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See detailEigenproblem formulation for electromechanical microsystem pull-in voltage optimization
Lemaire, Etienne ULg; Van Miegroet, Laurent ULg; Tromme, Emmanuel ULg 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 ▲]

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See detailInvestigations on a Level Set based approach for the optimization of flexible components in multibody systems with a fixed mesh grid
Tromme, Emmanuel ULg; Bruls, Olivier ULg; Van Miegroet, Laurent ULg 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 ▲]

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See detailGeneralized Shape Optimization using XFEM and Level Set Description
Van Miegroet, Laurent ULg

Doctoral thesis (2012)

CAD based shape optimization aims at finding the shapes of internal and external boundaries of a structural components. The method is able to improve the design of structures against var- ious criteria ... [more ▼]

CAD based shape optimization aims at finding the shapes of internal and external boundaries of a structural components. The method is able to improve the design of structures against var- ious criteria such as restricted displacements, stress criteria, eigenfrequencies, etc. However, this technique has been quite unsuccessful in industrial applications because of the mesh management problems coming from the large shape modifications. The main technical problems stems from the sensitivity analysis requiring the calculation of the so-called velocity field related to mesh modifications. If 2D problems are quite well mastered, 3D solid and shell problems are difficult to handle in the most general way. It turns out that shape optimization remains generally quite fragile and delicate to use in industrial context. To circumvent the technical difficulties of the moving mesh problems, a couple of methods have been proposed such as the fictitious domain approach, the fixed grid finite elements and the projection methods. The present work relies on the application of the extended finite element method (X-FEM) to handle parametric shape optimization. The X-FEM method is naturally associated with the Level Set description of the geometry to provide an efficient and flexible treatment of problems involving moving boundaries or discontinuities. On the one hand, the method proposed benefits from the fixed mesh approach using X-FEM to prevent from mesh management difficulties. On the other hand, the Level Set description provides a smooth curves representation while being able to treat topology modifications naturally. In this thesis, we focus on the material-void and bi-material X-FEM elements for mechanical structures. The representation of the geometry is realized with a Level Set description. Basic shapes can be modeled from simple Level Set such as plane, circle, ... NURBS curves and surfaces that can be combined together using a Constructive Solid Geometry approach to represent com- plex geometries. The design variables of the optimization problem are the parameters of basic Level Set features or the NURBS control points. Classical global (compliance, eigenfrequencies, volume) and local responses (such as stress constraint) can be considered in the optimization problem that is solved using a mathematical programming approach with the CONLIN optimizer. The problem of the computation of the shape sensitivity analysis with X-FEM is carefully ad- dressed and investigated using several original methods based on semi-analytical and analytical approaches that are developed. Academic examples are first considered to illustrate that the proposed method is able to tackle accurately shape optimization problems. Then, real life struc- tures including 2D and 3D complex geometries illustrate the advantages and the drawbacks of using X-FEM and Level Set description for generalized shape optimization. [less ▲]

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See detailTopology optimization of electrostatic micro-actuators including electromechanical stability constraint
Lemaire, Etienne ULg; Van Miegroet, Laurent ULg; Rochus, Véronique et al

Conference (2011, November 16)

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See detailElectrostatic Simulation using XFEM for Conductor and Dielectric Interfaces
Rochus, Véronique ULg; Rixen, Daniel; Van Miegroet, Laurent ULg et al

in International Journal for Numerical Methods in Engineering (2011), 85(10), 12071226

ManyMicro-Electro-Mechanical Systems (e.g. RF-switches, micro-resonators and micro-rotors) involve mechanical structures moving in an electrostatic field. For this type of problems, it is required to ... [more ▼]

ManyMicro-Electro-Mechanical Systems (e.g. RF-switches, micro-resonators and micro-rotors) involve mechanical structures moving in an electrostatic field. For this type of problems, it is required to evaluate accurately the electrostatic forces acting on the devices. Extended Finite Element (X-FEM) approaches can easily handle moving boundaries and interfaces in the electrostatic domain and seem therefore very suitable to model Micro-Electro-Mechanical Systems. In this study we investigate different X-FEM techniques to solve the electrostatic problem when the electrostatic domain is bounded by a conducting material. Preliminary studies in one-dimension have shown that one can obtain good results in the computation of electrostatic potential using X-FEM. In this paper the extension of these preliminary studies to 2D problem is presented. In particular a new type of enrichment functions is proposed in order to treat accurately Dirichlet boundary conditions on the interface. [less ▲]

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See detailMultiphysic topology optimization of electromechanical micro-actuators considering pull-in effect
Lemaire, Etienne ULg; Van Miegroet, Laurent ULg; Schoonjans, Thibaut et al

in Proceedings of the IVth European Conference on Computational Mechanics (ECCM 2010) (2010)

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See detailAPPLICATION DE L’OPTIMISATION DE FORME ET DE TOPOLOGIE A LA CONCEPTION INNOVANTE D’EJECTEURS POUR UN CONCASSEUR MAG’IMPACT
Van Miegroet, Laurent ULg; Lemaire, Etienne ULg; Duysinx, Pierre ULg

Report (2009)

La recherche concerne l'application des techniques d'optimisation de forme et de topologie à la conception innovante des ejecteurs du concasseurs MAG'IMPACT.

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See detailSensitivity in shape optimization of complex 3D geometries using level sets and non-conforming finite elements
Duysinx, Pierre ULg; Van Miegroet, Laurent ULg

Conference (2009, September)

For the last 20 years shape optimization has been stocking to penetrate industrial and real-life applications, whereas topology optimization was experiencing a fast growing soar and extensions to various ... [more ▼]

For the last 20 years shape optimization has been stocking to penetrate industrial and real-life applications, whereas topology optimization was experiencing a fast growing soar and extensions to various applications. By the way there is still a great interest in shape optimization because of the intrinsic capability of shape description to facilitate considering complex problems involving local stress and manufacturing constraints for instance. The level set description proposed by Osher and Sethian (1988) opened new perspectives to handle variable boundaries as in shape optimization. The implicit description of the geometrical entities allows for a more friendly and flexible manipulation of the geometry and overcome some restrictions related to the explicit approach of the geometry used in CAD systems: for example it is possible to reduce the topological complexity by removing or merging geometric entities (i.e. holes can merge or disappear) without degenerating the model, which was major restriction of shape optimization. A few years ago, the level set method was nicely complemented by the XFEM (eXtended Finite Element Method) proposed by Moes et al (1999). This approach greatly reduces the difficulty of considering time-variable boundaries and complex geometries by using non-conforming meshes. This is definitively an advantage to circumvent the so-called velocity field to carry out shape sensitivity and mesh relocation difficulties, especially with thin walled structures or 3D designs. The present research is continuing along and extending works by Duysinx et al (2006) and Van Miegroet and Duysinx (2007) to consider shape optimization based on a parametric level set description and XFEM. The work that is carried out in a common research project EFCONICO sponsored by the Walloon Region of Belgium aims at extending preliminary results 3 D structure and complex geometries, increasing the reliability of the method, enhancing the performances using advanced mesh generators as Gmsh, etc. In particular the paper presents new theoretical developments and their numerical implementation in sensitivity analysis with respect to parametric design variable of level sets. The developments are illustrated with numerical applications dealing with complex shape applications involving 3D geometries and the boundary conditions along design variable boundaries. [less ▲]

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See detailInfluence of the material model on local pull-in in electromechanical microdevices topology optimization
Lemaire, Etienne ULg; Van Miegroet, Laurent ULg; Duysinx, Pierre ULg et al

in PLATO-N International Workshop - Extended Abstracts (2009, September)

The appearance of local pull-in modes has been noticed during electromechanical microdevices topology optimization. The goal of the present research is to study the influence of material properties ... [more ▼]

The appearance of local pull-in modes has been noticed during electromechanical microdevices topology optimization. The goal of the present research is to study the influence of material properties (mechanical and electrical) modeling for intermediate densities to see if an appropriate choice allows avoiding such local modes. At first, a simple 1D model is developed to study the influence of the material properties interpolation. Finally, we evaluate if the conclusions from the 1D model can help to prevent the appearance of local modes for a 2D topology optimization problem. [less ▲]

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See detail3D Shape Optimization with X-FEM and a Level Set Constructive Geometry Approach
Van Miegroet, Laurent ULg; Duysinx, Pierre ULg

in Proceeding of the 8th World Congress on Structural and Multidisciplinary Optimization (2009, June)

This paper extends previous work on structural optimization with the eXtended Finite Element Method (X-FEM) and the Level Set description of the geometry. The proposed method takes advantage of fixed mesh ... [more ▼]

This paper extends previous work on structural optimization with the eXtended Finite Element Method (X-FEM) and the Level Set description of the geometry. The proposed method takes advantage of fixed mesh approach by using an X-FEM structural analysis method and from the geometrical shape representation of the Level Set description. In order to allow the optimization of complex geometries represented with a Level Set description, we apply here a Constructive Solid Geometry (CSG) approach with the Level Set geometrical representation. Hence, this extension allows to optimize any boundary of the structure that is defined with a coumpound Level Set. Design variables are the parameters of basic geometric primitives which are described with a Level Set representation and/or the control points of the NURBS curves that act as the definition of an advanced Level Set primitive. The number of design variables of this formulation remains small whereas global (i.e. compliance or eigenfrequency) and local constraints (i.e. stresses) can be considered. Our results illustrate that fixed grid optimization with X-FEM coupled to a Level Set geometrical description is a promising technique to achieve structural shape optimization. [less ▲]

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See detailMicrostructure design with generalized shape optimization based on level set geometrical description and XFEM
Qiu, Kepeng; Duysinx, Pierre ULg; Zhang, Wei-Hong et al

(2009, May)

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See detailTopology and generalized shape optimisation: why stress constraints are so important?
Duysinx, Pierre ULg; Van Miegroet, Laurent ULg; Lemaire, Etienne ULg et al

in International Journal of Simulation & Multidisciplinary Design Optimization (2008), 2(4), 253-258

The paper continues along the work initiated by the authors in taking into account stress constraints in topology optimization of continuum structures. Revisiting some of their last developments in this ... [more ▼]

The paper continues along the work initiated by the authors in taking into account stress constraints in topology optimization of continuum structures. Revisiting some of their last developments in this field, the authors point 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 in order to get the most appropriate structural lay-out. Numerical applications that can be solved using these new developments make possible to exhibit interesting results related to the specific nature of strength based structural lay out for maximum strength compared to maximum stiffness. This particular character of stress design is clearly demonstrated in two kinds of situations: once several load cases are considered and when unequal stress limits in tension and compression are involved. [less ▲]

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See detailStochastic Modal Analysis of Structures with Random Shape Using X-FEM
Lepage, Séverine; Van Miegroet, Laurent ULg; Duysinx, Pierre ULg

Conference (2008, July)

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See detailStress constrained topology and shape optimization : Specific character and large scale optimization algorithms
Duysinx, Pierre ULg; Fleury, Claude; Van Miegroet, Laurent ULg et al

in Proceedings of the 8th World Congress on Computational Mechanics (WCCM) (2008)

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See detailStress concentration minimization of 2D filets using X-FEM and level set description
Van Miegroet, Laurent ULg; Duysinx, Pierre ULg

in Structural and Multidisciplinary Optimization (2007), 33(4-5), 425-438

This paper presents and applies a novel shape optimization approach based on the level set description of the geometry and the extended finite element method (X-FEM). The method benefits from the fixed ... [more ▼]

This paper presents and applies a novel shape optimization approach based on the level set description of the geometry and the 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 that are described with a level set representation. The number of design variables of this formulation remains small, whereas global (i.e. compliance) and local constraints (i.e. stresses) can be considered. To illustrate the capability of the method to handle stress constraints, numerical applications revisit the minimization of stress concentration in a 2D filet in tension, which has been previously studied in Pedersen (2003). Our results illustrate the great interest of using X-FEM and level set description together. A special attention is also paid to stress computation and accuracy with the X-FEM. [less ▲]

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See detailGeneralized Shape And Topology Optimization: Recent Developments And Application Perspectives To Automotive Structures
Duysinx, Pierre ULg; Van Miegroet, Laurent ULg; Remouchamps, Alain et al

in New Advances in Body Engineering - Lightweight design, passive safety, pedestrian protection, and numerical optimization (2006, December)

More than 15 years after the seminal work by Bendsøe and Kikuchi, topology optimization of structures has taken advantage of my research efforts and has now become a commercial available tool (e.g ... [more ▼]

More than 15 years after the seminal work by Bendsøe and Kikuchi, topology optimization of structures has taken advantage of my research efforts and has now become a commercial available tool (e.g. OptiStruct by Altair, Topol by Samtech, etc.). These software tools are daily used in automotive industry and provide engineers with a rational tool for preliminary design of efficient structural components. This paper presents the status of available topology optimization tools and introduces the recent developments that extend their capabilities in order to handle stress constraints, manufacturing constraints, etc. The communication also presents a novel approach of generalized shape optimization that has been introduced to circumvent the difficulties of parametric shape optimization and to complement topology optimization. The approach is based on the eXtended Finite Element Method (XFEM) and the Level Set Description of the geometry. The Level Set description introduces smooth curve descriptions and allows modifying the connectivity of the wholes. The XFEM works with a fixed mesh as in topology optimization, which makes the method very convenient for engineers. Thus the novel approach is likely to bring the next future evolution of structural optimization. Impressive capabilities of this new generation approach will be demonstrated. Application examples from automotive and aerospace engineering will illustrate the different possibilities offered by two approaches. [less ▲]

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