An Adaptive Phase-Field Method for Structural Topology Optimization

Abstract

In this work, we develop an adaptive algorithm for the efficient numerical solution of the minimum compliance problem in topology optimization. The algorithm employs the phase field approximation and continuous density field. The adaptive procedure is driven by two residual type a posteriori error estimators, one for the state variable and the other for the first-order optimality condition of the objective functional. The adaptive algorithm is provably convergent in the sense that the sequence of numerical approximations generated by the adaptive algorithm contains a subsequence convergent to a solution of the continuous first-order optimality system. We provide several numerical simulations to show the distinct features of the algorithm.

31 pages, 10 figures, to appear at Journal of Computational Physics

References in corpus (2)

• A provably efficient monotonic-decreasing algorithm for shape optimization in Stokes flows by phase-field approaches
• Phase field topology optimisation for 4D printing

Cited by in corpus (4)

• Adaptive Computation of Elliptic Eigenvalue Topology Optimization with a Phase-Field Approach
• A level set topology optimization theory based on Hamilton's principle
• Convergence Analysis of an Adaptive Nonconforming FEM for Phase-Field Dependent Topology Optimization in Stokes Flow
• On the Crouzeix-Raviart Finite Element Approximation of Phase-Field Dependent Topology Optimization in Stokes Flow