Shape and topology optimization for closed liquid cell materials using extended multiscale finite element method

A new multiscale shape and topology optimization method is presented to design closed liquid cell materials based on the extended multiscale finite element method, which directly captures the small scale features to the large scale computation. The multiscale optimization method firstly focuses on seeking the optimum geometrical parameters and volume expansion of the fluid in the closed liquid cells in the microscale level in terms of maximizing the macroscale mechanical response of the structure. Furthermore, a new hierarchical multiscale optimization method is developed to optimize the macroscale distributions of closed liquid cells and the microscale shape of the fluid inclusion in the cells. In the macroscale level of the multiscale optimization method, the macroscale design domain is discretized by the multiscale coarse elements, while the shape of the fluid inclusions is set to be the design parameters in the microscale level. This method is firstly utilized to minimize the system compliance of the closed liquid cell structure. Moreover, due to the fact that non-uniform volume expansions of the fluid in cells can induce the elastic action, the multiscale optimization method is further extended to design biomimetic compliant actuators of the closed liquid cell materials. The multiscale optimization methods developed are implemented in the FE-package SiPESC, and the numerical examples are carried out to validate the accuracy of the methods proposed.

[1]  J. Lv,et al.  A New Multiscale Computational Method for Mechanical Analysis of Closed Liquid Cell Materials , 2010 .

[2]  Keith W. Waldron,et al.  Modelling of carrot tissue as a fluid-filled foam , 2003 .

[3]  Ole Sigmund,et al.  Design of multiphysics actuators using topology optimization - Part I: One-material structures , 2001 .

[4]  Robert L. Mullen,et al.  Analysis of closed cell metal composites , 1996 .

[5]  Michael R. Greenberg,et al.  Chapter 1 – Theory, Methods, and Applications , 1978 .

[6]  M. Bendsøe,et al.  Topology Optimization: "Theory, Methods, And Applications" , 2011 .

[7]  Anders Clausen,et al.  Efficient topology optimization in MATLAB using 88 lines of code , 2011 .

[8]  C. H. Hertz,et al.  On the Relation between Turgor Pressure and Tissue Rigidity. II , 1958 .

[9]  Anton P. J. Middelberg,et al.  On uniquely determining cell–wall material properties with the compression experiment , 1998 .

[10]  E. Sanchez-Palencia,et al.  Homogenization Techniques for Composite Media , 1987 .

[11]  Gengdong Cheng,et al.  Optimum structure with homogeneous optimum truss-like material , 2008 .

[12]  Thomas Y. Hou,et al.  Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients , 1999, Math. Comput..

[13]  Zhang Hong-wu.  Design and implementation of general integrated optimization design software SiPESC.OPT , 2011 .

[14]  Shutian Liu,et al.  Topology optimization of couple-stress material structures , 2009 .

[15]  Ole Sigmund,et al.  Saturated poroelastic actuators generated by topology optimization , 2011 .

[16]  Kozo Osakada,et al.  Finite element modelling of forming process of solid metal with liquid phase , 1991 .

[17]  Antonio Delgado,et al.  Mechanical stresses in cellular structures under high hydrostatic pressure , 2006 .

[18]  James K. Guest,et al.  Optimizing multifunctional materials: Design of microstructures for maximized stiffness and fluid permeability , 2006 .

[19]  Ole Sigmund,et al.  A 99 line topology optimization code written in Matlab , 2001 .

[20]  Hong-wu Zhang,et al.  Extended multiscale finite element method for mechanical analysis of heterogeneous materials , 2010 .

[21]  Lisa Mauck Weiland,et al.  High Energy Density Nastic Materials: Parameters for Tailoring Active Response , 2009 .

[22]  Bernard Rolfe,et al.  The configuration evolution and macroscopic elasticity of fluid-filled closed cell composites : micromechanics and multiscale homogenization modelling , 2011 .

[23]  Donald J. Leo,et al.  Chemo-mechanical Model for Actuation Based on Biological Membranes* , 2006 .

[24]  James K. Guest,et al.  Design of maximum permeability material structures , 2007 .

[25]  Hongwu Zhang,et al.  Two-Scale Model for Mechanical Analysis of Nastic Materials and Structures , 2011 .

[26]  Casper Schousboe Andreasen,et al.  Multiscale topology optimization of solid and fluid structures , 2011 .

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

[28]  Antonio Delgado,et al.  Numerical simulation of the mechanics of a yeast cell under high hydrostatic pressure. , 2004, Journal of biomechanics.

[29]  G. Cheng,et al.  A Uniform Optimum Material Based Model for Concurrent Optimization of Thermoelastic Structures and Materials , 2008 .

[30]  Peter Hartley,et al.  Modelling the mechanical properties of yeast cells , 2009 .

[31]  Zhen Luo,et al.  Shape and topology optimization for electrothermomechanical microactuators using level set methods , 2009, J. Comput. Phys..

[32]  Helder C. Rodrigues,et al.  A hierarchical model for concurrent material and topology optimisation of three-dimensional structures , 2008 .

[33]  Peng Haijun.  Advancement of design and implementation of SiPESC for development of integrated CAE software systems , 2011 .

[34]  C. H. Hertz,et al.  On the Relation between Turgor Pressure and Tissue Rigidity. II. Theoretical Calculations on Model Systems , 1958 .

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

[36]  Donald J. Leo,et al.  CONCEPTS FOR POWER AND ENERGY ANALYSIS IN NASTIC STRUCTURES , 2005 .

[37]  N. Kikuchi,et al.  A class of general algorithms for multi-scale analyses of heterogeneous media , 2001 .

[38]  Thomas Y. Hou,et al.  A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media , 1997 .

[39]  Gang Liu,et al.  Design optimization of stiffened storage tank for spacecraft , 2008 .

[40]  Eduard Rohan,et al.  Modeling Large-deformation-induced Microflow in Soft Biological Tissues , 2006 .

[41]  H. Rodrigues,et al.  Hierarchical optimization of material and structure , 2002 .

[42]  Bernard Budiansky,et al.  Seismic velocities in dry and saturated cracked solids , 1974 .

[43]  Gengdong Cheng,et al.  Recent development in structural design and optimization , 2010 .

[44]  Jun Yan,et al.  Optimum structure with homogeneous optimum cellular material for maximum fundamental frequency , 2009 .