Topological gradient in structural optimization under stress and buckling constraints

Abstract

Structural topology optimization aims to design mechanical structures by seeking the optimal material layout within a given design space. Within this framework, this paper addresses the minimization of the structural mass under stress and buckling constraints, formulated as a nonlinear combinatorial optimization problem. An algorithm is proposed for such a problem, that follows a topological gradient-based approach. The adjoint method is applied to efficiently compute the constraint gradients. An iterative algorithm for buckling analysis, featuring low memory requirements, is also proposed. Numerical results, including a real application arising in the aeronautical field, illustrate the efficiency of the two proposed algorithms.

Reliability‐based topology optimization of continuum structure under buckling and compliance constraints

“…Based on this concept, various TO methods under buckling constraints are constantly explored. Mitjana et al 8 developed a topological gradient‐based algorithm, which minimized the structural mass under both stress and buckling constraints. Deng and Suresh 9 studied the TO problem of thermo‐elastic structures with buckling constraints, and the results disclosed that a reasonable material layout could be obtained by considering buckling constraints.…”

Stress-Constrained Topology Optimization Using Approximate Reanalysis with on-the-Fly Reduced Order Modeling

“…However, with modern-day sophisticated numerical methods and the recent development of advanced manufacturing technologies, the performance requirements for mechanical parts in the aerospace industry have become increasingly demanding [21]. Modeling with highly refined finite element models typically results in a series of ultralarge-scale problems with degrees of freedom ranging from tens of millions to even billions.…”