisation on Employment in Industrialised Countries: a Survey[END_REF] for a discussion.

The share of developing countries in world trade was doubled from 1987 to 1997.

See also[START_REF] Jean | The Impact of Globalisation on Employment in Industrialised Countries: a Survey[END_REF]), p. 13, Jean & Bontout (1999),Cortes & Jean (1997a),[START_REF] Jean | L'impact du commerce international sur l'élasticite-prix de la demande de travail. (The Impact of International Trade on Price-Elasticity of Demand for Labour. With English summary[END_REF].

We only mention here macro-econometric studies. The only microeconometric study we are aware of that does compute a microeconomic, firm-level, effect of international trade on employment:[START_REF] Biscourp | Internationalisation des entreprises industrielles et emploi: une analyse sur la période 1986-1992[END_REF].

homogeneity between foreign and domestic goods, use of an average coefficient rather than a marginal coefficient etc 19 . The seven empirical studies based on "job content of trade" method as reported in Table 6 differ in terms of sample (period, total versus manufactured trade, all versus developing partners) and methodology (substitution in value versus volume, treatment of trade balance disequilibrium etc.). Nevertheless, it is possible to summarize their main results as follows.

First, in all cases, the estimated net impact of international trade on total French employment is modest and, on average, positive. That is, international trade tends to be a net creator of jobs over a long time period, even if the net creation of jobs accounts for less than 1 % of total employment. Second, the negative net impact of international trade on jobs is generally concentrated on the end of 1980s/beginning of 1990s and due to trade with developing countries. After 1992, all the studies agree to indicate the positive impact of trade on French employment. Third, different sectors are unevenly affected by international trade. Most losses are concentrated in traditional industries (shoes and hosiery) and some in natural-resources intensive industries. That seems to suggest that, even if the net impact of international trade


Flavien Boussuge
email: flavien.boussuge@eads.net

Ahmad Shahwan
email: ahmad.shahwan@grenoble-inp.fr

Jean-Claude Léon
email: jean-claude.leon@grenoble-inp.fr

Stefanie Hahmann
email: stefanie.hahmann@inria.fr

Gilles Foucault
email: gilles.foucault@ujf-grenoble.fr

Lionel Fine
email: lionel.fine@eads.net

Template-based geometric transformations of a functionally enriched DMU into FE assembly models

Keywords: Assembly, DMU, CAD -CAE integration, Functional information BC: boundary condition, DMU: digital mock-up, FE: finite elements, FEA: finite element analysis(es), KBE: Knowledge-based engineering, PDP: product development process

Pre-processing of CAD models derived from Digital Mock-Ups (DMUs) into finite element (FE) models is usually completed after many tedious tasks of model preparation and shape transformations. It is highly valuable for simulation engineers to automate time-consuming sequences of assembly preparation processes. Here, it is proposed to use an enriched DMU with geometric interfaces between components (contacts and interferences) and functional properties. Then, the key concept of template-based transformation can connect to assembly functions to locate consistent sets of components in the DMU. Subsequently, sets of shape transformations feed the template content to adapt components to FE requirements. To precisely monitor the friction areas and the mesh around bolts, the template creates sub-domains into their tightened components and preserves the consistency of geometric interfaces for the mesh generation purposes. From a user-selected assembly function, the method is able to robustly identify, locate and transform groups of components while preserving the consistency of the assembly needed for FE models. To enlarge the scope of the template in the assembly function taxonomy, it is shown how the concept of dependent function enforces the geometric and functional consistency of the transformed assembly. To demonstrate the proposed approach, a business oriented prototype processes bolted junctions of aeronautical structures.

RDF: resource description framework; STEP: Standard for the Exchange of Product model data;

Acronyms specific to the paper: CI: conventional interface; CIG: conventional interface graph; C C : compatibility conditions between T and S T ; FD: functional designation of a component; FI: functional interface; I C : set of components such that each of its components has all its FIs in T; P C : set of components such that each of its components has some of its FIs in T; T CI : taxonomy of conventional interfaces; T FD : taxonomy of functional designations of components; T FI : taxonomy of functional interfaces; T FN : taxonomy of functions; S ME : reference state expressing static mechanical equilibrium of a component; S LC : reference state expressing a static load cycle inside an assembly; S T : shape transformation incorporated in a template, hence S T (T); S T1 : removal of a threaded link; S T2 : cylindrical sub domain around a screw shaft to localize friction effects; S T3 : removal of the locking nut of a bolted junction; S T4 : screw head transformations; S T5 : preserve the cylindrical loose fit between screw and plates to set up contact friction BCs; T: function-based template performing shape transformations;

T I : union of all components belonging to I C .

INTRODUCTION

To speed up a PDP, aeronautical, automotive and other companies face increasing needs in setting up FE simulations of large sub-structures of their products. The challenge is to study not only standalone components but to simulate the structural behavior of large assembly structures containing up to thousands of components [START_REF] Boussuge | An analysis of DMU transformation requirements for structural assembly simulations[END_REF]. DMUs are widely used during a PDP as the virtual geometric product reference. This model contains detailed 3D representation of the whole product structure available for simulation engineers. To prepare large sub-structure models for simulation (such as wings or aircraft fuselage section); the DMU offers a complete geometric input model. However, speeding up the simulation model generation strongly relies on the time required to perform the geometric transformations needed to adapt the DMU to FE requirements.

Currently, time and human resources involved in pre-processing CAD models derived from DMUs into FE models prevent engineers from setting up structural analyses. Very tedious tasks are required to process the large amount of DMU components and the connections between them. The shape transformations required for each assembly component, and interactively performed by engineers, can cover defeaturing [START_REF] Fine | A new approach to the Preparation of models for F.E. analyses[END_REF][START_REF] Thakur | A survey of CAD model simplification techniques for physics-based simulation applications[END_REF], idealization [START_REF] Armstrong | Techniques for interactive and automatic idealisation of CAD models[END_REF][START_REF] Armstrong | Integrating CAE concepts with CAD geometry[END_REF], domain decomposition [START_REF] Quadros | A computational framework for automating generation of sizing function assembly meshing via disconnected skeletons[END_REF][START_REF] Robinson | Automated mixed dimensional modelling from 2D and 3D CAD models[END_REF] as well as the definition of contact areas. Even on repetitive configurations such as junctions, similar geometric transformations must be repeated on all the components and interfaces of all the assembly junctions. Aeronautical structures are particularly complex to transform due to their many independent connectors such as bolts or rivets (see Fig. 1). Even though CAE software possess specific operators for bolted junctions, pre-stressed configurations, …, to speed up FEA pre-processing, the user must already have available a DMU incorporated all the desired geometric transformations. Automated domain decomposition, geometric simplifications, selection of target components are examples of functions still interactive and error prone that a user must perform tediously. Within the available resources and time scale planned in an industrial PDP, the analyst is therefore limited to simulate small models rather than complete assembly structures. Compared to standalone components, the above observations highlight the prominence of geometric interfaces processing when preparing an assembly model for FEA. Their mechanical behavior and the new shape transformations they convey are specific features of assemblies [START_REF] Boussuge | An analysis of DMU transformation requirements for structural assembly simulations[END_REF]. As described in [START_REF] Shahwan | Qualitative behavioral reasoning from components' interfaces to components' functions for DMU adaption to FE analyses[END_REF], component's geometric interfaces are the basis of component's functional designation. Effectively, to speed up the transformation of a DMU into a FE model, the engineer would process the components in accordance to their mechanical effect in the assembly, i.e. their function. Consequently, the relationship between FE simulation hypotheses, component's functions and component's interfaces appears as a key issue to improve the efficiency of DMU transformation for FEA. Indeed, setting up a FEA aims at studying the mechanical behavior of an assembly. Function, behavior and shape share strong connections, as studied by Gero [START_REF] Gero | The situated function-behaviour[END_REF][START_REF] Gero | Design prototypes: a knowledge representation schema for design[END_REF] and Albers [START_REF] Albers | Contact and channel modeling to support early design of technical systems[END_REF][START_REF] Albers | Contact and Channel Model for Pairs of Working Surfaces[END_REF] among others, hence the aforementioned example of the FE preparation process contributing to the representation of bolted connections in an aeronautical assembly.

In this paper, we propose an approach to reduce the FE model preparation time to adapt CAD assembly models derived from DMUs, into FE assembly models. Based on the analysis of DMU transformation requirements for FE assembly model preparation [START_REF] Boussuge | An analysis of DMU transformation requirements for structural assembly simulations[END_REF], the method uses an enriched DMU as input. It is obtained from previous developments and contains explicit geometric interfaces between components (contacts and interferences) as well as their functional designations. This last step is achieved using a qualitative reasoning process. From this enriched model, it is shown that further enrichment is needed to reach a level of product functions where simulation objectives can be used to specify new geometric operators that can be robustly applied to automate components' and interfaces' shape transformations during an assembly preparation process for FEA. If close to KBE, this scheme is nonetheless more generic and more robust than KBE approaches because functional designations and functions are generic concepts. KBE aims at structuring engineering knowledge and processing it with symbolic representations [START_REF] Chapman | Design engineering -a need to rethink the solution using knowledge based engineering[END_REF][START_REF] Rocca | Knwledge based engineering: between AI and CAD. Review of a language based technology to support engineering design[END_REF] using language based approaches. Here, the focus is on a robust connection between geometric models and symbolic representations featuring functions.

To prove the validity of our approach and the methodology proposed in [4][START_REF] Armstrong | Techniques for interactive and automatic idealisation of CAD models[END_REF][START_REF] Armstrong | Integrating CAE concepts with CAD geometry[END_REF][START_REF] Barbau | OntoSTEP: Enriching product model data using ontologies[END_REF][START_REF] Bickford | Introduction to the Design and Behavior of Bolted Joints[END_REF][START_REF] Boussuge | An analysis of DMU transformation requirements for structural assembly simulations[END_REF], this paper presents a template-based operator dedicated to automate shape transformations of bolted junctions. Using the functional information and geometric interfaces, the operator applies a user-defined template to simplify bolts and sets control sub-domains around them in their associated tightened components to enable the description of the friction phenomenon between these components. This template is used to precisely monitor the meshing process while preserving the consistency of contacts and adapting the assembly model to simulation objectives.

The rest of the paper is organized as follows. In Section 2, we review the CAD-CAE integration research for FE assembly models. Section 3 reviews the method to enrich the DMU with geometric interfaces between components and functional designations of components. New requirements are introduced to connect functional designations with functions. Section 4, describes the concept of template-based transformation operator and illustrates it with a template-based operator of bolted Junctions transformation. Finally, the paper presents the result of this operator on an industrial aeronautical use-case and section 5 exemplifies an extension of the template definition with idealization transformations.

RELATED WORK

Assembly models have been studied throughout the development of solid modeling concepts. Essentially, assembly models have been proposed for design and manufacture applications [START_REF] Rahmani | Ontology based interface design and control methodology for collaborative product development[END_REF][START_REF] Robinson | Automated mixed dimensional modelling from 2D and 3D CAD models[END_REF][START_REF] Roy | Design with part behaviors: behavior model, representation and applications[END_REF][START_REF] Roy | Function-to-form mapping: model, representation and applications in design synthesis[END_REF] with recent applications to collaborative design. With the development of features, approaches set assemblies as components related to each other through geometric constraints [START_REF] Van Holland | Assembly features in modeling and planning[END_REF]. These approaches share a common denominator where assemblies are described as geometric models progressively enriched with technological and then, functional data [START_REF] Dixon | Assembly Feature Tutor and Recognition Algorithms Based on Mating Face Pairs[END_REF]. However, the closer the functional information, the higher is the requirement to obtain external information to CAD environments and the greater is the need of user's interactions during a design process. Though these additional informations are mandatory in a design process, it does not seem efficient to incorporate them into a preparation process for FE simulation when time reduction is critical to insert simulations into a PDP. If these informations were available at the level of FE simulation, a dedicated approach could be set up to process them but companies are currently not able to set up a digital representation of these data that is connected to the DMUs they produce with CAD systems. Within this framework, Roy and Bharadwaj [START_REF] Roy | Design with part behaviors: behavior model, representation and applications[END_REF] set up a design approach to connect functions to 3D geometry using a Part Function Model (PFM). There, they address the relationships between function, behavior and geometry of a part in a top-down manner from function to geometry to obtain parts from functional specifications. The PFM described requires up to low level functions that connect part boundary faces to function since the behavior model builds up on interfaces between parts, i.e. contact surfaces to position parts with respect to each other. At the level of complex assemblies with hundreds to thousands of parts, adding the amount of complementary data defining such a behavioral model becomes too tedious. Recent approaches [START_REF] Kim | Design formalism for collaborative assembly design[END_REF] reduce the description of junctions between components to global parameters describing bolted and riveted connections without referring to the individual surfaces of each bolt or rivet. This fits well with a design process but simulation objectives may require a detailed representation of interfaces when the purpose is to assess the stress field distribution in a bolted connection with tens or hundreds of bolts.

Developments of ontology-based approaches take advantage of new capabilities to structure concepts and to connect them with component models [START_REF] Kitamura | Ontology-based systematization of functional knowledge[END_REF][START_REF] Rahmani | Ontology based interface design and control methodology for collaborative product development[END_REF] or at the level of 3D geometry entities [START_REF] Barbau | OntoSTEP: Enriching product model data using ontologies[END_REF][START_REF] Bickford | Introduction to the Design and Behavior of Bolted Joints[END_REF][START_REF] Boussuge | An analysis of DMU transformation requirements for structural assembly simulations[END_REF][START_REF] Choudria | Identifying and re-meshing contact interfaces in a polyhedral assembly for digital mock-up[END_REF][START_REF] Clark | Conformal Assembly Meshing with Tolerant Imprinting[END_REF][START_REF] Champaney | A domain decomposition method for studying the effects of missing fasteners on the behavior of structural assemblies with contact and friction[END_REF][START_REF] Champaney | Adaptive multi-analysis strategy for contact problems with friction[END_REF][START_REF] Dixon | Assembly Feature Tutor and Recognition Algorithms Based on Mating Face Pairs[END_REF][START_REF] Fine | A new approach to the Preparation of models for F.E. analyses[END_REF][START_REF] Fiorentini | An Ontology for Assembly Representation[END_REF][START_REF] Gero | The situated function-behaviour[END_REF][START_REF] Gero | Design prototypes: a knowledge representation schema for design[END_REF][START_REF] Horvath | Towards an ontology-based definition of design features[END_REF]. Some of these approaches have been applied to assemblies [START_REF] Barbau | OntoSTEP: Enriching product model data using ontologies[END_REF][START_REF] Kim | Ontology-based assembly design and information sharing for collaborative product development[END_REF][START_REF] Rahmani | Ontology based interface design and control methodology for collaborative product development[END_REF] and can take advantage of reasoners to set up inference rules to ensure the consistency of the assembly description or extract information that is not readily available in the dataset describing an assembly. In [START_REF] Kim | Ontology-based assembly design and information sharing for collaborative product development[END_REF][START_REF] Rahmani | Ontology based interface design and control methodology for collaborative product development[END_REF], there is no direct connection between the ontology content and the 3D model of components. Here, ontologies support a design process where the engineer gets consistent information in a collaborative context but the ontology does not connect to boundary entities of component geometric models. Barbeau et al. [START_REF] Barbau | OntoSTEP: Enriching product model data using ontologies[END_REF] cover a larger description of a product with an ontological description incorporating the geometry and structure levels as available through STEP APIs [START_REF]-Application Protocol: Configuration controlled 3D design of mechanical parts and assemblies[END_REF][START_REF]Part 214 -Application Protocol: Core data for automotive mechanical design processes[END_REF], up to the functional description that can be inserted through ontological representation of the Core Product Model (CPM) [START_REF] Fiorentini | An Ontology for Assembly Representation[END_REF]. The authors showed that not all concepts of STEP could be rigorously expressed using OWL standard [START_REF]OWL Web Ontology Language Overview[END_REF] leading to limitations in detecting inconsistencies. If CPM is able to relate component functions to form features, the content of the CPM reflects the designers' choices to determine the level of product features inserted in this model and its level of connection with each component's geometry. Consequently, there is no guarantee that functional information can be available downward to the level of B-Rep entities of each component. Reasoning capabilities associated with ontologies are set up to browse the whole assembly ontology but they are not applied to derive new functional information or reinforce the connection between function and geometry in an assembly model. Consequently, we can observe that assembly processing is often addressed in a design context of top-down approach from primary product function point of view and there is no low level robust connection between components' geometry and low level functions. Additionally, the reasoning capabilities of ontology-based approaches are exploited to browse existing assembly data and derive data not readily available. These reasoning processes do not extend further than relative positioning constraints between components. KBE approaches [START_REF] Chapman | Design engineering -a need to rethink the solution using knowledge based engineering[END_REF][START_REF] Rocca | Knwledge based engineering: between AI and CAD. Review of a language based technology to support engineering design[END_REF] formalize engineering knowledge to automate some design tasks. KBE concepts take advantage of artificial intelligence techniques and strongly rely on language-based approaches. As such, they follow top-down approaches based on enterprise 'best practices' and address preliminary design stages rather than embodiment or detailed design ones, which is the product geometric description addressed here with DMUs. This is hardly applicable to other companies and even more to other products. Still, if KBE approaches incorporate connections with geometric models, geometry is perceived as attribute of higher level concepts like components, which does not bring new structure to the geometric models of components. Recently, Shahwan et al. [START_REF] Shahwan | Qualitative behavioral reasoning from components' interfaces to components' functions for DMU adaption to FE analyses[END_REF] inserted a qualitative reasoning process that can relate geometric interfaces up to the functional designation of components, thus creating a robust and automated connection between 3D geometric entities and functional designations of components. It is a bottom-up approach that fits to our current requirements.

Research in CAD-CAE integration has mainly focused on the use of global geometric transformations of standalone CAD components [START_REF] Thakur | A survey of CAD model simplification techniques for physics-based simulation applications[END_REF]. Few contributions addressed the automation of assembly pre-processing. Automatic simplifications of assembly for collaborative environment as the multi-resolution approach of Kim [START_REF] Kim | An integrated approach to realize multiresolution of b-rep model[END_REF] or surface simplification of Andujar [START_REF] Andujar | Topology-reducing surface simplification using a discrete solid representation[END_REF] transform assembly components independently of each other. This is not sufficient to pre-process FE assembly models because mechanical joints and interfaces tightening the different components must be part of their pre-processing. Commercial software proposes to automatically detect geometric interfaces between assembly components. However, their algorithms use a global proximity tolerance to find face pairs of components and they don't produce explicitly the geometric model of their contact area. In the assembly simplification method of Russ et al. [START_REF] Russ | Automated assembly model simplification for finite element analysis[END_REF], the authors propose to set components dependencies to remove groups of components having no influence on a simulation or to replace them by defeatured equivalent ones. However, the parent/child relationships created from constraint placement of components do not guarantee to obtain the entire neighborhood of a component because these constraints are not necessarily related to the components' geometric interfaces. In addition, DMUs don't contain components' location constraints when assemblies are complex, as occurring in the automotive and aeronautic industries, to ease design modifications during a PDP. Moreover, part naming identification used in this approach is not sufficient because it locates only individual components contained in the assembly without establishing relations with their adjacent components and their associate geometric model, i.e. replacing a bolted junction by an idealized fastener implies simplifying its nut, its screw as well as the hole connected to them in the tightened components. To provide mesh domains connectivity, Lou [START_REF] Lou | Merging enriched Finite Element triangle meshes for fast prototyping of alternate solutions in the context of industrial maintenance[END_REF] and Chouadria [START_REF] Choudria | Identifying and re-meshing contact interfaces in a polyhedral assembly for digital mock-up[END_REF] proposes to identify and re-mesh contact interfaces. Quadros [START_REF] Quadros | A computational framework for automating generation of sizing function assembly meshing via disconnected skeletons[END_REF] establishes sizing functions to control assembly meshes. However, these methods are used directly on already meshed models, which addresses specific PDP configurations where CAD models are not readily available. Clark [START_REF] Clark | Conformal Assembly Meshing with Tolerant Imprinting[END_REF] detects interfaces in CAD assemblies to create non-manifold models before mesh generation but does not consider the interactions between interfaces and components' shapes transformation processes. In [START_REF] Boussuge | An analysis of DMU transformation requirements for structural assembly simulations[END_REF], we underline that if a component is simplified or idealized, its shape transformation has an influence on the transformation of its neighbors, e.g. a component idealized as a punctual mass impacts its neighboring component interfaces. Indeed, to adapt an assembly to FEA requirements, geometric transformations derive from simulation objectives and components' functions are needed to geometrically transform groups of components. It is also critical to structure the geometric models of components so that their shape transformations can preserve the DMU consistency [START_REF] Boussuge | An analysis of DMU transformation requirements for structural assembly simulations[END_REF]. We propose an approach where a DMU is enriched with geometric interfaces between its components, i.e. contacts and interferences, and functional properties. From this enriched model, simulation objectives can be used to specify geometric operators that can be robustly applied to automate components and interfaces shape transformations during an assembly preparation process.

DMU ENRICHMENT WITH FUNCTIONAL INFORMATION

From a component geometry to its functional designation

The principle of DMU functional enrichment can be summarized with the process flow shown on Fig. 2. Its detailed description can be found in [START_REF] Shahwan | Qualitative behavioral reasoning from components' interfaces to components' functions for DMU adaption to FE analyses[END_REF]. The focus is placed on this approach because, to the authors' knowledge, Shahwan's approach can automatically produce a functionally enriched DMU from a pure geometric input model, which is the reliable input data addressed here.

Fig. 2 starts from the STEP [START_REF]-Application Protocol: Configuration controlled 3D design of mechanical parts and assemblies[END_REF][START_REF]Part 214 -Application Protocol: Core data for automotive mechanical design processes[END_REF] representation of an assembly model with the extraction of geometric interfaces between components. Two categories of interfaces are addressed: contacts (surface and line ones) and interferences. The latter originates from the conventional representations of components, e.g. a screw is represented with a threaded part defined as a cylinder whose diameter equals the outer diameter of the thread and its nut is represented with a threaded part defined as a cylinder whose diameter equals an inner diameter of the thread; this produces a geometric interference between these components. At this stage, each component boundary gets modified to incorporate the imprints of its neighboring components through contacts and interferences. The geometric interfaces feed instances of 'conventional interfaces' (CI) classes structured into a taxonomy, T CI , that binds geometric and symbolic data, e.g. planar contact, spherical partial contact, cylindrical interference, … Simultaneously, CIs and assembly components are organized into a CI graph: CIG(C, I) where the components C are nodes and CIs I are arcs. Then, instances of functional interfaces (FIs) are derived from CI ones, possibly with multiple instances of FIs originated from a single instance of CI, e.g. a cylindrical contact can become either a cylindrical loose fit or cylindrical tight fit but a planar contact becomes only a planar support. Instances of FIs fit also into a taxonomy T FI . Now, the duality between geometry and interaction forces is used to derive mechanical parameters, i.e. screws (resulting force, resulting moment), from each instance of FI. These parameters are expressed qualitatively and feed symbolic behaviors of the assembly in order to take advantage of the shape, behavior, function relationship [START_REF] Albers | Contact and channel modeling to support early design of technical systems[END_REF][START_REF] Albers | Contact and Channel Model for Pairs of Working Surfaces[END_REF][START_REF] Gero | The situated function-behaviour[END_REF][START_REF] Gero | Design prototypes: a knowledge representation schema for design[END_REF]. Assembly behaviors are characterized by reference states and aim at reducing a single FI instance per CI instance. Here, two reference states are of interest: the mechanical equilibrium reference state, S ME , and the static load cycle one, S LC . S ME expresses the fact that each component must hold tight when the assembly has no mechanical interaction with its environment, i.e. each component can satisfy the static equilibrium equations. S LC expresses the fact that any threaded link between any two components of an assembly must generate close loops of forces, i.e. force cycles so that the corresponding components stay at static equilibrium. Fig. 3 illustrates this concept with a bolted junction and a force cycle in magenta. As a result, components models as well as their geometric model get structured, i.e. their 3D model contain imprints of their FIs and geometric relationships with FIs of functionally related components; FIs contain the lowest symbolic information describing the elementary functions of a component and each functional designation expresses uniquely the necessary relations between these elementary functions. Fig. 4 illustrates this result with a cap screw. Fig. 4: Structuring the model of a component with functional properties after analyzing its geometric interactions and assigning it a functional designation, here a 'cap screw'.

From components' functional designations to functions

Though the bottom-up approach summarized in the previous section provide assembly components with a structured model incorporating functional information that is independent of their dimensions, their functional designation does not appear as an appropriate entry point to derive shape transformation operators as required for FE analyses. Indeed, to set up FE assembly models, an engineer looks for bolted junctions that he, resp. she, wants to transform to express friction phenomena, pre-stressed state in the screw, … Consequently, the functional level needed is not the functional designation, which is bound to a single component, it is the function itself to address the corresponding set of components and their FIs.

To this end, it is mandatory to refer to functions. This is achieved with a taxonomy of functions, T FN , that can produce a functional structure of an assembly (see Fig. 5). Blue items define the sub-path in T FN hierarchy that characterizes bolted junctions.

Fig. 5: Subset of T FN , defining a functional structure of an assembly.

Each instance of a class in T FN contains a set of components identified by their functional designation, i.e. it contains their structured geometric models and FIs. The generation of these instances takes advantage of the functional designations of components, e.g. adjusted cap screw in the present case, and the load cycles attached to them and derived from S LC . This generation is achieved with inferences on functional designations and properties of load cycles. To this end, it is mandatory to distinguish statically determined configurations from statically undetermined ones. These details are not described here to preserve the paper consistency and concentrate on the exploitation of these functional informations.

As a result of the use of T FN , a component of a DMU can be automatically identified when it falls into the category of cap screws, nuts, locking nuts that are required to define bolted junctions. This means that their B-Rep model incorporates their geometric interfaces with neighboring components, the graph of interfaces identifies the components a bolted junction contains, the components are assigned functional designations that intrinsically identifies cap screws, nuts, locking nuts, …, and connects them with and assembly instance in T FN . It is now the purpose of the next section to take advantage of this information to set up the template-based transformations.

TEMPLATE-BASED TRANSFORMATIONS FOR FE MODELS

As a result, the DMU is now geometrically structured, components are linked by their geometric interfaces, and groups of components can be accurately identified and located in the DMU using their function and geometric structure, e.g. 'adjusted bolted junctions with screw+nut' (see Fig. 5). Now, the geometric transformations needed to adapt the DMU to FEA objectives are strengthened because screws, nuts, locking nuts can be robustly identified, groups of tightened components are also available through the load cycles attached to cap screws.

Two possible accesses are proposed to define a function-based template related to an assembly function:

-A component through a user-defined selection: from it and its FD, a datastructure gives access to the functions it contributes to. After selecting this component, the user selects the function of interest. Other components are recovered through the selected function this component participates to, -The function itself that can lead to the set of components needed to define this function and all the instances of this function existing in the targeted assembly.

These accesses can be subjected to constraints that can help identifying the proper set of instances. Constraints aim at filtering out instances when a template is defined from a function to reduce a set of instances to the user's needs, e.g. assembly function with bolts 'constrained with' tightening plates 'plate_i' and 'plate_j' where these designations are functional designations of these components.

Constraints aim at extending a set of instances when a template is defined from a component, i.e. a single function instance recovered, and needs to be extended, e.g. assembly function with bolts 'constrained with' same tightened components and screw head FI of type 'planar support' or 'conical fit'.

Function-based template and compatibility conditions of transformations

The previous paragraph has sketched how component functions can be used to identify sets of components in an assembly. Indeed, this identification is based on classes appearing in T FN . Here, the purpose is to define more precisely how the template can be related to T

FN and what constraints are set on shape transformations to preserve the geometric consistency of the components and assembly. Shape transformations are application-dependent and the present context is structural mechanics and FEA to define a range of possible transformations.

The simplest relationship between a template T and T FN is to relate T to a leaf of T FN . In this case, T covers instances defining sets of components that contain a variable number of components. T is also dimension independent since it covers any size of component, i.e. it is a parameterized entity. Shape transformations on T are designated as S T and the template devoted to an application becomes S T (T). Now, reducing the scope to disassemblable assembly functions and more specifically bolted junctions, one leaf of T FN can be used to define more precisely T and S T (T). Conforming to Fig. 5, let us restrict first to the leaf 'screw+nut' of T FN . Then, T contains the following FIs: one threaded link, two or more planar supports (one between nut and plate and at least one between two plates), either one planar support or one conical fit between the screw head and a plate, as many cylindrical loose fits as plates between the screw and plates because the class of junctions is of type adjusted. The shape transformations S T (T) of T set up to process bolted junctions can be summarized as: Each of these transformations will detailed throughout the following sections.

Now, the purpose is to define S T so that S T (T) exists and preserves the consistency of the components and the assembly. This defines compatibility conditions, C C , between T and S T that are conceptually close to attachment constraints of form features on an object [START_REF] Van Den Berg | Specification of free-form features[END_REF]. C C apply to S T and are introduced briefly here. Given the set of components contained in T, this set can be subdivided into two disjoint subsets as follows:

-I C is the set of components such that each of its components has all its FIs in T, e.g. the screw belongs to I C . Consequently, components belonging to I C are entirely in T; -P C is the set of components such that each of its components has some of its FIs in T, e.g. a plate belongs to P C . Components belonging to I C are partially in T. I C can be used to define a 3D sub domain of T, T I defined as the union of all components belonging to I C . Now, if a transformation S T takes place in I C and geometrically lies inside T I , S T (T) is valid because it cannot create interferences with other components of the assembly, i.e. C C is satisfied. Let us consider some of these transformations to illustrate some C C . As an objective of FEA, the purpose of the assembly model is to analyze the stress distribution between plates and their interactions with bolts. To this end, the stress distribution around the threaded link between a screw and a nut is not relevant. Therefore, one shape transformation, S T1 is the removal of the threaded link to merge the screw and the nut (see Fig. 6a). S T1 is always compatible since the screw and the nut belong to I C , hence the validity of C C . Now, considering another transformation, S T2 , is the localization of friction effects between plates around the screw shaft and the representation of the stress distribution nearby the screw shaft. This is modeled with a circular area centered on the screw axis and a cylindrical sub domain around the screw shaft (see Fig. 6b). Indeed, S T2 , is a domain decomposition [START_REF] Champaney | A domain decomposition method for studying the effects of missing fasteners on the behavior of structural assemblies with contact and friction[END_REF][START_REF] Champaney | Adaptive multi-analysis strategy for contact problems with friction[END_REF] taking place in the plates belonging to T. Because the plates belong to P C , C C are not trivial. However, S T2 , takes place inside the plates so they cannot interfere with other components, rather they can interfere with the boundary of the plates or they can interfere between them when several screws are close to each other on the same plate (see Fig. 7). In this case, C

C can be simply expressed, in a first place, as a non interference constraint. Other shape transformations will be listed when describing one example template in section 4.4.

Shape transformations and function dependency

The previous section has connected T to T FN in the simplest way possible, i.e. using a leaf that characterizes a single function. The purpose of this section is to analyze into which extent T can connect to classes of T FN that perform several functions in the assembly. In a first place, let us review shortly some concepts of functional analysis [START_REF] Ullman | The Mechanical Design Process[END_REF]. There, it is often referred to several categories of functions that are related to a design process, i.e. external, internal, auxiliary, … However, this does not convey consistency conditions among these functions, especially from a geometric point of view. Here, the current content of T FN refers to internal functions, i.e. functions strictly performed by components of the assembly. The 'screw+nut' function, as part of bolted junctions, is one of them. Bolted junctions can contain other functions. Let us consider the locking function, i.e. the bolt is locked to avoid any loss of tension in the screw when the components are subjected to vibrations. The locking process can take place either on the screw or on the nut. For the purpose of the analysis, we consider here a locking process on the nut, using a locking nut (see Fig. 9a). In functional analysis, this function is designated as auxiliary function but this concept does not characterize geometric properties of these functions.

From a geometric point of view, it can be observed that FIs of the screw, nut and locking nut are located in 3D such that the FI (planar support) between the nut and locking nut cannot exist if the nut does not tighten the plates. Consequently, the locking function cannot exist if the tightening function does not exist. Rather than using the designation of auxiliary function, which is geometrically imprecise, it is referred to dependent function.

The concept of dependent functions is inserted in T

FN at different levels of T FN to attach the corresponding functions when they exist (see Fig. 5). Based on the concept of dependent function, it is possible to extend the connection rule between T and T FN . Rather than connections at the leaf level, higher level classes can be connected to T if the dependent functions are taken into account in the C C of shape transformations S T so that S T (T) exists and preserves the consistency of the assembly. As an illustration, let us consider T connected to 'Bolted adjusted' (see Fig. 5). Now, S T can cover the class of bolted junctions with locking nut. Let S T3 , be the transformation that removes the locking nut of a bolted junction, which meets also the FEA objectives mentioned earlier. Because S T3 , applies to a dependent function of 'screw+nut', is satisfies the C C and the resulting model has a consistent layout of FIs. Consequently, T can be effectively connected to 'Bolted adjusted', which is a generalization of T.

Template generation

T is generated on the basis of the components involved in its associated function in T FN . T incorporates the objectives of the FEA to specify S T . Here, S T covers all the transformations described previously, i.e. S T1 , S T2 , S T3 . Fig. 6 and7 illustrates the key elements of these shape transformations. Other shape transformations, S T4 , can be defined to cover screw head transformations and extend the range of screws to flat head ones.

Then, the set of shape transformations structures the dialog with the user to allow him, resp. her, to select some of these transformations. However, the user settings are applied to instances whenever possible, i.e. when the instance belongs to a class where the shape transformations are applicable.

Interference No interference

User Meshing Tolerance Ø Subdomains = User Ratio X Ø Screw From the physical testing and preliminary numerical models, the following simulation objectives have been set up that initiate the requirements for the proposed template-based transformations.

To adapt the FE model to these simulation objectives while representing the physical behavior of the structure, an efficient domain decomposition approach [START_REF] Champaney | A domain decomposition method for studying the effects of missing fasteners on the behavior of structural assemblies with contact and friction[END_REF][START_REF] Champaney | Adaptive multi-analysis strategy for contact problems with friction[END_REF] uses a coarse mesh far enough from the bolted junctions and a specific sub domain around each bolted junction with friction and preload phenomena (see Fig. 8a,b). The objective is not to generate a detailed stress distribution everywhere in this assembly but to observe the load distribution areas among bolts using the mechanical models set in the sub domains. The objective of this section is to validate the template-based approach based on a demonstrator that transforms automatically the bolts into simplified sub domains ready for meshing with friction area definition while preserving the consistency of the assembly. The template features are aligned with the needs for setting up a simulation model able to exhibit some of the physical phenomena observed during testing and expressed in the above simulations results.

5.4.1

Operator description Having enriched the assembly with functional information, the template interface lets the user select a node of T FN that is compatible with T. In this example, the function to select is: 'assembly with Bolted junction' (see Fig. 10). Now, several S T are either pre set or user accessible. S T3 is user accessible and set here to remove the dependent function 'locking with locking nut' because the simulation objective does not focus on dynamic effects. Then, S T5 is pre set in T to preserve the cylindrical loose fit between screw and plates to set up contact friction BCs without interpenetration over these FIs. S T1 is also pre set as well as S T4 . The latter is performed on the FI (planar support) between the screw head/nut and the plates to obtain a meshing process independent of nut and screw head shapes. Now, T can cover any bolted junction to merge screw, nut and locking-nut into a single domain, reduce the screw and nut shapes to a simple shape of revolution while preserving the consistency of its interfaces. To precisely monitor the stress distribution around bolts and friction between plates, S T2 is user-selected. It a simplified model of the Rotscher's cone [START_REF] Bickford | Introduction to the Design and Behavior of Bolted Joints[END_REF] (see Fig. 9) that enables generating a simple mesh pattern around bolts. Based on T, S T (T) is fairly generic and parameterized to intelligently select and transform bolts, i.e. it is independent of the number and thicknesses of plates, of the screw diameter, the length and head type (cylindrical (see Fig. 9a) versus flat ones) in addition to the location of each bolt.

Here, S T (T) contains S T2 , a generation of sub domains taking into account the physical effects of the Rotscher's cone. This geometric transformation could interact with plate boundaries to change the shape of these sub domains and influence the mesh generation process. Presently, templates are standalone entities and are not taking into account these effects left for future developments. At present, the user can adjust the sub domain to avoid these interactions (see Fig. 10a).

Computer-Aided Design & Applications, 10(a), 2013, bbb-ccc © 2013 CAD Solutions, LLC, http://www.cadanda.com

Implementation and results

The developed prototype is based on OpenCascade and Python scripting language. The DMU is imported as STEP assembly models, the geometric interfaces between components are represented as independent trimmed CAD faces with identifiers of the initial face pairs of the FI. The assembly functional description is imported as a text file from the specific application performing the functional enrichment described in [START_REF] Shahwan | Qualitative behavioral reasoning from components' interfaces to components' functions for DMU adaption to FE analyses[END_REF] and linked to the assembly model by components' identifiers. Fig. 10a shows the user interface of the prototype. When selecting the 'assembly with Bolted Junction' function, the user has a direct access to the list of bolted junctions in the assembly. To allow the user filtering his selection, DMU parameters are extracted from the FD of components, e.g. the screw and nut type, the number of tightened components, or from geometry processing based on FDs, e.g. screw diameter. Using these parameters, the user is able to select bolted junctions with diameter between 10 and 16 mm (see Fig. 10b) or bolted junctions with screw and locking nut (see Fig. 10c), etc. The user can monitor the Rotscher's cone dimension with a FEA parameter called 'sub domain ratio' that represents the ratio between the screw nominal diameter and the sub-domain diameter (see Fig. 10d ande). Then, the user-defined 'meshing tolerance' is used during the verification phase to check the compatibility conditions, C C , between instances and their surrounding geometry (see Fig. 7). The final CAD assembly (see Fig. 11b) with simplified bolted junctions has been exported to a CAE software, i.e. Abaqus. STEP files transfer the geometric model and associated xml files describes the interfaces between components to trigger meshing strategies with friction area definition.

Comparing with the process pipeline used with existing industrial software, the figures are as follows. The model preparation from CAD software to Abaqus simulation model takes 5 days of interactive work for aircraft structure 1 mentioned above. Using the pipeline performing the functional enrichment of the DMU and the proposed template-based shape transformations, to directly produce the meshable model in Abaqus and perform the mesh in Abaqus, the overall time is reduced to one hour. The adequacy of this model conforms to the preliminary numerical models set up in ROMMA project and extending this conformity to testing results is ongoing since the template enables easy adjustments of the mesh model. Regarding the aircraft structure 2, there is no reference evaluation of its model preparation time from CAD to mesh generation because it is considered as too complex to fit into the industrial product development process. However, it is possible to estimate the time reduction since the interactive time can be linearly scaled according with the number of bolted junction. This ends up with 25 days of interactive work compared to 1.5 hour with the proposed approach where the time is mostly devoted to the mesh generation phase rather than the templatebased transformations, which stay automated.

Though the automation is very high, the template-based approach leaves the user with meaningful parameters enabling him/her to adapt the shape transformations to subsets of bolted junctions when FE it is required models.

CONCLUSION

In this work, a template-based method empowers the use of DMUs enriched with geometric interfaces and functional information, to automate CAD assembly pre-processing and generate a FE-friendly equivalence of this assembly. Because the template is directly connected to assembly functions, its instances contain a group of components consistently involved in the same assembly function. When selecting a specific function, the user has a direct access to the associated components, their structured model as well as their FIs. It has been shown also that the template can cover a rather large range of configurations since it is parameterized with respect to components' dimensions, components' number, components' shapes and finally, component function with the concept of dependent function. Using the template-based transformations, the user can robustly and efficiently define the geometric transformations according to his/her FEA objectives and meshing constraints. Thus, new components' shapes adapted to CAE software requirements are produced while the consistency of the assembly model is preserved. The template can be instantiated over the whole assembly to transform quickly repetitive configurations such as bolted junctions which were highly time consuming with interactive processing. Finally, a demonstrator has been presented to prove the efficiency of the template-based transformation approach and its valuable contribution to a PDP. The template-based approach show how shape transformations highly benefit from functional information and strengthen these transformations in the context of complex models like assemblies where many components interact with each other. Bolted junctions of two industrial use-cases have been automatically transformed into simplified macro elements with sub-domains generation. The resulting model produces a seamless generation of FE models conforming to the simulation objectives while taking into account meshing constraints.

Fig. 1 :

 1 Fig. 1: Examples of aeronautical DMUs with a variety of bolted junctions.

Fig. 2 :

 2 Fig. 2: Process flow to enrich a DMU with functional designations of components and their associated structured geometric models.

Fig. 3 :

 3 Fig. 3: Example of force cycle, as subset of the CIG, initiated by a threaded link.

-

  S T1 : merging screw and nut; -S T2 : localization of friction effects with a sub domain around a screw; -S T3 : removal of locking nut if it exists; -S T4 : screw head transformation for mesh generation purposes; -S T5 : cylindrical loose fit around the screw shaft to support the contact condition with tightened plates.

Fig. 6 :

 6 Fig. 6: Compatibility conditions (C C ) of shape transformations S T applied to T.

Fig. 7 :

 7 Fig. 7: Checking the compatibility of S T (T) with respect to the surrounding geometry of T. 5.4 Example of template-based operator of bolted junctions transformation During the PDP of an aeronautical company, simulation engineers perform specific FEAs on assembly sub structures such as the aircraft junction between wings and fuselage. Based on pre-existing physical testing performed by ROMMA project partners, this structure can be subjected to tensile and compressive forces to analyze: • The distribution of the load transfer among the bolted junctions; • The admissible extreme loads throughout this structure.

Fig. 8 :

 8 Fig. 8: (a) Multi-scale simulation with domain decomposition around bolted junctions (b) Load transfers at critical holes (courtesy of ROMMA project [4]).

Fig. 9 :

 9 Fig. 9: Template based transformation S T (T) of a bolted junction into simple mesh model with friction and contact areas definition around screw and nut.

Fig. 11 Fig. 10 :

 1110 Fig.10ashows the user interface of the prototype. When selecting the 'assembly with Bolted Junction' function, the user has a direct access to the list of bolted junctions in the assembly. To allow the user filtering his selection, DMU parameters are extracted from the FD of components, e.g. the screw and nut type, the number of tightened components, or from geometry processing based on FDs, e.g. screw diameter. Using these parameters, the user is able to select bolted junctions with diameter between 10 and 16 mm (see Fig.10b) or bolted junctions with screw and locking nut (see Fig.10c), etc. The user can monitor the Rotscher's cone dimension with a FEA parameter called 'sub domain ratio' that represents the ratio between the screw nominal diameter and the sub-domain diameter (see Fig.10d and e). Then, the user-defined 'meshing tolerance' is used during the verification phase to check the compatibility conditions, C C , between instances and their surrounding geometry (see Fig.7). Fig.11shows two results of the template-based transformations on aircraft structures:1. A junction between the wing and the fuselage. The assembly contains 45 bolted junctions with 3 different diameters and 2 different screw heads;2. An engine pylon. The assembly contains over 250 bolted junctions with identical screws and nuts.

Fig. 11 :

 11 Fig. 11: (a) CAD model with functional designations and geometric interfaces, (b) model after applying S T (T) on bolts, (c) mesh assembly model with friction area definition.

Computer-Aided Design & Applications, 10(a), 2013, bbb-ccc © 2013 CAD Solutions, LLC, http://www.cadanda.com

ACKNOWLEDGMENT

This work is carried out as part of the ROMMA (RObust Mechanical Models for Assemblies) project [4] under the reference ANR-09-COSI-012. The authors are very grateful for the financial support from the Agence Nationale de la Recherche (ANR). This work is also supported by the ERC Expressive.