Topology Optimization With a Local‐Like Global Stress Constraint Using a Fully Differentiable Aggregation Function

Over the last few decades, topology optimization (TO) has been developed into a valuable optimization method in many engineering fields. In structural optimization, limiting maximum mechanical stress is critical to the design of safe and reliable structures, a constraint that can be handled using TO. However, the non‐differentiability of the calculation of maximum stress, as well as the local nature of stress, led to a variety of approaches, such as smooth aggregation functions and Lagrange‐based local stress constraints, each with its own advantages and disadvantages. This paper, however, proposes a new aggregation function which is able to combine the strengths of both of those approaches: it consists of a single aggregated constraint which behaves similarly to local stress constraints. Some sample problems are used to illustrate its properties as well as the effects of the parameters it requires, so that the appropriate ones may be chosen for each problem. It is shown that it manages to obtain topologies with highly homogeneous stress distributions, with maximum stress arbitrarily close to the specified limit (but generally less than it), although it depends on the correct choice of parameters in order to avoid undesirable oscillations in the optimization process.