Parametric Study on the Element Size Effect for Optimal Topologies

Topology optimization is complex engineering design tool. It needs intensive mathematical, mechanical and computing tools to perform the required design. During its hundred years of history it has become clear that the non-unique solution property of the method is affected by the material parameters (Poisson ratio) and the ways of the discretization. The aim of the paper is to investigate the influence of parameter changes to optimal design property in tasks with great number of degrees of freedom. The parametric study includes influence of material parameter (Poisson ratio) as well as the size of the ground elements which are commonly applied during the discretization. Increasing the size of the ground elements while the total number of the finite elements is constant, the computational time is significantly reduced. Therefore the study on changing accuracy versus ground element resolution may be important factor in choosing ground element size. In addition to it the effective properties of arrangements of the strong and weak materials (black and white elements) in a checkerboard fashion are also investigated. The Michell-type problem is investigated by the minimization of the weight of the structure subjected to a compliance constraint.

[1]  János Lógó,et al.  New Type of Optimal Topologies by Iterative Method , 2005 .

[2]  Giovanni Monegato,et al.  Quadrature Rules for Regions Having Regular Hexagonal Symmetry , 1977 .

[3]  István Hegedűs,et al.  The sensitivity of the flutter derivatives and the flutter speed to the eccentricity of the cross section , 2012 .

[4]  C. S. Jog,et al.  Stability of finite element models for distributed-parameter optimization and topology design , 1996 .

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

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

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

[8]  O. Sigmund,et al.  Checkerboard patterns in layout optimization , 1995 .

[9]  M. Beckers,et al.  Topology optimization using a dual method with discrete variables , 1999 .

[10]  George I. N. Rozvany,et al.  A critical review of established methods of structural topology optimization , 2009 .

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

[13]  George I. N. Rozvany,et al.  Quality Control in Topology Optimization Using Analytically Derived Benchmarks , 2006 .

[14]  R. Kohn,et al.  Topology optimization and optimal shape design using homogenization , 1993 .

[15]  Glaucio H. Paulino,et al.  Honeycomb Wachspress finite elements for structural topology optimization , 2009 .

[16]  G. A. Hegemier,et al.  On Michell trusses , 1969 .

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

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