Analytical sensitivity analysis for decoupling multi-scale topology optimization of composites

The present study proposes an analytical sensitivity analysis for a so-called multi-scale topology optimization introduced to minimization of compliance of three dimensional structural problems. The multiscale topology optimization is a strategy to optimize topology of microstructures applying a decoupling multi-scale analysis based on a homogenization method. The stiffness of the macrostructure is maximized with a prescribed material volume of constituents under linear elastic regime. A gradient–based optimization strategy is applied and an analytical sensitivity approach based on the adjoint method is proposed to reduce the computational costs. It was verified from a series of numerical examples that the proposed method has great possibility for microscopic advanced material designs.

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

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

[3]  K. Terada,et al.  A method of predicting macroscopic yield strength of polycrystalline metals subjected to plastic forming by micro–macro de-coupling scheme , 2010 .

[4]  Fpt Frank Baaijens,et al.  An approach to micro-macro modeling of heterogeneous materials , 2001 .

[5]  W. Brekelmans,et al.  Prediction of the mechanical behavior of nonlinear heterogeneous systems by multi-level finite element modeling , 1998 .

[6]  Surya N. Patnaik,et al.  Merits and limitations of optimality criteria method for structural optimization , 1995 .

[7]  Kenjiro Terada,et al.  A method of two-scale analysis with micro-macro decoupling scheme: application to hyperelastic composite materials , 2013 .

[8]  Ekkehard Ramm,et al.  Multiphase material optimization for fiber reinforced composites with strain softening , 2009 .

[9]  J. Chaboche,et al.  FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials , 2000 .

[10]  M. Denda,et al.  A dual homogenization and finite-element study on the in-plane local and global behavior of a nonlinear coated fiber composite , 2000 .

[11]  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.

[12]  O. Sigmund.  Materials with prescribed constitutive parameters: An inverse homogenization problem , 1994 .

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

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

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

[16]  J. C. Simo,et al.  Consistent tangent operators for rate-independent elastoplasticity☆ , 1985 .

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

[18]  T. Hisada,et al.  Study of efficient homogenization algorithms for nonlinear problems , 2010 .

[19]  Daniel A. Tortorelli,et al.  Nonlinear structural design using multiscale topology optimization. Part I: Static formulation , 2013 .

[20]  Z. Więckowski.  Dual finite element methods in homogenization for elastic–plastic fibrous composite material , 2000 .

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

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