Topology design of thermomechanical actuators

The paper deals with topology design of thermomechanical actuators. The goal of shape optimization is to maximize the output displacement in a given direction on the boundary of the elastic body, which is submitted to a thermal excitation that induces a dilatation/contraction of the thermomechanical device. The optimal structure is identified by an elastic material distribution, while a very compliant (weak) material is used to mimic voids. The mathematical model of an actuator takes the form of a semi-coupled system of partial differential equations. The boundary value problem includes two components, the Navier equation for linear elasticity coupled with the Poisson equation for steady-state heat conduction. The mechanical coupling is the thermal stress induced by the temperature field. Given the integral shape functional, we evaluate its topological derivative with respect to the nucleation of a small circular inclusion with the thermomechanical properties governed by two contrast parameters. The obtained topological derivative is employed to generate a steepest descent direction within the level set numerical procedure of topology optimization in a fixed geometrical domain. Finally, several finite element-based examples for the topology design of thermomechanical actuators are presented.

[1]  J. D. Eshelby.  The determination of the elastic field of an ellipsoidal inclusion, and related problems , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[2]  C. G. Lopes,et al.  Topology design of compliant mechanisms with stress constraints based on the topological derivative concept , 2016 .

[3]  Sebastián M. Giusti,et al.  TOPOLOGY DESIGN OF PLATES CONSIDERING DIFFERENT VOLUME CONTROL METHODS , 2014 .

[4]  Noboru Kikuchi,et al.  Topology optimization of thermally actuated compliant mechanisms considering time-transient effect , 2004 .

[5]  Antonio André Novotny,et al.  Topological optimization of structures subject to Von Mises stress constraints , 2010 .

[6]  Michael Hintermüller,et al.  Second-order topological expansion for electrical impedance tomography , 2011, Advances in Computational Mathematics.

[7]  Leah Blau,et al.  Polarization And Moment Tensors With Applications To Inverse Problems And Effective Medium Theory , 2016 .

[8]  Hae Chang Gea,et al.  A strain based topology optimization method for compliant mechanism design , 2014 .

[9]  Heiko Andrä,et al.  A new algorithm for topology optimization using a level-set method , 2006, J. Comput. Phys..

[10]  A. Novotny,et al.  Topological sensitivity analysis for elliptic differential operators of order 2m , 2014 .

[11]  J. Zolésio,et al.  Introduction to shape optimization : shape sensitivity analysis , 1992 .

[12]  Grégoire Allaire,et al.  Damage and fracture evolution in brittle materials by shape optimization methods , 2011, J. Comput. Phys..

[13]  Jan Sokolowski,et al.  On the Topological Derivative in Shape Optimization , 1999 .

[14]  Antonio André Novotny,et al.  Crack nucleation sensitivity analysis , 2010 .

[15]  Larry L. Howell,et al.  Handbook of Compliant Mechanisms: Howell/Handbook , 2013 .

[16]  Antonio André Novotny,et al.  Topological Derivatives in Shape Optimization , 2012 .

[17]  Noboru Kikuchi,et al.  Design optimization method for compliant mechanisms and material microstructure , 1998 .

[18]  A. Novotny,et al.  Strain energy change to the insertion of inclusions associated to a thermo-mechanical semi-coupled system , 2013 .

[19]  Long Chen.  FINITE ELEMENT METHOD , 2013 .

[20]  Shinji Nishiwaki,et al.  Design of compliant mechanisms considering thermal effect compensation and topology optimization , 2010 .

[21]  E. A. de Souza Neto,et al.  Topological derivative for multi‐scale linear elasticity models applied to the synthesis of microstructures , 2010 .

[22]  Michael Hintermüller,et al.  Multiphase Image Segmentation and Modulation Recovery Based on Shape and Topological Sensitivity , 2009, Journal of Mathematical Imaging and Vision.

[23]  A. Zochowski.  Optimal Perforation Design in 2-Dimensional Elasticity , 1988 .

[24]  Zenon Mróz,et al.  Shape and topology sensitivity analysis and its application to structural design , 2012 .

[25]  Toshio Mura,et al.  The Elastic Field Outside an Ellipsoidal Inclusion , 1977 .

[26]  Larry L. Howell,et al.  Handbook of compliant mechanisms , 2013 .

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

[28]  J. D. Eshelby,et al.  The elastic field outside an ellipsoidal inclusion , 1959, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.