Sufficiency of a finite exponent in SIMP (power law) methods

By A. Rietz. 2001

257 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/d4b978f7c601b2aa3020c803b230fd17b9795da9

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In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method (2007, methodology): “Various techniques have been developed for topology optimization, for example, the homogenization method [1,2], solid isotropic material with penalization (SIMP) method [3–6] and the evolutionary structural optimization (ESO) method [7,8].”
A critical review of established methods of structural topology optimization (2009, methodology): “As was shown by Rietz (2001, consistently mis-spelled as “ Reitz ” by the authors), grey elements can be eliminated (in practice, nearly eliminated).”
Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials (2009, methodology): “In SIMP method one defines at each element a density of material that varies continuously between 0 and 1. The elastic properties for intermediate densities are expressed in terms of the density, for example, using a power-law interpolation which leads to nearly 0/1 designs throughout optimization [”
On some fundamental properties of structural topology optimization problems (2010, background): “see e.g. Stolpe and Svanberg (2001 )a nd Rietz (2001) .”
A reevaluation of the SIMP method with filtering and an alternative formulation for solid–void topology optimization (2005, methodology): “Rietz (2001) defines an optimization problem that mirrors the SINH method as a substitute problem for the topology optimization problem with the SIMP method through a change of variables.”
A survey of structural and multidisciplinary continuum topology optimization: post 2000 (2014, methodology): “Some theoretical convergence properties of the SIMP method have been discussed by Rietz (2001), Martinez (2005), and Stolpe and Svanberg (2001b).”
Connections between topological sensitivity analysis and material interpolation schemes in topology optimization (2011, background): “Remark 3.7 Of course, Theorem 3.4 does not imply that Problems (1)–(2 )a nd (7)–(8) are equivalent since there is no guarantee that the solutions (global or local) to (7)–(8) belong to E. We mention in this respect the paper Rietz (2001) , where it is proven that, for θ(γ ) = γ p ,i n the self-”
Evolutionary level set method for structural topology optimization (2011, background): “It consists with the result in paper [33].”
A note on the theoretical convergence properties of the SIMP method (2005, methodology): “Under these assumptions, Rietz proved that, for some p > 0, the solution of (2) coincides with the solution of (1).”