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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: 37 (3 ULg)A semi-analytical sensitivity analysis for multibody systems described using Level Sets Tromme, Emmanuel ; Bruls, Olivier ; Duysinx, Pierre et al Conference (2014, June) Detailed reference viewed: 27 (8 ULg)Shape Optimization of Interior Permanent Magnet Motor for Torque Ripple Reduction Kuci, Erin ; Geuzaine, Christophe ; Dular, Patrick 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 ▲] Detailed reference viewed: 164 (24 ULg)Discussion on the optimization problem formulation of flexible components in multibody systems Tromme, Emmanuel ; Bruls, Olivier ; 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 ▲] Detailed reference viewed: 90 (19 ULg)Simultaneous design of structural layout and discrete fiber orientation using bi-value coding parameterization and volume constraint ; ; Duysinx, Pierre 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 ▲] Detailed reference viewed: 42 (3 ULg)Comparison of parameterization schemes for solving the discrete material optimization problem of composite structures Duysinx, Pierre ; Guillermo Alonso, Maria ; 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 ▲] Detailed reference viewed: 56 (3 ULg)Contact model between superelements in dynamic multibody systems Virlez, Geoffrey ; Bruls, Olivier ; Sonneville, Valentin et al in Proceedings of ASME2013 International Design Engineering Technical Conference & Computers and Information in Engineering Conference IDETC/CIE 2013 (2013, August) In this paper, a new contact formulation defined between flexible bodies modeled as superelements is investigated. Unlike rigid contact models, this approach enables to study the deformation and vibration ... [more ▼] In this paper, a new contact formulation defined between flexible bodies modeled as superelements is investigated. Unlike rigid contact models, this approach enables to study the deformation and vibration phenomena induced by hard contacts. Compared with full-scale finite element models of flexible bodies, the proposed method is computationally more efficient, especially in case of a large number of bodies and contact conditions. The compliance of each body is described using a reduced-order elastic model which is defined in a corotational frame that follows the gross motion of the body. The basis used to reduce the initial finite element model relies on the Craig-Bampton method which uses both static boundary modes and internal vibration modes. The formulation of the contact condition couples all degrees of freedom of the reduced model in a nonlinear way. The relevance of the approach is demonstrated by simulation results first on a simple example, and then on a gear pair model. [less ▲] Detailed reference viewed: 156 (28 ULg)EVALUATION OF PERFORMANCES OF HYBRID ELECTRIC ENERGY STORAGE SYSTEM (LI-ION BATTERIES/ SUPERCAPACITORS) EV AND HEV APPLICATIONS Lemaire, Julien ; Nzisabira, Jonathan ; Duysinx, Pierre Conference (2013, June) Electric and hybrid electric vehicles sound the best alternative to internal combustion engines. However, energy storage systems must have a sufficient power and energy density (to answer accelerations ... [more ▼] Electric and hybrid electric vehicles sound the best alternative to internal combustion engines. However, energy storage systems must have a sufficient power and energy density (to answer accelerations, regenerate breaking power and have sufficient autonomy). The advantage of batteries is their relatively large energy capacity. But batteries life time and capacity are limited by the number and the magnitude of current peaks [1]. The efficiency also depends on the discharge current regime. More there is high peak current, more the efficiency decreases [2]. Electrical double layer capacitors (EDLC) have a huge specific power and long life cycle because of their internal working principles especially based on charges transfer [3]. The main disadvantage is low specific energy. A combination of the two systems is interesting to gain energy capacity and lengthens the life of the batteries by limiting current peaks inside. The aim of this study is to evaluate the performances of a hybrid energy storage system (Li-ion batteries and EDLC) using a simulation tool. Batteries and EDLC are assembled in parallel in a high power bus. Batteries are directly linked on the bus because their nearly constant voltage. Conversely EDLC have to be connected with a DC/DC converter. Efficiencies of the elements are dependent on the actual current within each component. Given a total energy capacity and a current profile, the difference in final energy capacity may vary from about 15% whether the storage system is composed of batteries and EDLC or not. With hybrid energy storage the batteries are less discharged because of presence of EDLC (particularly due to efficiency difference) and their life cycle is longer. [less ▲] Detailed reference viewed: 136 (6 ULg)Comparison of parameterization schemes for solving the discrete material optimization problem of composite structures Duysinx, Pierre ; Guillermo Alonso, Maria ; et al in Halftka, Raphael; KIM, Nam Ho (Eds.) Proceeding of the 10th World Congress on Structural And Multidisciplinary Optimization (2013, May 19) Optimal design of composite structures can be formulated as an optimal selection of material in a list of different laminates. Based on the seminal work by Stegmann and Lund, the optimal problem can be ... [more ▼] Optimal design of composite structures can be formulated as an optimal selection of material in a list of different laminates. Based on the seminal work by Stegmann and Lund, the optimal problem can be stated as a topology optimization problem with multiple materials. The research work carries out a large investigation of different interpolation and penalization schemes for the optimal material selection problem. Besides the classical Design Material Optimization (DMO) scheme and the recent Shape Function with Penalization (SFP) scheme by Bruyneel, the research introduces a generalization of the SFP approach using a bi-value coding parameterization (BCP) by Gao, Zhang and Duysinx. The paper provides a comparison of the different parameterization approaches. It also proposes alternative penalization schemes and it investigates the effect of the power penalization. Finally, we discuss the solution aspects in the perspective of solving large-scale industrial applications. The conclusions are illustrated by a numerical application for the compliance maximization of an in-plane composite ply. [less ▲] Detailed reference viewed: 48 (1 ULg)Shape optimization of periodic microstructures subject to stiffness and local stress constraints Noël, Lise ; ; Duysinx, Pierre in Proceedings of the 10th World Congress on Structural and Multidisciplinary Optimization: Orlanda (USA), 19-24 mai 2013 (2013, May) As suggested by Sigmund, material tailoring can be formulated as a structural optimization problem. However microstructural geometries can be rather complex while optimization process may introduce large ... [more ▼] As suggested by Sigmund, material tailoring can be formulated as a structural optimization problem. However microstructural geometries can be rather complex while optimization process may introduce large shape modifications of boundaries and material interfaces. To circumvent the technical difficulties of classical shape optimization relying on numerous and tedious CAD model manipulations and remesh- ing, the Level Set description combined with a non-conforming XFEM analysis is a promising approach. In the present work, this approach that has been developed in work by Van Miegroet is extended to the investigation of periodic microstructures subject to compliance or stress constraints. The approach is illustrated on the famous problem of the Vigdergauz microstructure. [less ▲] Detailed reference viewed: 123 (52 ULg)Structural optimization of flexible components under dynamic loading within a multibody system approach: a comparative evaluation of optimization methods based on a 2-dof robot application. Tromme, Emmanuel ; Bruls, Olivier ; Virlez, Geoffrey et al in Proceedings of the 10th World Congress on Structural and Multidisciplinary Optimization: Orlanda (USA), 19-24 mai 2013 (2013, May) This paper is dedicated to a comparative evaluation between two methods of optimization to realize the structural optimization of flexible components in mechanical systems modeled as multibody systems. A ... [more ▼] This paper is dedicated to a comparative evaluation between two methods of optimization to realize the structural optimization of flexible components in mechanical systems modeled as multibody systems. A nonlinear finite element method based formalism is considered for the dynamic simulation of the flexible multibody system. The first method is the Equivalent Static Load method which enables to transform a dynamic response optimization problem into a set of static response optimization problems. The second method treats directly the dynamic optimization problem in an integrated manner where the optimization process is carried out directly based on the time response coming from the multibody system approach. However, the first method proposed by Kang, Park and Arora was developed under the assumption that the multibody system is described using a floating frame of reference. Therefore, in order to carry on the comparison using a unique multibody system approach, a method is first proposed to derive the equivalent static loads when using a nonlinear finite element method based formalism. The comparative evaluation is then carried out on the simple academic example of the mass minimization of a two-arm robot subject to tracking deviation constraints. Conclusions are finally drawn for future work and stringent comparison. [less ▲] Detailed reference viewed: 70 (22 ULg)A stress-based approach to the optimal design of structures with unilateral behavior of material or supports ; Duysinx, Pierre in Structural and Multidisciplinary Optimization (2013), 48 The paper presents a stress-based approach that copes with the optimal design of truss-like elastic structures in case of unilateral behavior of material or ground supports. The conventional volume ... [more ▼] The paper presents a stress-based approach that copes with the optimal design of truss-like elastic structures in case of unilateral behavior of material or ground supports. The conventional volume-constrained minimization of compliance is coupled with a set of local stress constraints that are enforced, all over the domain or along prescribed boundaries, to control the arising of members with tension-only or compression-only strength. A Drucker–Prager failure criterion is formulated to provide a smooth approximation of the no-tension or no-compression conditions governing the stress field. A selection strategy is implemented to handle efficiently the multi-constrained formulation that is solved through mathematical programming. Benchmark examples are investigated to discuss the features of the achieved optimal designs, as compared with problems involving material and ground supports with equal behavior in tension and compression. Numerical simulations show that a limited set of constraints is needed in the first iterations to steer the solution of the energy-driven optimization towards designs accounting for the prescribed assumption of unilateral strength. [less ▲] Detailed reference viewed: 61 (7 ULg)Modeling of joints with clearance and friction in multibody dynamic simulation of automotive differentials Virlez, Geoffrey ; Bruls, Olivier ; Tromme, Emmanuel et al in Theoretical and Applied Mechanics Letters (2013), 3(1), 013003 Defects in kinematic joints can sometimes highly influence the simulation response of the whole multibody system within which these joints are included. For instance, the clearance, the friction, the ... [more ▼] Defects in kinematic joints can sometimes highly influence the simulation response of the whole multibody system within which these joints are included. For instance, the clearance, the friction, the lubrication and the flexibility affect the transient behaviour, reduce the component life and produce noise and vibration for classical joints such as prismatics, cylindrics or universal joints. In this work, a new 3D cylindrical joint model which accounts for the clearance, the misalignment and the friction is presented. This formulation has been used to represent the link between the planet gears and the planet carrier in an automotive differential model. [less ▲] Detailed reference viewed: 83 (27 ULg)Eigenproblem formulation for electromechanical microsystem pull-in voltage optimization Lemaire, Etienne ; Van Miegroet, Laurent ; Tromme, Emmanuel et al Conference (2013) Electrostatic actuators are often used in MEMS since they are relatively easy to manufacture and provide a short response time. Previous studies have already considered topology optimization of such micro ... [more ▼] Electrostatic actuators are often used in MEMS since they are relatively easy to manufacture and provide a short response time. Previous studies have already considered topology optimization of such micro-actuators like the work by Raulli and Maute [1] and by Yoon and Sigmund [2]. Raulli considers maximization of the actuator output displacement for given electric potential input locations. The paper by Yoon et al. goes further by replacing the staggered modeling used by Raulli by a monolithic approach where both physical fields (electric and mechanical) are solved at once. However, electrostatic micro-actuators possess a limit input voltage called the pull-in voltage, beyond which they become unstable. If a voltage greater than the pull-in voltage is applied to the device, elastic forces of the suspension system are not able to balance electrostatic forces and electrodes stick together. In some cases, the pull-in effect can damage the device. Previous researches by the authors [3] have considered the possibility to control pull-in voltage using topology optimization. In this first approach, pull-in voltage itself was included in the optimization problem and treated as objective function. Nevertheless, in some applications, the developed pull-in voltage optimization procedure suffers from design oscillations that prevent from reaching solution. As illustrated in this paper, the issue is similar to the mode switching problem that arises in eigenvalue optimization problems. The classical solution to this issue consists in including several eigenvalues in a ‘max-min’ formulation. However as the classical pull-in voltage optimization problem is not formulated as an eigenproblem, direct application is not possible. Indeed, pull-in being a nonlinear instability phenomenon, strictly speaking, it is only possible to compute one instability mode and upcoming instability modes cannot be captured. Therefore, this paper is dedicated to the development of a linear eigenproblem approximation for the nonlinear stability problem after the work on nonlinear buckling by Lindgaard and Lund [4]. The proposed stability eigenproblem leads to an alternative optimization procedure aiming at maximizing pull-in voltage. The first eigenmode corresponds to the actual pull-in mode while higher order modes allow estimating upcoming instability modes. Using a multiobjective formulation to maximize the smallest eigenvalue of the stability problem, it is possible to circumvent oscillation issues met with pull-in voltage optimization. Moreover, numerical results show that even if the eigenproblem formulation is an approximation of the actual pull-in voltage optimization problem, eigenproblem formulation leads to significant improvement of pull-in voltage. References [1] M. Raulli and K. Maute, Topology optimization of electrostatically actuated Microsystems, Struct. & Mult. Opt., 30(5):342-359, November 2005. [2] G.H. Yoon and O. Sigmund, A monolithic approach for topology optimization of electrostatically actuated devices, Comput. Methods Appl. Mech. Engrg., 194:4062-4075, 2008. [3] E. Lemaire, V. Rochus, J.-C. Golinval, and P. Duysinx, Microbeam pull-in voltage topology optimization including material deposition constraint, Comput. Methods Appl. Mech. Engrg., 194:4040-4050, 2008. [4] E. Lindgaard and E. Lund, Nonlinear bucking optimization of composite structures, Comput. Methods Appl. Mech. Engrg., 199:37-40, 2010. [less ▲] Detailed reference viewed: 88 (27 ULg)Modelling of contact between stiff bodies in automotive transmission systems Virlez, Geoffrey ; Bruls, Olivier ; et al in Fisette, Paul; Samin, Jean-Claude (Eds.) Multibody Dynamics: Computational Methods and Applications (2013) Many transmission components contain moving parts, which can come into in contact. For example, the TORSEN differentials aremainly composed of gear pairs and thrust washers. The friction involved by ... [more ▼] Many transmission components contain moving parts, which can come into in contact. For example, the TORSEN differentials aremainly composed of gear pairs and thrust washers. The friction involved by contacts between these two parts is essential in the working principle of such differentials. In this chapter, two different contact models are presented and exploited for the modelling of differentials. The former uses an augmented Lagrangian technique or a penalty method and is defined between two flexible bodies or between a rigid body and a flexible structure. The second contact formulation is a continuous impact modelling based on a restitution coefficient. [less ▲] Detailed reference viewed: 114 (37 ULg)Topology optimization for minimum weight with compliance and stress constraints ; Duysinx, Pierre in Structural and Multidisciplinary Optimization (2012), 46(3), 269-384 The paper deals with a formulation for the topology optimization of elastic structures that aims at minimizing the structural weight subject to compliance and local stress constraints. The global ... [more ▼] The paper deals with a formulation for the topology optimization of elastic structures that aims at minimizing the structural weight subject to compliance and local stress constraints. The global constraint provides the expected stiffness to the optimal design while a selected set of local enforcements require feasibility with respect to the assigned strength of material. The Drucker–Prager failure criterion is implemented to handle materials with either equal or unequal behavior in tension and compression. A suitable relaxation of the equivalent stress measure is implemented to overcome the difficulties related to the singularity problem. Numerical examples are presented to discuss the features of the achieved optimal designs along with performances of the adopted procedure. Comparisons with pure compliance–based or pure stress–based strategies are also provided to point out differences arising in the optimal design with respect to conventional approaches, depending on the assumed material behavior. [less ▲] Detailed reference viewed: 49 (3 ULg)Modelling of joints with clearance and friction in multibody dynamic simulation of automotive differentials Virlez, Geoffrey ; Bruls, Olivier ; Tromme, Emmanuel et al in Proceedings of the 6th Asian Conference on Multibody Dynamics (2012, August 27) Defects in kinematic joints can sometimes highly influence the simulation response of the whole multibody system within which these joints are included. For instance, the clearance, the friction, the ... [more ▼] Defects in kinematic joints can sometimes highly influence the simulation response of the whole multibody system within which these joints are included. For instance, the clearance, the friction, the lubrication and the flexibility affect the transient behaviour, reduce the component life and produce noise and vibration for classical joints such as prismatic, cylindric or universal joint. In this work, a new 3D cylindrical joint model which accounts for the clearance, the misalignment and the friction is presented. This formulation has been used to represent the link between the planet gears and the planet carrier in an automotive differential model. [less ▲] Detailed reference viewed: 59 (13 ULg)Investigations on a Level Set based approach for the optimization of flexible components in multibody systems with a fixed mesh grid Tromme, Emmanuel ; Bruls, Olivier ; Van Miegroet, Laurent et al in Proceedings of The 6th Asian Conference on Multibody Dynamics: Shanghai (China), 26-30 aout 2012 (2012, August) This paper considers the optimization of flexible components in mechanical systems thanks to a "fully integrated" optimization method which includes a flexible multibody system simulation based on ... [more ▼] This paper considers the optimization of flexible components in mechanical systems thanks to a "fully integrated" optimization method which includes a flexible multibody system simulation based on nonlinear finite elements. This approach permits to better capture the effects of dynamic loading under service conditions. This process is challenging because most state-of-the-art studies in structural optimization have been conducted under (quasi-)static loading conditions or vibration design criteria and also because this ``fully integrated" optimization method is not a simple extension of static optimization techniques. The present paper proposes an approach based on a Level Set description of the geometry. This method leads to an intermediate level between shape and topology optimizations. Gradient-based optimization methods are adopted for their convergence speed. Numerical applications are conducted on the optimization of a connecting rod of a reciprocating engine with cyclic dynamic loading to show the feasibility and the promising results of this approach. [less ▲] Detailed reference viewed: 155 (31 ULg)Analysis of Stresses in Vehicle Driveline Systems Using a Flexible Multibody Approach Virlez, Geoffrey ; Bruls, Olivier ; Tromme, Emmanuel et al Conference (2012, July 10) Detailed reference viewed: 46 (17 ULg)A bi-value coding parameterization scheme for the discrete optimal orientation design of the composite laminate Gao, Tong ; ; Duysinx, Pierre in International Journal for Numerical Methods in Engineering (2012), 91(1), 98-114 The discrete optimal orientation design of the composite laminate can be treated as a material selection problem dealt with by continuous topology optimization method. In this work, a new bi-value coding ... [more ▼] The discrete optimal orientation design of the composite laminate can be treated as a material selection problem dealt with by continuous topology optimization method. In this work, a new bi-value coding parameterization (BCP) scheme is proposed to this aim. The idea of the BCP scheme is to “code” each material phase using integer values of +1 and -1. Each available material phase has one unique “code” consisting of +1 and/or -1 assigned to design variables. Theoretical and numerical comparisons between the proposed BCP scheme and existing schemes show that the BCP has the advantage of an evident reduction of the number of design variables in logarithmic form. This is very beneficial when the number of candidate materials becomes important. Numerical tests with up to 36 candidate material orientations are illustrated for the first time to indicate the reliability and efficiency of the proposed scheme in solving this kind of problem. It proves that the BCP is an interesting and potential scheme to achieve the optimal orientations for large-scale design problems. [less ▲] Detailed reference viewed: 55 (3 ULg) |
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