A framework for plasticity‐based topology optimization of continuum structures

Abstract

In this paper, a framework is proposed for topology optimization of continuum structures considering plasticity. The method merges the rigid‐plastic analysis and the density‐based topology optimization. To obtain a clean black‐and‐white design, the density in the objective function is penalized using an exponential function. The solution of the final plasticity‐based topology optimization problem exhibits as a sequence of second‐order cone programming (SOCP) problems that can be resolved efficiently using the advanced primal‐dual interior point method. Compared to the conventional stress‐constrained topology optimization techniques, the developed method accounts for plasticity and the finite element analysis of structures does not need to be carried out separately. Furthermore, the proposed method requires no relaxation techniques for imposing local stress‐constrain and possesses good computational efficiency for large‐scale problems.

Topology Optimization based Integrated Design of Structure-Foundation System

“…According to [3,7], plasticity-based topology optimization can be formulated within the context of rigidperfectly-plastic analysis. Introducing a novel design variable, denoted as 'density' 𝜌 ∈ [0,1], the optimization problem takes the form of minimizing material volume while adhering to force balance equations and yield criteria:…”

“…(3). The optimization problem (1) can be reformulated as a standard secondorder cone programming (SOCP) problem following [3,8] which then can be resolved straightforward using the advanced primal-dual interior point method available in MOSEK [9]. Notably, due to the incorporation of plasticity in the framework, the presented approach leads to a more cost-efficient structure than these from the traditional stress-constrained topology optimization, as demonstrated in [3,7] IOP Publishing doi:10.1088/1755-1315/1332/1/012006 3…”

“…While novel, the topology optimization method developed in [2] only yields grayscale designs rather than definitive black and white designs, diminishing its appeal. Addressing this limitation, an extension was proposed in [3], allowing for black-and-white designs. Notably, this extension shows that the method does not necessitate a stress-relaxation technique.…”

“…Another formulation for topology optimization incorporating plastic limit analysis was presented in [4]. Unlike the approaches in [3,5,6], the formulation in [4] aims to maximize the load-bearing capacity of the structure, considering material strength properties and a material volume constraint. More recently, Li [7] introduced a plasticity-based method tailored for three-dimensional topology optimization.…”