On the trajectories of penalization methods for topology optimization

By Mathias Stolpe, Krister Svanberg. 2001

168 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Control and Systems Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/dc794b0f2d667d1a680ff5738235ea148773fd5e

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In Civil and Structural Engineering

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Citations in the corpus

A note on the theoretical convergence properties of the SIMP method (2005, methodology): “See [5] for an analysis of the limitations of continuation methods for obtaining global solutions in SIMP subproblems.”
A survey of structural and multidisciplinary continuum topology optimization: post 2000 (2014, methodology): “A modified SIMP formulation is suggested to overcome these effects and it is also proposed that an alternative interpolation scheme (RAMP, Stolpe and Svanberg 2001a) may be suitable as well.”
SFP—a new parameterization based on shape functions for optimal material selection: application to conventional composite plies (2011, methodology): “This occurs even when a continuation approach is used with a penalization technique ( Stolpe and Svanberg 2001 ).”
A general formulation of structural topology optimization for maximizing structural stiffness (2011, methodology): “, the six-bar truss (Stolpe and Svanberg 2001) and the MBB beam.”
Isogeometric Analysis for Topology Optimization with a Phase Field Model (2012, methodology): “[11, 12, 99], low order Finite Element approximations are used to approximate the density function ρ, even if other choices are possible (see [45] for a Finite Volume Method).”
A reevaluation of the SIMP method with filtering and an alternative formulation for solid–void topology optimization (2005, methodology): “There are several interpolation scheme variants that improve the SIMP method with a power law, e.g., the rational function of the Rational Approximation of Material Properties (RAMP) (Stolpe and Svanberg 2001b) or more implementation-intensive, spline-based interpolation schemes (Pedersen 2002).”
An alternative interpolation scheme for minimum compliance topology optimization (2001, methodology): “It was shown by Stolpe and Svanberg (2001) , that the penalized compliance cp(x) does not necessarily become a concave function on XP , no matter how large p is chosen.”
The Limits of Porous Materials in the Topology Optimization of Stokes Flows (2005, background): “... might converge quite slowly, and the approximating designs might contain quite a large amount of porous material with intermediate values of permeability, we think it is instructive to mention this approach, owing to its clear mathematical and physical interpretations (compare with, e.g., the mo”
An enhanced genetic algorithm for structural topology optimization (2006, background): “or converge to an infeasible solution to the original 0-1 problem [12].”
Length scale and manufacturability in density-based topology optimization (2016, background): “For general discussion and comparison, the readers are referred to [130] and the recent review papers on topology optimization [37,125].”
Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials (2009, methodology): “To avoid premature convergence to local minima in SIMP method, the continuation method was proposed by gradually increasing penalty parameter from lower bound to upper bound [30, 31 ].”