A robust and stable phase field method for structural topology optimization

TL;DR

This paper introduces a new phase-field method for topology optimization that ensures robustness, stability, and strict adherence to constraints, effectively handling domain-dependent forces in 2D and 3D problems.

Contribution

It develops a novel operator-splitting algorithm with a limiter for phase-field topology optimization, ensuring bound preservation, volume conservation, and functional decay.

Findings

Robustness demonstrated through extensive 2D and 3D benchmarks.

Guarantees strict bound preservation and volume conservation.

Ensures correct decay rate of the objective functional.

Abstract

This paper presents a novel phase-field-based methodology for solving minimum compliance problems in topology optimization under fixed external loads and body forces. The proposed framework characterizes the optimal structure through an order parameter function, analogous to phase-field models in materials science, where the design domain and its boundary are intrinsically represented by the order parameter function. The topology optimization problem is reformulated as a constrained minimization problem with respect to this order parameter, requiring simultaneous satisfaction of three critical properties: bound preservation, volume conservation, and monotonic objective functional decay throughout the optimization process. The principal mathematical challenge arises from handling domain-dependent body forces, which necessitates the development of a constrained optimization framework. To address this, we develop an operator-splitting algorithm incorporating Lagrange multipliers, enhanced by a novel limiter mechanism. This hybrid approach guarantees strict bound preservation, exact volume conservation, and correct objective functional decaying rate. Numerical implementation demonstrates the scheme's robustness through comprehensive 2D and 3D benchmarks.