Work

A null space algorithm for solving multiple-constrained topology optimization problems with topological derivatives

Year: 2026

Type: article

Abstract: Topology optimization is widely regarded as one of the most effective techniques for structural design. However, current algorithms used for level-set approaches often introduce fine tuning of parameters and generally exhibit low speed of convergence, specially when dealing with multiple constraints. Consequently, a fundamental aspect in topology optimization is to have access to a robust optimization scheme. Recently, the null space algorithm has exhibit solid performance when considering density and shape optimization approaches. The aim of this paper is to extend the null space approach to also consider topological derivatives for level-set methods. The idea relies on continuing the current fix-point techniques with the null space algorithm. The proposed optimizer has much less free parameters in comparison with the well-known augmented Lagrangian algorithm. Besides, we also consider box constraints in the dual computation to reduce the oscillations in the density case. The proposed method naturally handles inactive constraints, which are particularly relevant for engineering applications. Several numerical examples, including multiple constraints, show that results are obtained effectively with an adequate numerical stability.

Source: Structural and Multidisciplinary Optimization

DOI: 10.1007/s00158-026-04338-2

Authors: Jose Torres, Fermin Otero, Alex Ferrer

Institutions: Universitat Politècnica de Catalunya, International Center for Numerical Methods in Engineering

Language: English

Topic: Topology Optimization in Engineering

Subfield: Civil and Structural Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,990

Funders: Ministerio de Ciencia, Innovación y Universidades, Universitat Politècnica de Catalunya, Agència de Gestió d'Ajuts Universitaris i de Recerca