Design of multiphysics actuators using topology optimization - Part I: One-material structures

This is the second part of a two-paper description of the topology optimization method applied to the design of multiphysics actuators and electrothermomechanical systems in particular. The first paper is focussed on one-material structures, the second on two-material structures. The extensions of the topology optimization method in this part include design descriptions for two-material structures, constitutive modelling of elements with mixtures of two materials, formulation of optimization problems with multiple constraints and multiple materials and a mesh-independency scheme for two-material structures. The application in mind is the design of thermally and electrothermally driven micro actuators for use in MicroElectroMechanical Systems (MEMS). MEMS are microscopic mechanical systems coupled with electrical circuits. MEMS are fabricated using techniques known from the semi-conductor industry. Several of the examples from Part I are repeated, allowing for the introduction of a second material in the design domain. The second material can differ in mechanical properties such as Young's modulus or electrical and thermal conductivity. In some cases there are significant gains in introducing a second material. However, the gains depend on boundary conditions and relations between the material properties and are in many cases insignificant.

[1]  L. Walpole.  On bounds for the overall elastic moduli of inhomogeneous systems—I , 1966 .

[2]  Ole Sigmund,et al.  Compliant thermal microactuators , 1999 .

[3]  N. Kikuchi,et al.  Optimal design of piezoelectric microstructures , 1997 .

[4]  G. K. Ananthasuresh,et al.  Topology Synthesis of Compliant Mechanisms for Nonlinear Force-Deflection and Curved Path Specifications , 2001 .

[5]  N. L. Pedersen.  Maximization of eigenvalues using topology optimization , 2000 .

[6]  M. Bendsøe.  Optimal shape design as a material distribution problem , 1989 .

[7]  Ole Sigmund.  Systematic design of micro actuators using topology optimization , 1998 .

[8]  J. Thomsen,et al.  Topology optimization of structures composed of one or two materials , 1992 .

[9]  Matthias Müllenborn,et al.  Laser direct etching of silicon on oxide for rapid prototyping , 1996 .

[10]  S. Shtrikman,et al.  A variational approach to the theory of the elastic behaviour of multiphase materials , 1963 .

[11]  T. E. Bruns,et al.  Topology optimization of non-linear elastic structures and compliant mechanisms , 2001 .

[12]  S. Timoshenko.  Theory of Elastic Stability , 1936 .

[13]  T. Buhl.  Simultaneous topology optimization of structure and supports , 2002 .

[14]  Ole Sigmund,et al.  On the design of 1–3 piezocomposites using topology optimization , 1998 .

[15]  C. S. Jog,et al.  Distributed-parameter optimization and topology design for non-linear thermoelasticity , 1996 .

[16]  H. Rodrigues,et al.  A material based model for topology optimization of thermoelastic structures , 1995 .

[17]  Ole Sigmund,et al.  Topology synthesis of large‐displacement compliant mechanisms , 2001 .

[18]  J. Z. Zhu,et al.  The finite element method , 1977 .

[19]  Claude Fleury,et al.  CONLIN: An efficient dual optimizer based on convex approximation concepts , 1989 .

[20]  O. Sigmund,et al.  Stiffness design of geometrically nonlinear structures using topology optimization , 2000 .

[21]  M. Bendsøe,et al.  Material interpolation schemes in topology optimization , 1999 .

[22]  W. Riethmuller,et al.  Thermally excited silicon microactuators , 1988 .

[23]  C. Swan,et al.  Voigt–Reuss topology optimization for structures with linear elastic material behaviours , 1997 .

[24]  G. K. Ananthasuresh,et al.  Micromechanical Devices With Embedded Electro-Thermal-Compliant Actuation , 1999, Micro-Electro-Mechanical Systems (MEMS).

[25]  M. Zhou,et al.  The COC algorithm, Part II: Topological, geometrical and generalized shape optimization , 1991 .

[26]  Ole Sigmund,et al.  On the Design of Compliant Mechanisms Using Topology Optimization , 1997 .

[27]  J. Petersson,et al.  Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima , 1998 .

[28]  Niels Leergaard Pedersen,et al.  DESIGN OF CANTILEVER PROBES FOR ATOMIC FORCE MICROSCOPY (AFM) , 2000 .

[29]  Duong Hien Tran,et al.  Parameter Sensitivity in Nonlinear Mechanics: Theory and Finite Element Computations , 1997 .

[30]  Martin P. Bendsøe,et al.  Optimization of Structural Topology, Shape, And Material , 1995 .

[31]  K. Svanberg.  The method of moving asymptotes—a new method for structural optimization , 1987 .

[32]  Zvi Hashin,et al.  Effective thermal expansion coefficients and specific heats of composite materials , 1970 .

[33]  Victor M. Bright,et al.  Thermal microactuators for surface-micromachining processes , 1995, MOEMS-MEMS.

[34]  Jan H. J. Fluitman,et al.  Performance of thermally excited resonators , 1990 .

[35]  O. Sigmund,et al.  Multiphase composites with extremal bulk modulus , 2000 .

[36]  S. Torquato,et al.  Design of materials with extreme thermal expansion using a three-phase topology optimization method , 1997 .

[37]  S. Torquato,et al.  Composites with extremal thermal expansion coefficients , 1996 .

[38]  K.E. Petersen,et al.  Silicon as a mechanical material , 1982, Proceedings of the IEEE.

[39]  Ole Sigmund,et al.  Some Inverse Problems in Topology Design of Materials and Mechanisms , 1996 .

[40]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

[41]  Noboru Kikuchi,et al.  Optimal design of periodic piezocomposites , 1998 .

[42]  O. Sigmund,et al.  Design and fabrication of compliant micromechanisms and structures with negative Poisson's ratio , 1996, Proceedings of Ninth International Workshop on Micro Electromechanical Systems.

[43]  Richard Schapery.  Thermal Expansion Coefficients of Composite Materials Based on Energy Principles , 1968 .

[44]  B. Bourdin.  Filters in topology optimization , 2001 .

[45]  C. Swan,et al.  VOIGT-REUSS TOPOLOGY OPTIMIZATION FOR STRUCTURES WITH NONLINEAR MATERIAL BEHAVIORS , 1997 .

[46]  O. Sigmund,et al.  Compliant electro-thermal microactuators , 1999, Technical Digest. IEEE International MEMS 99 Conference. Twelfth IEEE International Conference on Micro Electro Mechanical Systems (Cat. No.99CH36291).

[47]  D. Tortorelli,et al.  Tangent operators and design sensitivity formulations for transient non‐linear coupled problems with applications to elastoplasticity , 1994 .

[48]  Ole Sigmund,et al.  On the Optimality of Bone Microstructure , 1999 .

[49]  H. P. Mlejnek,et al.  Some aspects of the genesis of structures , 1992 .

[50]  Cv Clemens Verhoosel,et al.  Non-Linear Finite Element Analysis of Solids and Structures , 1991 .