Eigenproblem folmulation for electromechanical microsystem pull-in voltage optimization

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 ▲]

Topology optimization of compliant mechanisms: Application to vehicle suspensions.

Conference (2011, November 14)

An efficient method to design a compliant vehicle suspension with only topology optimization.

Multiphysic topology optimization of electromechanical micro-actuators considering pull-in effect

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

APPLICATION DE L’OPTIMISATION DE FORME ET DE TOPOLOGIE A LA CONCEPTION INNOVANTE D’EJECTEURS POUR UN CONCASSEUR MAG’IMPACT

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.

Microstructure design with generalized shape optimization based on level set geometrical description and XFEM

(2009, May)

Multiphysic topology optimization of electromechanical microdevices considering pull-in voltage using an electrostatic force filter

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

Electrostatic actuation is often used in microsystems as it is relatively easy to implement and provides a short response time. However, because of the non-linearity of electrostatic forces, these devices ... [more ▼]

Electrostatic actuation is often used in microsystems as it is relatively easy to implement and provides a short response time. However, because of the non-linearity of electrostatic forces, these devices may suffer from an unstable behavior called pull-in effect. Previous work of the authors intended to delay pull-in effect by maximizing pull-in voltage studying a simplified problem where the optimization domain was purely mechanical. The present paper generalizes the approach by considering a multiphysic optimization domain. However, the generalization of the optimization problem is not straightforward as local pull-in modes appear after a few optimization iterations. Therefore, the paper investigates several solutions to prevent the appearance of local pull-in modes. [less ▲]

Design of mechanism components using topology optimization and flexible multibody simulation

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

This work addresses the topology optimization of structural components embedded in multibody systems with large amplitude motions. For example, in deployable space structures, piston engines, automotive ... [more ▼]

This work addresses the topology optimization of structural components embedded in multibody systems with large amplitude motions. For example, in deployable space structures, piston engines, automotive suspensions, robots and high-speed machine-tools, the articulated components undergo large displacements and elastic deformations, and are subject to transient loads and nonlinear dynamic effects. The performance of such systems often depends on the mechanical design in a non-intuitive way. <br />Several researchers have addressed the optimization of the geometric parameters of mechanisms and also of the connectivity of mechanisms made of rigid members. In contrast, topology optimization techniques are often based on continuum mechanics assumptions, and usually aim at optimizing the layout of an isolated structural component under the assumption of small displacements and small deflections. In order to apply topology optimization to mechanism components, one may consider that each structural component is isolated from the rest of the mechanism and use simplified quasi-static load cases to mimic the complex loadings in service. However, two main drawbacks are associated with this approach. Firstly, defining the equivalent load cases is a rather difficult task, which is often based on trials and errors and which requires some expertise. Secondly, topology optimization is often sensitive to loading conditions, especially for multiple load cases and stress constraints, so that the optimal character of the resulting design becomes questionable if the loading is approximative. For these reasons, in order to obtain better optimal layouts, this paper proposes an optimization procedure based on dynamic simulations of the full flexible multibody system. <br />For this purpose, the nonlinear finite element approach is selected for the modelling and the simulation of the flexible multibody system. The present work is thus similar to the usual approach used in topology optimization in which the continuum domain is discretized into finite elements. The nonlinear finite element formalism accounts for both large rigid-body motions and elastic deflections of the structural components. The design variables are classically density-like parameters associated to a power law interpolation of effective material properties for intermediate densities, also known as Simply Isotropic Material with Penalization (SIMP). <br />The nonlinear equations of motion are solved using a generalized-alpha time integration scheme, and the sensitivity analysis of mechanical responses is based on a direct differentiation method. The efficient solution of the optimization problem relies on the sequential convex programming concept at the core of the CONLIN software. <br />In the present study, the method is applied to various types of mechanical systems. Firstly, planar mechanisms with truss structural components are considered. Each truss is represented by a structural universe of beams with a topology design variable attached to each one. Secondly, the discussion is extended to similar mechanisms with 3D motions. Finally, the topology optimization of spatial bodies represented by 3D finite element meshes is considered. [less ▲]

Stress constrained topology and shape optimization : Specific character and large scale optimization algorithms

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

Microbeam pull-in voltage topology optimization including material deposition constraint

in Computer Methods in Applied Mechanics & Engineering (2008), 197

Because of the strong coupling between mechanical and electrical phenomena existing in electromechanical microdevices, some of them experience, above a given driving voltage, an unstable behavior called ... [more ▼]

Because of the strong coupling between mechanical and electrical phenomena existing in electromechanical microdevices, some of them experience, above a given driving voltage, an unstable behavior called pull-in effect. The present paper investigates the application of topology optimization to electromechanical microdevices for the purpose of delaying this unstable behavior by maximizing their pull-in voltage. Within the framework of this preliminary study, the pull-in voltage maximization procedure is developed on the basis of electromechanical microbeams reinforcement topology design problem. The proposed sensitivity analysis requires only the knowledge of the microdevice pull-in state and of the first eigenmode of the tangent stiffness matrix. As the pull-in point research is a highly non-linear problem, the analysis is based on a monolithic finite element formulation combined with a normal flow algorithm (homotopy method). An application of the developed method is proposed and the result is compared to the one obtained using a linear compliance optimization. Moreover, as the results provided by the developed method do not comply with manufacturing constraints, a deposition process constraint is added to the optimization problem and its effect on the final design is also tested. [less ▲]

Topology Optimization of Structural Components Included in Flexible Multibody Systems

in Proceedings of the 7th World Congress on Structural and Multidisciplinary Optimization (2007, May)

This work addresses the topology optimization of structural components embedded in multibody systems with large amplitude motions. Generally, topology optimization techniques consider that the structural ... [more ▼]

This work addresses the topology optimization of structural components embedded in multibody systems with large amplitude motions. Generally, topology optimization techniques consider that the structural component is isolated from the rest of the mechanism and use simplified quasi-sta tic load cases to mimic the complex loadings in service. In contrast, this paper proposes an optimization procedure based on the dynamic simulation of the full multibody system with large amplitude motions and elastic deflections. We show that the simulation model, which involves a nonlinear finite element formulation, a time integration scheme and a sensitivity analysis, can be efficiently exploited in an optimization loop. The method is applied to truss structural components. Each truss is represented by a structural universe of beams with a topology design variable attached to each one. A SIMP model (or a variant of the power law) is used to penalize intermediate densities. The optimization formulation is stated as the minimization of the mean compliance over a time period or as the minimization of the mean tip deflection during a given trajectory, subject to a volume constraint. In order to illustrate the benefits of the integrated design approach, the case of a two degrees-of-freedom robot arm is developed. [less ▲]