1 introduction - wit press · cad based optimisation of composite structures patrick morelle^, ......

CAD based optimisation of composite

structures

Patrick Morelle , Y. Radovcic*

*Samtechs.a., 25, BdFrere ORBAN, B4000 Liege, Belgium

Pole Universitaire Leonard de Vinci, 92916 Paris La Defense

Cedex, France

Email: [email protected]

Abstract

Optimisation methods are today a very classical tool as far as classical, metallic orat least homogeneous structures are concerned. However, the application of thesetechniques to composite structures are faced with many difficulties as soon as theproblem is formulated outside the classical area of ply thickness/orientation.

1. CAD capabilities are not as common as far as composite structures modellingis concerned. Furthermore, a change of topology is nearly impossible (even forthe most recent parametric modellers) thus making it difficult to optimisestacking sequences or laminate geometries for example

2. Algorithms are not well adapted to the kind of discontinuity/nonlinearityexhibited by these kinds of structures.

3. Manufacturing constraints are hardly taken into account so that "optimal"solutions provided cannot always been actually applied to the real structures.Stochastic aspects are also not trivial and can strongly influence the realbehaviour with respect to the "ideal" one

The goal of the COMPOPT project is to improve design methodology, especiallyin SMEs, for composite structures by developing customised design tools devotedto these kinds of structures. This paper presents the state in the art and theadvancements of the project, which is now reaching mid-term. New ideas and newsolutions are presented, allowing the handling of shape optimisation together withstacking sequence optimisation for some classes of structures. Some pre-resultsare presented and the software tools largely discussed.

Transactions on the Built Environment vol 37 © 1999 WIT Press, www.witpress.com, ISSN 1743-3509

312 Computer Aided Optimum Design of Structures

1 Introduction

In an over-competing world, where products have to be designed more and moreefficiently, in less and less time and in a multidisciplinary context, CAD basedmethods a must for the companies looking for optimising performance and costof their products. As a guideline for the designer, Finite Element Method is todayable to simulate nearly every type of composite, allowing better and bettercontrol of the performances. However, the situation today remains unsatisfactoryas far as automatic design and optimisation are concerned. The methods whichare today "classical" and well established for homogeneous materials cannot yetbe reproduced and transposed to the composites. One of the main reasons is thefact that parameterization capabilities, which are a key factor for automaticlooping and model rebuilding, are not yet fully extended to this kind of structures

The goal of the COMPOPT project is to develop an architecture allowing totest/prototype new solutions in this area. New parameterization tools andalgorithms will be developed and integrated within the new architecture, togetherwith optimisation algorithms allowing to formulate and solve new classes ofcomposite optimisation problems. As a wide range of composite users SME's areparticularly targeted in this project. The problem for them is twofold : most of thepresently available CAE software are too expensive/too difficult to use in such acontext and, on the other hand, the design of composite structures involves a lotof manufacturing constraints, very specific to the sector, which are difficult, if notimpossible, to take into account in the present commercial systems.

On those aspects, the COMPOPT project, which is currently reaching its mid-term, will propose an architecture allowing full customisation to SME specificneeds. During the second half of the project, the team will also examine thisquestion of the manufacturing constraints and provide some ways to take theminto account.

2 CAD and composite design : a painful history

Within the design process, CAD models are more and more widely used fromconceptual design to detailed/final design. Analysis models are now based onCAD entities and optimisation techniques widely use the new parameterizationcapabilities of the modern CAD systems, pioneered by the Pro-Engineer one. Ithas now been followed by a lot of competitors (CATIA, EUCLID etc.), not all ofthem being able to extend those capabilities to composite materials and

structures.

2.1 A survey of the situation in CAD/CAE systems

As far as automatic design is concerned, commercially available CAE systemsprovide two important capabilities :


Computer Aided Optimum Design of Structures 313

• parametric geometry and fall model associativity• automatic lay-up procedures and material definition

The goal is to be able to loop on the analysis models that means to be able torebuild the CAB models in a quasi-automatic way. However, reality is far awayfrom that ideal picture and commercial CAE systems are still lacking capabilities,specially in the field of composite structures.

The coupling between geometry modification/lay-up procedure for example, canlead to silly solutions (because of the non-unicity of the solution in case thegeometry exhibits some non developable surfaces) that the system is far to beable to manage on its own.

CAE systems also require mesh definition. Some of the commercial pre-processor are now able to mesh automatically a laminated shell based on a givennumber of patches. But not all of them are able to deal with a modified number ofpatches (means a modified topology) when an optimisation procedure is about tomodify it.

Those examples illustrate the problems of existing systems. Lack offlexibility/capability/user friendliness, high price, are some of the problems theuser is facing. And they are still amplified when used in an SME context!

2.2 The situation in optimisation of composite structures

As an example of existing systems, we can point out the MSC/Patran laminatemodeler. The aim here is an accurate definition of laminated structures based onshell FEM models. Ply are defined on surfaces, imported from CAD modelers.Material is then associated to ply, including a starting point for the drapingprocess and an orientation vector. After selection of an algorithm for lay-upprocedure, fibre angle computation is automatic. The various algorithm allows tosimulate the manufacturing process including scissors draping for example. Fornon developable surfaces, the algorithm simulates what happens when the ply isforced in place. Last but not least, the system includes an adaptive mesherallowing automatic detection of ply drops.

The FibreSim software of Composite Design Technologies is another similarsystem. It operates entirely from within CAE interfaces and systems like IDEAS,PATRAN, ANSYS, MARC. Catia-GH integrates composite definition tool andinclude some manufacturing constraints. This system is much closer to the BOSSarchitecture described in paragraph 4 and used in the COMPOPT project.



3 Scenario for stacking sequence optimisation

There are indeed more than one way to modify the stacking sequence, eitherdirectly (combinations of a set of plies) or indirectly (elimination of some pliesinitially introduced in a laminate). Different scenario are now considered andcompared.

3.1 Direct solution using discrete variables

The most direct way to modify a predefined stacking sequence is off course to"combine" the set of existing plies using some discrete variable optimisationalgorithm. Genetic algorithms are able to do it but at a very high cost and cannotbe used in the context of structural optimisation. Furthermore, parametricdescription of a given stacking sequence is not a classical capability of CAEsoftware.

3.2 Direct solution using laminate shape/topology optimisation

Another very promising idea explored in COMPOPT is related to the possibilityof laminate shape optimisation. Parametric CAD description of laminates on ashell can be used in such a way that patches can be moved all over the supportingshell and possibly superimposed ...with the consequence of anothercombinatorial problem in order to determine the position of the new patchsuperimposing an existing one. To avoid this problem, it is better to start with"every layer everywhere" and then allow some layers to move away anddisappear locally. This leads naturally to another idea : it is to put a set oflaminates and then, layer by layer, to perform an optimisation of topologycreating holes and voids inside each layers. This would involve de factomodifications of the stacking sequence. Topology optimisation is mature todayfor homogeneous (metallic) structures. The idea is to extend its capabilities tonon homogeneous materials [1]

3.3 Indirect solution using ply thickness variables

The most classical way to optimise stacking sequence is to use ply thickness asdesign variables (discrete or continuous ones) allowing some plies to vanish andso the sequence to be modified. When the previous topology problem isformulated with one variable by layer/element, the idea here is more to associateone variable to the whole ply of a laminate.

4 The COMPOPT architecture

Design optimisation is today more and more muti-disciplinary. The design has tobe more and more global and takes into account as many constraints as possiblein the early design phases.



In order to solve that kind of problems, the BOSS-QUATTRO system has beendesigned with the architecture illustrated on Figure 1

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metersModels - -;

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D Ax''' -:->:"*

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\,/ ResDonses /

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Figure 1

With the following architecture, parameters can be accessed within the nativesystems, provided the requested driver is designed. They can also be mixedperforming simultaneous design/shape/material optimisation. The purpose of thisdriver will be to allow the following operations :

=> access the parameter, read its name, value=> update the parameter, give him a new value=> rebuild the model using now the updated parameter value

Another set of drivers is designed to communicate with CAE result files toprovide "functions" to the optimisation algorithm. Those functions can be, forexample, the weight, local stresses, displacements, safety margins.

The BOSS architecture allows to combine parameters, functions and algorithmsto formulate and solve an optimisation problem.

5 Optimisation problem resolution : algorithms and methods

Even if a part of the COMPOPT project is devoted to those incoming methodslike Genetic Algorithms and other non deterministic methods (like SimulatedAnnealing and so on), the first and most important task is devoted to the use ofMathematical Programming techniques. Rather than Response Surface Methods,the used methodology here is based on local approximations and the so-calledMethod of Successive Approximation. The idea is to replace the initial, nonexplicit problem:



GJ<CJ<CJ j = l,m (1)

Pt Pi Pi ' = !»"

by an explicit, linearised one whose solution provide a first approximation of theoptimal solution. The process is then looped until convergence. The very firstsuccessful methodology has been the Method of Convex Linearisation [2], wherethe non explicit functions are linearised in the following way :

/(/>,) s /(/>,„) + I ~~(P> - Ac) +>o "Pio \

<o

Clearly, when this type of approximation works for functions exhibiting limitednon linearity, it fails with sin/cos functions and their multiplicity of local optima!!! The problem using (2) is that, because of the use of monotonous functionsonly (x, 1/x), situation may arise where the process is oscillating and no moreconverging to even a local optimum.

Method of Moving Asymptotes [3] was the first generalized strategy using l/(x-a) and l/((5-x) to linearize the function, the asymptotes a and p being used totune the curvature of the approximation. In the present project, the latestenhancements is used. It is called the Globally convergent Method of MovingAsymptotes [4]

6 Manufacturing constraints

There are several aspects of that question which are treated in the COMPOPTproject (including cost functions and special constraints directly included in the(1) formulation) but the most interesting aspect is the one concerned with thestochastic variations of properties involved in composite structures. PoleUniversitaire Leonard de Vinci is in charge of this task and is providing asolution based on "Interval Arithmetic" to deal with robust design and

probabilistic aspects. [5]

The goal here is to identify designs which are insensitive to small stochasticvariations of some physical parameters. Rather than to use Monte Carlosimulations or Stochastic Finite Element techniques, the IA method is envisagedas providing a cheap but usable approximation of the probabilities.



7 An example of application

Optimisation of a composite pipe will be considered here. A three dimensionalfinite element model (Figure 2) is created using the SAMCEF system andlaminate properties defined in such a way they can be automatically updated.

The pipe is submitted to aninternal pressure of 70 bars.The design variables are theply thickness and orientations.

The optimisation problemconsists in minimising weightwith strength ratio > 1.2

Figure 2 : finite elementmodel of a laminated pipe

This problem exhibits non monotone behaviour due to the presence of the anglesas design variables, involving sin type functions in the model behaviour. As aconsequence, an optimal mass value can be found (2.52.10-3 t, the initial valuebeing 8.48 10-3 t). Table 1 summarises the results using different optimisationalgorithms. CONLIN procedure can hardly solve that kind of problem as far as awide variation of angle is considered. So, non surprisingly, it just allows to reacha convergence if a; 3 [30°, 60° ]

algorithmCONLINCONLINGCMMA

angle variation

<Xj 3 [30°, 60° ]oti 3 [10°, 80°]cti 3 [10°, 80°]

optimum reached2.52.10-3none2.52.10-3

Table 1

Using the new GCMMA algorithm, convergence is reached even for widervariations of the angles : a; 3 [10°, 80° ].So, clearly, the benefit of the newalgorithms is to increase stability and robustness of the process.



46-a**"* - j , , , , |

10 15 20 25

Iterations

& 8_A1 0 o_A2 *——*_A3 x-~•--*

Figure 3 : Ply Angles histories during the iterative process

10 15 20 25

Iterations

0 o T2 * T4

Figure 4 : Ply thickness histories during the iterative process

1.5-

1.4-

B U m ED 03 qjiQl m CD CD fflCD ED pj ED H3 CD gl-ffl« i i i i t | * i 1 * 1 i « » * i i i

0 5 10 15 20 25

Iterations

G o strrat

Figure 5 : Stress ratio coming to the imposed bound after convergence



25

Figure 6 : Mass history (objective function)

8 Conclusions

Progress in algorithms are a crucial question in the resolution of real lifecomposite design problems. The next problems which shall be addressed in theproject are :

• CAD/CAE parameterization of composite structures• formulation of the optimisation problem, including the question of the

incorporation of manufacturing constraints and of a realistic cost function

The COMPOPT system will lead to a customisable architecture allowing to beadapted to SME environment. Process design knowledge encapsulation ispossible in some extend in the classical approach provided those conditions aresatisfied.

The work described in this work is part of the COMPOPT BRITE/EURAMproject (BRPR-CT96-0332)

References

[1] Beckers M., Fleury C;, Topology Optimization involving discrete variables,in 3Ext. abstracts of 2 World Congress on Structural and MultidisciplinaryOptimisation, Zakopane, 1997, pp 67-68[2] Fleury C., Braibant V., Structural Optimisation : A new dual method usingmixed variables, Int. J. for Num. Meth. In Eng., Vol. 23, 1986, pp 409-428[3] Svanberg, K., The Method of Moving Asymptotes - A New Method forStructural Optimisation, Int. J. for Num. Meth. In Eng., Vol. 24, 1987, pp 359-373



[4] Svanberg, K., A Globally Convergent Version of MMA without Linesearch,Proc. of the First World Congress of Structural and MultidisciplinaryOptimisation, Goslar, Germany, May 28 -June 2, 1995, pp 9-16

[5] Delcroix F., Braibant V., Oudshoorn A., Interval arithmetics based numericalsolution of linear systems for non-deterministic analysis of structures, Proc. Of1997 ASME Deisgn Engineering Technical Conf. and Comp. In Eng.Conference.


1 introduction - wit press · cad based optimisation of composite structures patrick morelle^, ......

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