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On the equivalent static load method for flexible multibody systems described with a nonlinear finite element formalism Tromme, Emmanuel ; Sonneville, Valentin ; Bruls, Olivier et al in International Journal for Numerical Methods in Engineering (2016) The equivalent static load (ESL) method is a powerful approach to solve dynamic response structural optimization problems. The method transforms the dynamic response optimization into a static response ... [more ▼] The equivalent static load (ESL) method is a powerful approach to solve dynamic response structural optimization problems. The method transforms the dynamic response optimization into a static response optimization under multiple load cases. The ESL cases are defined based on the transient analysis response whereupon all the standard techniques of static response optimization can be used. In the last decade, the ESL method has been applied to perform the structural optimization of flexible components of mechanical systems modeled as multibody systems (MBS). The ESL evaluation strongly depends on the adopted formulation to describe the MBS and has been initially derived based on a floating frame of reference formulation. In this paper, we propose a method to derive the ESL adapted to a nonlinear finite element approach based on a Lie group formalism for two main reasons. Firstly, the finite element approach is completely general to analyze complex MBS and is suitable to perform more advanced optimization problems like topology optimization. Secondly, the selected Lie group formalism leads to a formulation of the equations of motion in the local frame, that turns out to be a strong practical advantage for the ESL evaluation. Examples are provided to validate the proposed method. [less ▲] Detailed reference viewed: 9 (2 ULg)Design Sensitivity Analysis for Shape Optimization of Nonlinear Magnetostatic Systems Kuci, Erin ; ; Duysinx, Pierre et al in Magnetics, IEEE Transactions on (Volume:PP , Issue: 99 ) (2015) The paper discusses the sensitivity analysis for the shape optimization of a nonlinear magnetostatic system, evaluated both by direct and adjoint approaches. The calculations rely on the Lie derivative ... [more ▼] The paper discusses the sensitivity analysis for the shape optimization of a nonlinear magnetostatic system, evaluated both by direct and adjoint approaches. The calculations rely on the Lie derivative concept of differential geometry where the flow is the velocity field associated with the modification of a geometrical parameter in the model. The resulting sensitivity formulas can be expressed naturally in a finite element setting through a volume integral in the layer of elements connected to the surface undergoing shape modification. The accuracy of the methodology is analyzed on a 2D model of an interior permanent magnet motor (IPM), and on a 3D model of a permanent magnet system. [less ▲] Detailed reference viewed: 27 (7 ULg)Simplified fatigue resistance in mechanical engineering using topology optimization Collet, Maxime ; ; Bauduin, Simon et al Conference (2015, July 09) Detailed reference viewed: 91 (11 ULg)Deterministic Manufacturing constraints for Optimal Distribution in the Case of Additive Manufacturing Bauduin, Simon ; Collet, Maxime ; Duysinx, Pierre et al Conference (2015, July 09) An overview of the difficulties of coupling additive manufacturing to topology optimization with various solution founded and implemented. Detailed reference viewed: 112 (19 ULg)Stress constrained topology optimization for additive manufacturing: Specific character and solution aspects Duysinx, Pierre 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 ▲] Detailed reference viewed: 223 (6 ULg)Optimal design of flexible mechanisms using the Equivalent Static Load method and a Lie group formalism Tromme, Emmanuel ; Sonneville, Valentin ; Bruls, Olivier et al Conference (2015, July 02) Detailed reference viewed: 74 (12 ULg)Structural optimization of multibody system components described using level set techniques Tromme, Emmanuel ; ; Bruls, Olivier 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 ▲] Detailed reference viewed: 65 (15 ULg)A level set approach for the structural optimization of flexible mechanisms Tromme, Emmanuel ; ; Bruls, Olivier 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 ▲] Detailed reference viewed: 64 (2 ULg)Topology optimization of mechanical and aerospace components subject to fatigue stress constraints Duysinx, Pierre ; Collet, Maxime ; Bauduin, Simon 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 ▲] Detailed reference viewed: 125 (13 ULg)Direct and Adjoint Sensitivity Analysis of Nonlinear Magnetostatic System: Application to Shape Optimization of Electrical Machines Kuci, Erin ; Geuzaine, Christophe ; Dular, Patrick et al Conference (2015, June 07) Detailed reference viewed: 10 (1 ULg)Design Sensitivity Analysis for Shape Optimization of Nonlinear Magnetostatic Systems Kuci, Erin ; Duysinx, Pierre ; Dular, Patrick et al in Proceedings of COMPUMAG 2015 (2015, June) In this paper, a direct and an adjoint analytic sensitivity analysis for a nonlinear magnetostatic system is obtained, in the context of shape optimization for any design function. The calculations are ... [more ▼] In this paper, a direct and an adjoint analytic sensitivity analysis for a nonlinear magnetostatic system is obtained, in the context of shape optimization for any design function. The calculations are based on the material derivative concept of continuum mechanics. The resulting sensitivity formula can be expressed as either a volume integral or as a boundary integral along the interface where shape modification occurs. A method for the calculation of the design velocity field and mesh updating scheme is introduced as well. The accuracy of the methodology is analysed on an inductor system, suggesting that the volume integration technique should be preferred. All methods are freely available for further testing in the open source environment GetDP/Gmsh. [less ▲] Detailed reference viewed: 20 (6 ULg)Damage process sensitivity analysis using an XFEM-Level Set framework Noël, Lise ; Duysinx, Pierre ; 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 ▲] Detailed reference viewed: 51 (12 ULg)L'optimisation topologique et la fabrication additive, amélioration de la chaine de conception Louvigny, Yannick ; Nzisabira, Jonathan ; 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 ▲] Detailed reference viewed: 93 (11 ULg)Quelle voiture pour demain? Existence des solutions alternatives et évolution nécessaire des systèmes de transport collectifs et individuels Duysinx, Pierre 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 ▲] Detailed reference viewed: 198 (4 ULg)Weakly and fully coupled methods for structural optimization of flexible mechanisms Tromme, Emmanuel ; Bruls, Olivier ; Duysinx, Pierre in Multibody System Dynamics (2015) The paper concerns a detailed comparison between two optimization methods that are used to perform the structural optimization of flexible components within a multibody system (MBS) simulation. The ... [more ▼] The paper concerns a detailed comparison between two optimization methods that are used to perform the structural optimization of flexible components within a multibody system (MBS) simulation. The dynamic analysis of flexible MBS is based on a nonlinear finite element formulation. The first method is a weakly coupled method, which reformulates the dynamic response optimization problem in a two-level approach. First, a rigid or flexible MBS simulation is performed, and second, each component is optimized independently using a quasi-static approach in which a series of equivalent static load (ESL) cases obtained from the MBS simulation are applied to the respective components. The second method, the fully coupled method, performs the dynamic response optimization using the time response obtained directly from the flexible MBS simulation. Here, an original procedure is proposed to evaluate the ESL from a nonlinear finite element simulation, contrasting with the floating reference frame formulation exploited in the standard ESL method. Several numerical examples are provided to support our position. It is shown that the fully coupled method is more general and accommodates all types of constraints at the price of a more complex optimization process. [less ▲] Detailed reference viewed: 18 (2 ULg)Stress-based topology optimization with fatigue failure constraints Collet, Maxime ; ; Bauduin, Simon 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 ▲] Detailed reference viewed: 93 (16 ULg)Shape optimization of bimaterial (micro)structures using XFEM and a level set description Noël, Lise ; Duysinx, Pierre 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 ▲] Detailed reference viewed: 35 (3 ULg)Calculation of crankshaft twist angle using multibody simulation and finite element method Louvigny, Yannick ; Duysinx, Pierre Conference (2014, July 21) Detailed reference viewed: 36 (5 ULg)Dynamic simulation of flexible gear pairs using a contact modelling between superelements Virlez, Geoffrey ; Bruls, Olivier ; Tromme, Emmanuel et al Conference (2014, July 02) Detailed reference viewed: 74 (18 ULg)Sensitivity analysis with the extended finite element method on bimaterial structures Noël, Lise ; Duysinx, Pierre 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 ▲] Detailed reference viewed: 36 (3 ULg) |
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