An improved soft-kill BESO algorithm for optimal distribution of single or multiple material phases

Finding the optimum distribution of material phases in a multi-material structure is a frequent and important problem in structural engineering which involves topology optimization. The Bi-directional Evolutionary Structural Optimization (BESO) method is now a well-known topology optimization method. In this paper an improved soft-kill BESO algorithm is introduced which can handle both single and multiple material distribution problems. A new filtering scheme and a gradual procedure inspired by the continuation approach are used in this algorithm. Capabilities of the proposed method are demonstrated using different examples. It is shown that the proposed method can result in considerable improvements compared to the normal BESO algorithm particularly when solving problems involving very soft material or void phase.

[1]  S. A. Gregory Design of Materials , 1966 .

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

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

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

[5]  Y. Xie,et al.  A simple evolutionary procedure for structural optimization , 1993 .

[6]  Grant P. Steven,et al.  Shape Optimisation of Metallic Inserts in Composite Bolted Joints , 1995 .

[7]  Ole Sigmund,et al.  Design of materials with extreme thermal expansion using a three-phase topology optimization method , 1997, Smart Structures.

[8]  Yi Min Xie,et al.  Evolutionary structural optimisation (ESO) using a bidirectional algorithm , 1998 .

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

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

[11]  Sei-ichiro Kamata,et al.  A New Algorithm for , 1999 .

[12]  Y. Xie,et al.  Bidirectional Evolutionary Method for Stiffness Optimization , 1999 .

[13]  K. Svanberg,et al.  An alternative interpolation scheme for minimum compliance topology optimization , 2001 .

[14]  George I. N. Rozvany,et al.  On the validity of ESO type methods in topology optimization , 2001 .

[15]  Xiaoming Wang,et al.  Color level sets: a multi-phase method for structural topology optimization with multiple materials , 2004 .

[16]  Erik Lund,et al.  Discrete material optimization of general composite shell structures , 2005 .

[17]  Y. Xie,et al.  A new algorithm for bi-directional evolutionary structural optimization , 2006 .

[18]  Erik Lund,et al.  Eigenfrequency and Buckling Optimization of Laminated Composite Shell Structures Using Discrete Material Optimization , 2006 .

[19]  Shiwei Zhou,et al.  Multimaterial structural topology optimization with a generalized Cahn–Hilliard model of multiphase transition , 2006 .

[20]  Y. Xie,et al.  Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method , 2007 .

[21]  Feng Jin,et al.  A fixed‐grid bidirectional evolutionary structural optimization method and its applications in tunnelling engineering , 2008 .

[22]  Y. Xie,et al.  Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials , 2009 .

[23]  Kazem Ghabraie,et al.  Exploring topology and shape optimisation techniques in underground excavations , 2009 .

[24]  Yi Min Xie,et al.  Using BESO method to optimize the shape and reinforcement of underground openings , 2010 .

[25]  Gang Ren,et al.  Shape and Reinforcement Optimization of Underground Tunnels , 2010 .

[26]  Michaël Bruyneel,et al.  SFP—a new parameterization based on shape functions for optimal material selection: application to conventional composite plies , 2011 .

[27]  Tong Gao,et al.  A mass constraint formulation for structural topology optimization with multiphase materials , 2011 .

[28]  José Pedro Albergaria Amaral Blasques,et al.  Multi-material topology optimization of laminated composite beam cross sections , 2012 .

[29]  Pierre Duysinx,et al.  Simultaneous design of structural layout and discrete fiber orientation using bi-value coding parameterization and volume constraint , 2013 .

[30]  Rouhollah Tavakoli,et al.  Alternating active-phase algorithm for multimaterial topology optimization problems: a 115-line MATLAB implementation , 2013, Structural and Multidisciplinary Optimization.

[31]  Kazem Ghabraie,et al.  Applying bi-directional evolutionary structural optimisation method for tunnel reinforcement design considering nonlinear material behaviour , 2014 .

[32]  Rouhollah Tavakoli,et al.  Multimaterial topology optimization by volume constrained Allen–Cahn system and regularized projected steepest descent method , 2014 .

[33]  Ramana V. Grandhi,et al.  A survey of structural and multidisciplinary continuum topology optimization: post 2000 , 2014 .

[34]  Kazem Ghabraie,et al.  The ESO method revisited , 2015 .

[35]  Osvaldo M. Querin,et al.  Layout optimization of multi-material continuum structures with the isolines topology design method , 2015 .

[36]  Alok Sutradhar,et al.  A multi-resolution method for 3D multi-material topology optimization , 2015 .

[37]  Z. Kang,et al.  A multi-material level set-based topology and shape optimization method , 2015 .