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Note on singular optima in laminates design problems Bruyneel, Michaël ; Duysinx, Pierre in Structural and Multidisciplinary Optimization (2006), 31(2), 156-159 This paper studies the design of laminates subject to restrictions on the ply strength. The minimum weight design is considered. It is shown that this formulation includes singular optima, which are ... [more ▼] This paper studies the design of laminates subject to restrictions on the ply strength. The minimum weight design is considered. It is shown that this formulation includes singular optima, which are similar to the ones observed in topology optimization including local stress constraints. In laminate design, these singular optima are linked to the removal of 'zero thickness' plies from the stacking sequence. It is shown how the fiber orientation variables can circumvent the singularity by relaxing the strength constraints related to such vanishing plies. This demonstrates the key role of fiber orientations in the optimization of laminates and the need for their efficient treatment as design variables. [less ▲] Detailed reference viewed: 69 (5 ULg)Improvement of Pull-in Voltage of Electromechanical Microbeams Using Topology Optimization Lemaire, Etienne ; Duysinx, Pierre ; Rochus, Véronique et al in 3rd European Conference on Computational Mechanics (ECCM) (2006) The present work is dedicated to the application of topology optimization in the coupled simulation of multiphysic field problems as in MEMS. Precisely, it describes how it is possible to maximize pull-in ... [more ▼] The present work is dedicated to the application of topology optimization in the coupled simulation of multiphysic field problems as in MEMS. Precisely, it describes how it is possible to maximize pull-in voltage of an electromechanical microsystem for which the optimization domain is insulated from the electric field. The electromechanical coupling is modeled by the use of a monolithic analysis. The monolithic modeling combined with a Riks-Crisfield algorithm allows computing accurately the pull-in conditions. The optimization task is completed with the help of a sequential convex linear approximation schemes (CONLIN). [less ▲] Detailed reference viewed: 124 (20 ULg)MAXIMIZATION OF PULL-IN VOLTAGE OF MICRO-ELECTROMECHANICAL STRUCTURES USING TOPOLOGY OPTIMIZATION Lemaire, Etienne ; Rochus, Véronique ; Fleury, Claude et al Conference (2006) The design problem consists in maximizing the pull-in voltage using topology optimization method, which is formulated as an optimal material distribution. In addition to the classical volume constraint ... [more ▼] The design problem consists in maximizing the pull-in voltage using topology optimization method, which is formulated as an optimal material distribution. In addition to the classical volume constraint, different structural constraints could be taken into consideration. Sensitivity analysis is one of the key issues of the optimization process and is performed with the formulation of eigenvalue topology optimization problems. Here the paper investigates topology optimization of strongly coupled electromechanical systems. To avoid important modifications of the electric field by the optimization process, this first study considers a non design electrode and use topology optimization to design an optimal suspension structure. Solution procedure of the optimization problem is based on CONLIN optimizer using a sequential convex programming. This method that has proved its efficiency in many structural problems (sizing, shape) is here tailored to strongly coupled multiphysics design problems under consideration. The choice of appropriate explicit convex approximations schemes for multiphysic problems is investigated. The proposed method is illustrated and validated on microbeam optimization applications. [less ▲] Detailed reference viewed: 25 (2 ULg)Stress constrained optimization using X-FEM and Level-Set description Van Miegroet, Laurent ; ; Lemaire, Etienne et al in Proceedings of III European Conference on Computational Mechanics. Solids, Structures and Coupled Problems in Engineering (2006) This paper presents and describes an intermediate approach which takes its place between the two classical methods of shape and topology optimization. It is based on using the recent Level Set description ... [more ▼] This paper presents and describes an intermediate approach which takes its place between the two classical methods of shape and topology optimization. It is based on using the recent Level Set description of the geometry and the novel eXtended Finite Element Method (X-FEM). The method benefits from the fixed mesh work using X-FEM and from the curves smoothness of the Level Set description. Design variables are shape parameters of basic geometric features. The number of design variables of this formulation remains small whereas various global and local constraints can be considered. A key problem which is investigated here is the sensitivity analysis and the way it can be carried out precisely and efficiently. Numerical applications revisit some classical 2D (academic) benchmarks from shape optimization and illustrate the great interest of using X-FEM and Level Set description together. The paper presents the results of stress constrained problems using the proposed X-FEM and Level Set based formulation. A central issue is the sensitivity analysis (related to the compliance and/or the stresses) and the way it can be carried out efficiently. A special attention is also paid to stress constrained problems which are often neglected in other Level Set Methods works. [less ▲] Detailed reference viewed: 50 (5 ULg)Topology optimization of electromechanical microsystems against pull-in voltage Lemaire, Etienne ; Duysinx, Pierre ; Rochus, Véronique et al (2006) The present work is dedicated to the application of topology optimization in the multiphysic field of MEMS. Precisely, it describes how it is possible to maximize pull-in voltage of an electromechanical ... [more ▼] The present work is dedicated to the application of topology optimization in the multiphysic field of MEMS. Precisely, it describes how it is possible to maximize pull-in voltage of an electromechanical microsystem for which the optimization domain is insulated from the electric field. The electromechanical coupling is modeled by the use of a monolithic analysis. The optimization task is completed with the help of a sequential convex linear approximation schemes (CONLIN). [less ▲] Detailed reference viewed: 35 (10 ULg)Generalized shape optimization using X-FEM and Level Set methods Duysinx, Pierre ; Van Miegroet, Laurent ; et al in Bendsoe, M.-P.; Olhoff, N.; Sigmund, O. (Eds.) IUTAM Sumposium on Topological Design Optimization of Structures, Machines, and Materials. Status and Perspectives (2006) This paper presents an intermediate approach between parametric shape optimization and topology optimization. It is based on using the recent Level Set description of the geometry and the novel eXtended ... [more ▼] This paper presents an intermediate approach between parametric shape optimization and topology optimization. It is based on using the recent Level Set description of the geometry and the novel eXtended Finite Element Method (XFEM). The method takes benefit of the fixed mesh work using X-FEM and of the curves smoothness of the Level Set description. Design variables are shape parameters of basic geometric features. The number of design variables of this formulation is small whereas various global and local constraints can be considered. The Level Set description allows to modify the connectivity of the structure as geometric features can merge or separate from each other. However no new entity can be introduced. A central problem that is investigated here is the sensitivity analysis and the way it can be carried out efficiently. Numerical applications revisit the classical elliptical hole benchmark from shape optimization. [less ▲] Detailed reference viewed: 62 (3 ULg)A model reduction method for the control of rigid mechanisms Bruls, Olivier ; Duysinx, Pierre ; Golinval, Jean-Claude in Multibody System Dynamics (2006), 15(3), 213-227 This paper presents a reduction method to build closed-form dynamic equations for rigid multibody systems with a minimal kinematic description. Relying on an initial parameterization with absolute ... [more ▼] This paper presents a reduction method to build closed-form dynamic equations for rigid multibody systems with a minimal kinematic description. Relying on an initial parameterization with absolute displacements and rotations, the method is able to tackle complex topologies with closed-loops in a systematic way and its extension to flexible multibody systems will be investigated in the future. Thus, it would be of great use in the framework of model-based control of mechanisms. The method is based on an interpolation strategy. The initial model is built and reduced for a number of selected points in the configuration space. Then, a piecewise polynomial model is adjusted to match the collected data. After the presentation of the reduction procedure and of the interpolation strategy, two applications of the reduction method are considered: a four-bar mechanism and a parallel kinematic machine-tool called "Orthoglide". [less ▲] Detailed reference viewed: 44 (12 ULg)Generalized shape optimization with X-FEM and Level Set description applied to stress constrained structures Van Miegroet, Laurent ; ; Duysinx, Pierre et al Conference (2006) Detailed reference viewed: 41 (3 ULg)Generalized shape optimization using XFEM and Level Set methods Duysinx, Pierre ; Van Miegroet, Laurent ; et al in Bendsoe, M.-P.; Olhoff, N.; Sigmund, O. (Eds.) Proceedings of Topopt SYMP2005, IUTAM Symposium. Topological Design Optimization of Structures, Machines and Materials. Status and Perspectives (2005, October) This paper presents an intermediate approach between parametric shape optimization and topology optimization. It is based on using the recent Level Set description of the geometry and the novel eXtended ... [more ▼] This paper presents an intermediate approach between parametric shape optimization and topology optimization. It is based on using the recent Level Set description of the geometry and the novel eXtended Finite Element Method (XFEM). The method takes benefit of the fixed mesh work using X-FEM and of the curves smoothness of the Level Set description. Design variables are shape parameters of basic geometric features. The number of design variables of this formulation is small whereas various global and local constraints can be considered. The Level Set description allows to modify the connectivity of the structure as geometric features can merge or separate from each other. However no new entity can be introduced. A central problem that is investigated here is the sensitivity analysis and the way it can be carried out efficiently. Numerical applications revisit the classical elliptical hole benchmark from shape optimization. [less ▲] Detailed reference viewed: 93 (3 ULg)Optimal synthesis of mechanisms using time-varying dimensions and natural coordinates ; ; Duysinx, Pierre in Herskowitz, José (Ed.) Proceedings of the 6th World Congress of Structural and Multidisciplinary Optimization (WCSMO6) (2005, June) This paper presents a simple approach to optimize the dimensions and the positions of 2D mechanisms for path or function-generator synthesis. The proposed method is particularly adapted to assembled ... [more ▼] This paper presents a simple approach to optimize the dimensions and the positions of 2D mechanisms for path or function-generator synthesis. The proposed method is particularly adapted to assembled mechanisms since time-varying dimensions always satisfy the assembly conditions which may represent a real difficulty when dealing with closed-loop mechanisms. The objective is to minimize the strain energy of the bars - considered as flexible - of the mechanism when this one follows perfectly the desired path. Two optimization strategies are developed and criticized. The first one is based on separated optimizations of design parameters and point coordinates. The second one is more global and is performed in two stages : multiple local synthesis are needed first to find the initial point coordinates, and then a global synthesis stage is undertaken to find both the best dimensions and coordinates. The use of natural coordinates is also particularly interesting since the only non linear functions to optimize are distance functions, and the objective function is rather well-conditioned for a gradient-based optimizer. The question of finding the global optimum is addressed and discussed. Since a standard genetic algorithm may fail to find it, a different approach is proposed: exploring the design space to find several local optima among which the designer will choose the most relevant one taking other design constraints into account. A simple technique is applied which consists in running multiple optimization processes starting from uniformly-distributed initial dimensions (full-factorial design of experiments) across the parameter space. Three applications are presented: a simple four-bar path synthesis to illustrate the optimization strategies, a four-bar steering linkage synthesis for function generation – Ackermann relation to highlight the limits of both strategies, and eventually a six-bar steering mechanism to explore the design space and find different local optima. [less ▲] Detailed reference viewed: 73 (0 ULg)A unified finite element framework for the dynamic analysis of controlled flexible mechanisms Bruls, Olivier ; Duysinx, Pierre ; Golinval, Jean-Claude in Proceedings of the ECCOMAS Conference on Advances in Computational Multibody Dynamics (2005, June) This paper proposes a unified formalism for the simulation of mechatronic systems with complex flexible mechanisms. The equations of motion are formulated using a nonlinear Finite Element approach for the ... [more ▼] This paper proposes a unified formalism for the simulation of mechatronic systems with complex flexible mechanisms. The equations of motion are formulated using a nonlinear Finite Element approach for the mechanism, and the block diagram language for the control system. The set of strongly coupled equations of motion is constructed numerically, and integrated in the time domain using the generalized-alpha method. Convergence and stability properties are thus guaranteed for the simulation algorithm. Two illustrative examples are treated in the fields of vehicle dynamics and robotics respectively. [less ▲] Detailed reference viewed: 63 (5 ULg)Optimization of mechatronic systems: application to a modern car equipped with a semi-active suspension Duysinx, Pierre ; Bruls, Olivier ; et al in Herskowitz, José (Ed.) Proceedings of the 6th World Congress of Structural and Multidisciplinary Optimization (WCSMO6) (2005, May) The research aims at developing a global mechatronic approach to model, simulate and optimize complex industrial applications. The approach is illustrated with the simulation and the optimization of a ... [more ▼] The research aims at developing a global mechatronic approach to model, simulate and optimize complex industrial applications. The approach is illustrated with the simulation and the optimization of a modern car (an Audi A6) equipped with a controlled semi-active suspension. An optimization procedure is used to find the best sub-system parameters in order to improve the comfort of the passengers while preserving the car ride and handling performances. Two different modeling and optimization approaches are used and compared. The first one is realized in the MATLAB-SIMULINK environment and is based on a symbolic multibody model of the chassis while the hydraulic actuators, and the controller are integrated using S-functions. Optimization is also carried out in MATLAB using algorithms available in MATLAB libraries, especially a genetic algorithm (GA). On the other hand, the second approach relies on a multibody model based on the Finite Element method whereas the optimization can be realized with an industrial open optimization tool. [less ▲] Detailed reference viewed: 112 (2 ULg)Generalized Shape optimization based on the Level Set method Van Miegroet, Laurent ; ; Fleury, Claude et al in Herskowitz, José (Ed.) Proceedings of the 6th World Congress of Structural and Multidisciplinary Optimization (WCSMO6) (2005, May) This paper describes a first step work devoted to applying XFEM and Level Sets methods in optimization of structures. This first step work is based on integrating an existing XFEM code within a general ... [more ▼] This paper describes a first step work devoted to applying XFEM and Level Sets methods in optimization of structures. This first step work is based on integrating an existing XFEM code within a general open optimization tool, SAMCEF BOSS QUATTRO. Unlike most of the existing works, this approach is more shape optimization oriented. A library of pre-formatted basic geometric entities (such as ellipses, squares, triangles, etc.) described by Level Sets functions are used. These basic Level Set features can be combined to represent many kinds of interfaces and holes. The construction parameters of the basic Level Sets are considered as the design variables. In order to evaluate the sensitivities, a finite difference scheme over the design variables is used in this first work. Different mechanical responses (energy, weight, displacement, . . .) can be considered as objective functions or constraints in the problem formulation. Several academic 2D test cases of shape and topology optimization are presented within the XFEM and Level Set approach. In addition, a work by Missoum et al. [11], in which the shape and topology optimization of the structure is carried out by an optimal selection of holes characteristics with a genetic algorithm is presented. [less ▲] Detailed reference viewed: 107 (5 ULg)Note on topology optimization of continuum structures including self-weight Bruyneel, Michaël ; Duysinx, Pierre in Structural and Multidisciplinary Optimization (2005), 29 Detailed reference viewed: 13 (0 ULg)Note on topology optimization of continuum structures including self-weight ; Duysinx, Pierre in Structural and Multidisciplinary Optimization (2005), 29(4), 245-256 This paper proposes to investigate topology optimization with density-dependent body forces and especially self-weight loading. Surprisingly the solution of such problems cannot be based on a direct ... [more ▼] This paper proposes to investigate topology optimization with density-dependent body forces and especially self-weight loading. Surprisingly the solution of such problems cannot be based on a direct extension of the solution procedure used for minimum-compliance topology optimization with fixed external loads. At first the particular difficulties arising in the considered topology problems are pointed out: non-monotonous behaviour of the compliance, possible unconstrained character of the optimum and the parasitic effect for low densities when using the power model (SIMP). To get rid of the last problem requires the modification of the power law model for low densities. The other problems require that the solution procedure and the selection of appropriate structural approximations be revisited. Numerical applications compare the efficiency of different approximation schemes of the MMA family. It is shown that important improvements are achieved when the solution is carried out using the gradient-based method of moving asymptotes (GBMMA) approximations. Criteria for selecting the approximations are suggested. In addition, the applications also provide the opportunity to illustrate the strong influence of the ratio between the applied loads and the structural weight on the optimal structural topology. [less ▲] Detailed reference viewed: 90 (6 ULg)Contribution to the optimization of closed-loop multibody systems: Application to parallel manipulators ; ; Duysinx, Pierre in Multibody System Dynamics (2005), 13(1), 69-84 This paper describes an original and robust method to optimize the design of closed-loop mechanisms, especially parallel manipulators. These mechanisms involve non linear assembling constraints. During ... [more ▼] This paper describes an original and robust method to optimize the design of closed-loop mechanisms, especially parallel manipulators. These mechanisms involve non linear assembling constraints. During optimization, the Newton-Raphson algorithm we use to solve these constraints may fail when the Jacobian matrix of the constraints is ill-conditioned and stops the redesign process. To circumvent the difficulty, the technique we propose takes advantage of numerical conditioning to penalize the objective function. Applications to an academic example and parallel robots demonstrate the capabilities of the methodology. [less ▲] Detailed reference viewed: 41 (2 ULg)Generation of closed-form models for the control of flexible mechanisms: a numerical approach Bruls, Olivier ; Duysinx, Pierre ; Golinval, Jean-Claude in Proc. of the 7th Int. Conf. on Motion and Vibration Control (MOVIC) (2004, August) In robotics, most high performances control strategies require a closed-form representation of the mechanical dynamic behaviour. This is even more critical when significant flexible effects are to be ... [more ▼] In robotics, most high performances control strategies require a closed-form representation of the mechanical dynamic behaviour. This is even more critical when significant flexible effects are to be considered in the control algorithm. This paper presents a method to build closed-form dynamic equations for flexible multibody systems in terms of minimal coordinates. Relying on the Finite Element (FE) formulation, the method is able to tackle complex topologies with closed-loops in a systematic way. The method is based on an interpolation strategy. For a number of selected points in the configuration space, a full Finite Element model is built and reduced according to a component mode synthesis. Then, a piecewise polynomial model is adjusted to match the collected data. In order to guarantee the continuity of the model, a mode tracking strategy is implemented. After the presentation of the reduction procedure and of the interpolation strategy, a four-bar mechanism is analyzed as an illustrative example. [less ▲] Detailed reference viewed: 32 (1 ULg)A systematic model reduction method for the control of flexible multibody systems Bruls, Olivier ; Duysinx, Pierre ; Golinval, Jean-Claude in Proc. of the 21st Int. Congress of Theoretical and Applied Mechanics (ICTAM) (2004, August) This paper presents a method to build closed-form dynamic equations for flexible multibody systems with a minimal kinematic description. Relying on the Finite Element formalism, the method is able to ... [more ▼] This paper presents a method to build closed-form dynamic equations for flexible multibody systems with a minimal kinematic description. Relying on the Finite Element formalism, the method is able to tackle complex topologies with closed-loops in a systematic way. Thus, it will be of great use in the framework of model based control of flexible mechanisms. The reduction procedure is based on an interpolation strategy: a Finite Element model is built and reduced for a number of selected points in the configuration space, and then, a piecewise polynomial model is adjusted to match the collected data. A few applications of the reduction method are considered: a serial pick-and-place machine, a flexible four bar mechanism, and a parallel kinematic manipulator. [less ▲] Detailed reference viewed: 19 (0 ULg)Reliable simulation of mechatronic systems using Newmark algorithms Bruls, Olivier ; Duysinx, Pierre ; Golinval, Jean-Claude Conference (2004, March) In the framework of flexible multibody systems simulation, the stability and the accuracy of the time integration process can be guaranteed by a family of implicit integrators derived from the Newmark ... [more ▼] In the framework of flexible multibody systems simulation, the stability and the accuracy of the time integration process can be guaranteed by a family of implicit integrators derived from the Newmark scheme (Hilber-Hughes-Taylor and Generalized- methods). This paper deals with the extension of those reliable integrators for the simulation of mechatronic systems. In order to account for the strong coupling between the mechanism and the control system, the coupled set of equations contains mechanical and control variables. The generation of those equations, their numerical treatment and their time integration may become unmanageable for realistic control systems. In many cases, it is however sufficient to consider a weak coupling, which means that the action of the control system is treated as an external force disturbing the dynamic equilibrium. The weak coupling assumption is fully justified when a digital controller is present in the control loop. Then, the control actions exhibit discontinuous transitions at each sampling instant. The standard form of the Newmark scheme assumes continuity of the acceleration variables, and is thus not appropriate for this situation. Therefore, we propose an adapted Newmark scheme which achieves an explicit treatment of the acceleration jumps throughout the integration process, so that the proper simulation of the mechatronic system is guaranteed. The paper describes the detailed modifications of the integration algorithm. Illustrative examples are used to point out the critical situations where they prevent from substantial integration errors. [less ▲] Detailed reference viewed: 26 (2 ULg)AN INTRODUCTION TO ROBOTICS: MECHANICAL ASPECTS Géradin, Michel ; Duysinx, Pierre Learning material (2004) Detailed reference viewed: 279 (12 ULg) |
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