Generating optimal topologies in structural design using a homogenization method
Computer Methods in Applied Mechanics and Engineering
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
On the Topological Derivative in Shape Optimization
SIAM Journal on Control and Optimization
The Topological Asymptotic for PDE Systems: The Elasticity Case
SIAM Journal on Control and Optimization
Incorporating topological derivatives into level set methods
Journal of Computational Physics
Structural optimization using sensitivity analysis and a level-set method
Journal of Computational Physics
A new algorithm for topology optimization using a level-set method
Journal of Computational Physics
Level-set methods for structural topology optimization: a review
Structural and Multidisciplinary Optimization
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Material interpolation schemes, like SIMP, are very popular in topology optimization. They convert the difficult 0-1 problem into a nonlinear programming problem defined over a convex set by involving an interpolation (or penalization) function, usually constructed in rather empirical ways. This paper gives an insight into such methods with the help of the notion of topological sensitivity, and in particular provides some arguments for the choice of the penalization function. A simple algorithm based on these concepts is proposed and illustrated by numerical experiments.