Local constraints in topology optimization: a simultaneous analysis and design (SAND) approach

Abstract

Local constraints are a classical challenge in topology optimization: they require the enforcement of numerous constraints, which leads to prohibitive computational costs when standard optimization strategies are employed. This work investigates an aggregation-free approach requiring minimal tuning, based on the Simultaneous Analysis and Design (SAND) reformulation of the problem. The approach is applied using the Null Space Optimizer as an optimization solver, relying on sparse quadratic programming solvers for the identification of the descent directions. When using the Null Space Optimizer, there is a quantifiable relationship between the SAND and the more classically used Nested Analysis and Design (NAND) formulation, through the considered metric which identifies descent directions from the sensitivities. In the SAND formulation, this metric introduces a dependence between optimization variables related to the shape and the state of the design and must therefore be set appropriately. The method is tested on the design of a minimal volume 2D heat sink where the maximal temperature is constrained. The method is able to successfully enforce local constraints with an accuracy that is not achieved by the aggregation method, which uses a p-norm approximation of the maximal temperature. We further investigate the influence of various factors on the optimum, such as mesh resolution, quadratic programming solver and inner product.