An Adaptive Phase-Field Method for Structural Topology Optimization

TL;DR

This paper introduces an adaptive phase-field algorithm for topology optimization that uses residual-based error estimators to efficiently solve minimum compliance problems with proven convergence.

Contribution

It presents a novel adaptive algorithm employing phase-field approximation and a posteriori error estimators, with theoretical convergence guarantees for topology optimization.

Findings

Algorithm effectively reduces computational effort.

Numerical simulations demonstrate convergence and accuracy.

Adaptive method outperforms non-adaptive approaches.

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.