An alternative interpolation scheme for minimum compliance topology optimization

By Mathias Stolpe, Krister Svanberg. 2001

950 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/8d8570a328f62c819332ed8b7c413df76d28bc9c

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In Civil and Structural Engineering

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

A critical review of established methods of structural topology optimization (2009, methodology): “Alternative methods for suppressing intermediate densities were proposed by Stolpe and Svanberg (2001), Fuchs et al. (2005), and Sigmund (2007).”
A survey of structural and multidisciplinary continuum topology optimization: post 2000 (2014, methodology): “Torquato et al. (2003) demonstrated this concept via topology optimization for both maximum thermal and electrical conductivity.”
A geometric projection method for designing three‐dimensional open lattices with inverse homogenization (2017, neutral): “The sensitivity of d̂q is then Dd̂q = D||{d̃(i,j) q (x q , x f ) q , p)}||−p (35) = ||{d̃(i,j) q (x q , x f ) q , p)}||1+p −p d̃ q (x q , x f ) q , p)−p−1Dd̃ q (x q , x f ) q , p).”
A note on the theoretical convergence properties of the SIMP method (2005, methodology): “In [6] a material interpolation model is proposed by means of which the probability of obtaining global solutions of 0− 1-related subproblems is increased.”
Compliant mechanism design using multi-objective topology optimization scheme of continuum structures (2005, methodology): “model ( Stolpe and Svanberg 2001 ) incorporating the requisite convolution can be expressed in the form of a modified RAMP scheme:”
Optimization strategies for discrete multi-material stiffness optimization (2011, background): “Other interpolation schemes have been proposed and in particular the so-called RAMP (Rational Approximation of Material Properties) scheme seems to have gained acceptance as well (Stolpe and Svanberg 2001).”
Material interpolation schemes for unified topology and multi-material optimization (2011, methodology): “In Stolpe and Svanberg (2001) the so-called RAMP scheme was proposed as an alternative interpolation scheme for twophase topology optimization.”
Benchmarking optimization solvers for structural topology optimization (2015, result): “The RAMP (Rational Approximation Material Properties) interpolation scheme (Stolpe and Svanberg 2001) was also considered and implemented but it was removed in the final benchmark since the results were very similar.”
Topology optimization for braced frames: Combining continuum and beam/column elements (2012, methodology): “The topology optimization problem is solved by means of the SIMP model [31,32,12,33], however, other material models may be used, such as the Rational Approximation of Material Properties (RAMP) [34,13].”
Topology optimization approaches (2013, methodology): “The reason for introducing the RAMP approach was to alleviate non-concavity of the original SIMP interpolation scheme (Stolpe and Svanberg 2001b) and hence ensure convergence to 0-1 solutions.”