References of "Duysinx, Pierre"
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See detailSimplified fatigue resistance in mechanical engineering using topology optimization
Collet, Maxime ULg; Bruggi, Matteo; Bauduin, Simon ULg et al

Conference (2015, July 09)

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See detailDeterministic Manufacturing constraints for Optimal Distribution in the Case of Additive Manufacturing
Bauduin, Simon ULg; Collet, Maxime ULg; Duysinx, Pierre ULg et al

Conference (2015, July 09)

An overview of the difficulties of coupling additive manufacturing to topology optimization with various solution founded and implemented.

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See detailStress constrained topology optimization for additive manufacturing: Specific character and solution aspects
Duysinx, Pierre ULg

Conference (2015, July 07)

Since the fundamental work by Bendsøe and Kikuchi (1988), topology optimization has been based on compliance type formulations (Bendsoe & Sigmund, 2003) while the number of works considering stress ... [more ▼]

Since the fundamental work by Bendsøe and Kikuchi (1988), topology optimization has been based on compliance type formulations (Bendsoe & Sigmund, 2003) while the number of works considering stress constraints are rather limited (Duysinx & Bendsoe, 1998). More recently the generalized shape optimization approach using level set methods (see for instance Allaire, Jouve, Troader, 2004, Belytchko, Xiao, Parimi, 2003) has followed the tracks of topology optimization and has mainly been focusing on compliance minimization problems. The ‘compliance type’ formulation has produced quite interesting results in many problems because controlling the energy and the displacements under the loads is generally favourable for deflection control and because, for one load case, the compliance minimization leads to a fully stressed design nearly everywhere in the structure. However there are theoretical results that clearly show that the strongest and the stiffest structural layout can be quite different. As demonstrated in Rozvany & Birker (1994) truss topology optimization can lead to different results when there are several load cases, different stress limits in tension and compression, or when there are several materials involved. Therefore, the first goal of the paper points out the importance of considering stress constraints as soon as the preliminary design phase, that is, to include stress constraints in the topology optimization problem. Revisiting some contributions of the authors, this paper aims at illustrating the key role of stress constraints in the framework of topology optimization of continuum structures. The recent developments are able to treat: • Integrated stress criteria (i.e. global) relaxed stress constraints that aggregate the stress constraints in each finite element in order to be able to circumvent the large scale character of the local stress constraints. • Stress criteria that are able to tackle non equal stress limits in tension and compression. The usual von Mises criterion is unable to predict real-life designs when the structure is made of materials with unequal stress limits like concrete or composite materials. These different behaviours in tension and compression result in quite specific designs. Numerical applications make possible to point out the different nature of structural lay out for maximum strength and maximum stiffness. This one is clearly demonstrated in two kinds of particular situations: once several load cases are considered and when unequal stress limits in tension and compression are involved. The second contribution of the paper deals with the solution aspects of large scale constrained optimization problems. Because of the huge number of design variables, dual methods combined with local convex approximations such as CONLIN (Fleury, 1989) or MMA (Svanberg, 1987) are well indicated to solve classical topology optimization methods. However stress constrained problems introduce also a so large number of active constraints that one comes to a rather delicate situation. We show that the optimizer effort increases mostly as the cube of the number of constraints. In order to circumvent the problem, the idea developed in the paper is to combine first or second order approximations (Bruyneel, Duysinx, Fleury, 2002) with zero order approximations of stress constraints, especially for the subset of restrictions that are likely not to be active or not to change too fast. At first the paper presents the way to derive zero-order approximations of -relaxed stress constraints (that is necessary to cope with the singularity phenomenon of stress constraints in topology optimization). Then the proposed hybrid approach mixing approximation of different orders is benchmarked on numerical applications illustrating the reduction of computation time for solving optimization problems without sacrifying to the robustness and efficiency. Numerical applications will investigate topology optimized benchmark examples combined with additive manufacturing fabrication to illustrate the developments. [less ▲]

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See detailStructural optimization of multibody system components described using level set techniques
Tromme, Emmanuel ULg; Tortorelli, Daniel; Bruls, Olivier ULg et al

in Structural and Multidisciplinary Optimization (2015)

The structural optimization of the components in multibody systems is performed using a fully coupled optimization method. The design’s predicted response is obtained from a flexible multibody system ... [more ▼]

The structural optimization of the components in multibody systems is performed using a fully coupled optimization method. The design’s predicted response is obtained from a flexible multibody system simulation under various service conditions. In this way, the resulting optimization process enhances most existing studies which are limited to weakly coupled (quasi-) static or frequency domain loading conditions. A level set description of the component geometry is used to formulate a generalized shape optimization problem which is solved via efficient gradient-based optimization methods. Gradients of cost and constraint functions are obtained from a sensitivity analysis which is revisited in order to facilitate its implementation and retain its computational efficiency. The optimizations of a slider-crank mechanism and a 2-dof robot are provided to exemplify the procedure. [less ▲]

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See detailA level set approach for the structural optimization of flexible mechanisms
Tromme, Emmanuel ULg; Tortorelli, Daniel; Bruls, Olivier ULg et al

Conference (2015, June 08)

With the evolution of virtual prototyping, mechanical systems are commonly analyzed using a multibody system (MBS) approach to study the behavior of the entire system and notably the dynamic interactions ... [more ▼]

With the evolution of virtual prototyping, mechanical systems are commonly analyzed using a multibody system (MBS) approach to study the behavior of the entire system and notably the dynamic interactions between the components. Modern structural optimization of mechanical systems considers the dynamic loading exerted on the individual flexible components. The consideration is an essential feature and can be implemented in two ways. Firstly, one can consider a strong coupling wherein the component’s optimization is performed using the time dependent loading conditions coming directly from the MBS simulation. Secondly, one can consider a weak coupling wherein the component’s optimization is performed using a series of static load cases that do not fully account for the interactions between the components of the MBS. Rather this approach performs a MBS simulation to evaluate the loads for the initial design and then optimizes the component assuming the loads do not change. The process of evaluating the loads and then performing the optimization is repeated until suitable convergence criteria is satisfied, assuming convergence is possible. The present paper focuses on the strong coupling method wherein the flexible MBS dynamic analysis is based on a nonlinear finite element formalism [1]. A level set (LS) description of the component geometry is used to enable a generalized shape optimization. The LS approach combines the advantages of shape and topology optimizations. Moreover, since the component boundaries are defined by CAD features, the manufacturing process is facilitated as no post-processing step of a rasterized design is required. The design sensitivity analysis for MBS is revisited in order to facilitate its implementation. The optimization of a slider-crank mechanism and a 2-dof robot is provided to exemplify the procedure. [1] Géradin M., Cardona A. (2001) Flexible Multibody Dynamics: A Finite Element Approach. John Wiley & Sons, New York. [less ▲]

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See detailTopology optimization of mechanical and aerospace components subject to fatigue stress constraints
Duysinx, Pierre ULg; Collet, Maxime ULg; Bauduin, Simon ULg et al

Conference (2015, June 08)

While topology optimization has been based mostly on compliance type formulations, industrial applications call for more elaborated formulations including several restrictions on the local displacements ... [more ▼]

While topology optimization has been based mostly on compliance type formulations, industrial applications call for more elaborated formulations including several restrictions on the local displacements and the stress constraints in some critical zones. Topology optimization with stress constraints was initially considered in Duysinx & Bendsoe (1998). Later the stress constraint formulation was further extended to consider non equal stress constraints limits Bruggi & Duysinx (2012) and to improve the solution efficiency using different strategies such as global stress constraint formulations (Duysinx & Sigmund, 1998, Le et al. 2010). In the present work, the authors are investigating the formulations of stress constraint topology optimization to support the redesign of structural components that have to be fabricated using additive manufacturing. In this perspective, design problem requirements include tackling fatigue constraints during stress constrained topology optimization. The work investigates different formulations of fatigue resistance which could be appropriate in a topology approach. At first the classical approach of mechanical engineering based on SN curves and Goodman or Soderberg lines. The treatment of these fatigue restrictions can take advantage of former work developed for unequal stress constraints by considering mean and alternating components of the stress state. In a second step our research is now focussing on more complex situations (3D stress states) which require resorting to more advanced criteria. Dang Van fatigue theory (Dang Van, Griveau, Message, 1989) has been selected but calls for a more elaborated procedure that is currently validated. Topology optimized structural layouts predicted using classical stress criteria, Goodman and Dang Van theories are compared. [less ▲]

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See detailDamage process sensitivity analysis using an XFEM-Level Set framework
Noël, Lise ULg; Duysinx, Pierre ULg; Maute, Kurt

in Proceedings of the 11th World Congress on Structural and Multidisciplinary Optimization (WCSMO-11) (2015, June)

Designing efficient and lightweight structures is a key objective for many industrial applications such as in aerospace or the automotive industry. To this end, composite materials are appealing as they ... [more ▼]

Designing efficient and lightweight structures is a key objective for many industrial applications such as in aerospace or the automotive industry. To this end, composite materials are appealing as they combine high stiffness and light weight. The main challenge slowing down the integration of such materials in real structures is their damage be- havior. The latter should be considered in the design process of the structures. This work focuses on developing a systematic approach to designing structures that can sustain an acceptable amount of degradation or exhibit a low sensitivity to damage. An optimization approach is chosen to achieve this goal. To deal with complex geometries and to allow for large shape modifications in the optimization process, the extended finite element method (XFEM) is advantageously combined with a level set description of geometry. The degradation of materials is modeled by using a non-local damage model, motivated by the work of James and Waisman on a density approach to topol- ogy optimization. To solve design problems with damage constraints by gradient-based optimization method, a sensitivity analysis of the damage process is developed. Damage propagation and growth is an irreversible pro- cess. Therefore, the path dependence of the structural response needs to be accounted for in the sensitivity analysis. In this paper, we present an analytical approach for efficiently and accurately evaluating the design sensitivities, considering both direct and adjoint formulations. Finally, the sensitivity analysis approach is studied with simple benchmark problems and compared with the results obtained by finite differences. [less ▲]

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See detailL'optimisation topologique et la fabrication additive, amélioration de la chaine de conception
Louvigny, Yannick ULg; Nzisabira, Jonathan ULg; Meunier, Bertrand et al

in 14ème colloque national AIP PRIMECA : Produits, Procédés, Systèmes intelligents et durables (2015, March)

L'intérêt de combiner l'optimisation topologique avec les méthodes de fabrication additive vient du fait que d'une part, l'optimisation topologique permet de générer des géométries complexes que les ... [more ▼]

L'intérêt de combiner l'optimisation topologique avec les méthodes de fabrication additive vient du fait que d'une part, l'optimisation topologique permet de générer des géométries complexes que les procédés d'usinage conventionnels ne sont pas capables de réaliser et que, d'autre part, la fabrication additive permet de réaliser des formes complexes telles que des cavités emprisonnées dans un volume ou des canaux non rectilignes, impossibles à reproduire en fonderie ou par usinage. De plus et contrairement aux techniques traditionnelles, la réalisation des géométries complexes n'influence pas le coût pour les techniques additives. Pour ces techniques, le coût est lié principalement au volume de la pièce. La complexité de la pièce n'est plus un problème mais un atout. Toutefois cette combinaison n'est pas encore exploitable au niveau industriel. En effet, les résultats fournis par l'optimisation topologique doivent être modifiés, souvent manuellement, pour les rendre utilisables par les méthodes de fabrication additive. Et ces modifications coûtent cher. Il est donc intéressant de limiter ou au mieux d'éliminer les étapes manuelles de la chaîne de conception. Ce papier propose une chaîne de conception optimisée pour une pièce devant être fabriquée par les méthodes additives. En outre, la prise en compte des contraintes inhérentes aux procédés de fabrication par addition de matière reste problématique. Une démarche simplifiée est proposée pour identifier les types de contraintes inhérentes aux procédés de fabrication par addition de matière, les quantifier pour certaines techniques et les intégrer dans le code d'optimisation topologique. La nouvelle chaine de conception minimise les interventions du concepteur qui rendent le processus plus lourd et moins viable industriellement. Dans cette nouvelle chaîne de conception, certaines étapes sont réalisées plus rapidement et génèrent de meilleurs résultats. [less ▲]

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See detailQuelle voiture pour demain? Existence des solutions alternatives et évolution nécessaire des systèmes de transport collectifs et individuels
Duysinx, Pierre ULg

Scientific conference (2015, January 08)

Face aux défis du 21ème siècle, il est légitime de s’interroger sur l’existence et l’évolution nécessaire des systèmes de transports collectifs et individuels. L’exposé présente les lignes de forces qui ... [more ▼]

Face aux défis du 21ème siècle, il est légitime de s’interroger sur l’existence et l’évolution nécessaire des systèmes de transports collectifs et individuels. L’exposé présente les lignes de forces qui guident l’évolution des véhicules afin de les rendre plus soutenables : écologiques, économiques et socialement acceptables à l’horizon 2030-2050. [less ▲]

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See detailStress-based topology optimization with fatigue failure constraints
Collet, Maxime ULg; Bruggi, Matteo; Bauduin, Simon ULg et al

in Proceedings of the Fifteenth International Conference on Civil, Structural and Environmental Engineering Computing (2015)

This paper shows how the design of a structure can evolve when considering a stressbased topology optimization along with fatigue failure constraints. More precisely, fatigue failure is added in a stress ... [more ▼]

This paper shows how the design of a structure can evolve when considering a stressbased topology optimization along with fatigue failure constraints. More precisely, fatigue failure is added in a stress-based topology optimization Matlab code by following the approach of the design of machine elements, i.e. based on S-N curves or fatigue criteria. The fatigue is introduced through weel-known criteria for high-cycle fatigue such as the Sines and Crossland criteria. The paper presents how these criteria can be formulated for a topology optimization problem. Numerical results for both criteria are successively compared and discussed. The character of fatigue failure in the optimization procedure is illustrated as well as some issues that have to be improved in future work. [less ▲]

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See detailShape optimization of bimaterial (micro)structures using XFEM and a level set description
Noël, Lise ULg; Duysinx, Pierre ULg

Conference (2014, September 08)

This work focuses on the problem of finding the optimal microstructural design for a material to suit particular applications. For this purpose, an analysis method was developed and implemented to get the ... [more ▼]

This work focuses on the problem of finding the optimal microstructural design for a material to suit particular applications. For this purpose, an analysis method was developed and implemented to get the response of bimaterial structures. The analysis is based on the two following methods: • The level set description is used to represent the geometries of the (micro)structures, which can be rather complex. It allows to handle conveniently large shape modifications, which are often encountered in optimization process. • The extended finite element method (XFEM) allows circumventing the conform meshing of the (micro)structures. This is really advantageous for optimization applications, since a fixed mesh can be used throughout the simulations. To perform shape optimization, a sensitivity analysis of the design variables is needed. Fol- lowing the work by Van Miegroet (2007), an analytical approach to the computation of the derivatives has been developed. The stiffness matrix derivative is computed analytically starting from its discretized expression. Then, the expression of the stiffness matrix derivative is used to evaluate the sensitivity of various objective functions such as the compliance (global) or the stresses (local). The analytical sensitivity analysis is tested on simple examples, based on small scale struc- tures. Then, it is validated against other sensitivity approaches: a finite difference approach, a semi-analytical approach,... Finally, the analytical sensitivity analysis is illustrated by solving classic academic shape optimization problems. [less ▲]

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See detailSensitivity analysis with the extended finite element method on bimaterial structures
Noël, Lise ULg; Duysinx, Pierre ULg

Conference (2014, June 05)

Material tailoring can be formulated as a structural optimization problem. To design com- posite microstructures, which can exhibit very complex geometries, a level set description is used to efficiently ... [more ▼]

Material tailoring can be formulated as a structural optimization problem. To design com- posite microstructures, which can exhibit very complex geometries, a level set description is used to efficiently represent the microstructures. Fixed mesh methods and non conforming finite el- ement approximations, such as the extended finite element method (XFEM), presents several advantages to solve these problems of optimal material design. The key issue to solve an optimization problem is to perform an accurate sensitivity analysis. Recently, van Miegroet et Duysinx (2007) developed a semi-analytical procedure to achieve shape optimization using XFEM on void-material structures. The shape is represented by a level set function, whose parameters are considered as design variables. The optimization problem is solved by applying mathematical programming algorithms. To realize material tailoring, we extend this work to be able to deal with bimaterial structures. Working on void-material structures, the finite element approximation on a partially or on a fully filled element remains the same and the number of degrees of freedom does not change either. These characteristics of the approximation slightly ease the derivation procedure. A valid sensitivity analysis can be performed implementing a semi-analytical method based on a finite element computation of the stiffness matrix derivative. Dealing with material-material interfaces, the approximations and the number of degrees of freedom associated to an element filled with only one material or an element filled with two different materials are different. A new approach, adapted to the bimaterial framework, to achieve the sensitivity analysis is needed. To circumvent the problems linked to a finite difference computation, an analytical method is developed to perform the sensitivity analysis. Several other method, just like the global finite dif- ference, the semi-analytical computation, ... are also implemented to evaluate the performance and the validity of the analytical method. The developments are illustrated on academic test cases. Those are designed so that all the possible pathologic cases arise. The performance osf each method can then be easily evaluated. Finally, the analytical method is used in a simple optimization problem, where the shape of a solid inclusion is optimized to reach minimal compliance. [less ▲]

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See detailShape Optimization of Interior Permanent Magnet Motor for Torque Ripple Reduction
Kuci, Erin ULg; Geuzaine, Christophe ULg; Dular, Patrick ULg et al

in Proceedings of The 4th International Conference on Engineering Optimization: Lisbon (Portugal), 8-11 September 2014 (2014)

The objective of the paper is to present an open source environment to perform the design, simulation (Gmsh, GetDP) and optimization (OpenOpt) of electrical machines. The design of the permanent magnets ... [more ▼]

The objective of the paper is to present an open source environment to perform the design, simulation (Gmsh, GetDP) and optimization (OpenOpt) of electrical machines. The design of the permanent magnets of a v-shaped interior permanent magnet machine is then considered. The later is modeled using the finite element method with a formulation based on the magnetic vector potential. Optimization is based on mathematical programming approach. A semi-analytical sensitivity analysis is compared with the finite difference. Thanks to this approach, the design time is much shorter than that required by an approach of trial and error used by industry. The reduction of the torque ripple is about 70 \% with respect to the original design. [less ▲]

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See detailDiscussion on the optimization problem formulation of flexible components in multibody systems
Tromme, Emmanuel ULg; Bruls, Olivier ULg; Emonds-Alt, Jonathan et al

in Structural and Multidisciplinary Optimization (2013), 48(6), 1189-1206

This paper is dedicated to the structural optimization of flexible components in mechanical systems modeled as multibody systems. While most of the structural optimization developments have been conducted ... [more ▼]

This paper is dedicated to the structural optimization of flexible components in mechanical systems modeled as multibody systems. While most of the structural optimization developments have been conducted under (quasi-)static loadings or vibration design criteria, the proposed approach aims at considering as precisely as possible the effects of dynamic loading under service conditions. Solving this problem is quite challenging and naive implementations may lead to inaccurate and unstable results. To elaborate a robust and reliable approach, the optimization problem formulation is investigated because it turns out that it is a critical point. Different optimization algorithms are also tested. To explain the efficiency of the various solution approaches, the complex nature of the design space is analyzed. Numerical applications considering the optimization of a two-arm robot subject to a trajectory tracking constraint and the optimization of a slider-crank mechanism with a cyclic dynamic loading are presented to illustrate the different concepts. [less ▲]

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See detailSimultaneous design of structural layout and discrete fiber orientation using bi-value coding parameterization and volume constraint
TONG, Gao; ZHANG, Weihong; Duysinx, Pierre ULg

in Structural and Multidisciplinary Optimization (2013), 48(6), 1075-1088

The so-called bi-value coding parameterization (BCP) method is developed for the simultaneous optimization of layout design and discrete fiber orientations of laminated structures related to the ... [more ▼]

The so-called bi-value coding parameterization (BCP) method is developed for the simultaneous optimization of layout design and discrete fiber orientations of laminated structures related to the compliance minimization and natural frequency maximization. Both kinds of problems are transformed into a discrete material selection problem that is then solved as a continuous topology optimization problem with multiphase materials. A new form of the volume constraint is introduced in accordance with the BCP to control the material usage and material removal in the corresponding problem formulation. The BCP scheme assigning the integer value of +1 or -1 to each design variable for the unique “coding” is efficiently used to interpolate discrete fiber orientations and to identify the presence and removal of materials. Meanwhile, a general set-up strategy is proposed by assigning “uniform” weight values in BCP to ensure the feasibility of the initial starting point. Numerical tests illustrate that the BCP is efficient in dealing with both kinds of design problems including the volume constraint. [less ▲]

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See detailComparison of parameterization schemes for solving the discrete material optimization problem of composite structures
Duysinx, Pierre ULg; Guillermo Alonso, Maria ULg; Gao, Tong et al

Conference (2013, September)

In the context of weight reduction challenges in aerospace, automotive, and energy engineering problems, composite materials are gaining a revived interested. Because of the problem complexity and the ... [more ▼]

In the context of weight reduction challenges in aerospace, automotive, and energy engineering problems, composite materials are gaining a revived interested. Because of the problem complexity and the large number of design variables, their design of composite structures is greatly facilitated by using optimization techniques. While several formulations have been proposed for composite structure design, Stegmann and Lund [1] have showed that composite optimization can take advantage of the topology optimization approach. The fundamental idea of the Discrete Material Optimization (DMO) approach is 1/ to formulate the composite optimization problem as an optimal material selection problem in which the different laminates and ply orientations are considered as different materials and 2/ to solve the optimization problem using continuous existence variables. To transform the discrete problem into a continuous one, one introduces a suitable parametrization identifying each material by a unique set of design variables while the material properties are expressed as a weighted sum of all candidate materials. Using DMO approach, one can solve within a common approach, different design problems such as laminate distribution problem, stacking sequence optimization... The inherent difficulties of the discrete material selection using topology optimization are 1/ to find efficiency interpolation and penalization schemes of the material properties and 2/ to be able to tailor an efficient solution algorithm to handle very large scale optimization problems. Besides the reference DMO scheme by Lund and his co-authors, other interpolation schemes have been proposed: In this paper, work we are considering and comparing DMO with two other schemes namely the Shape Function with Penalization Parameterization (SFP) by Bruyneel [2] and it recent extension, the Bi-value Coding Parametrization (BCP) by Gao et al. [3]. In particular, the work considers the different schemes in the perspective of solving large-scale industrial applications. The work considers several aspects of the different schemes: • Nature of the different interpolation schemes, • Penalization strategies (power law (SIMP), RAMP, Tsai-Halpin or polynomial), • Number of design variables, the size and complexity of the optimization problem, • Sensitivity to local optima, to the initial design variable, and the development of continuous penalization techniques, • Ability to be extended to various formulations from compliance problems to local restrictions and buckling. As a major drawback, DMO, SFP and BCP approaches increase dramatically the number of design variables. Because of the computational burden to solve the optimization problems, in most of DMO implementations, the considered structural responses are generally limited to compliance-like objective functions. In order to extend the DMO formulation, the work investigates the selection of the most appropriate and efficient optimization algorithms to handle the problems. Different schemes of the sequential convex programming are compared. At first the classic schemes MMA and CONLIN are tested. Then more advanced schemes of the MMA family (Bruyneel et al. [4]) are experimented. The work and the comparisons are carried out on several numerical applications related to the selection of optimal local fibre orientations (with up to 36 candidate material orientations) in membrane and shell aerospace or automotive structures. The various numerical test problems include academic examples and benchmarks inspired by industrial applications. [less ▲]

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