Topology optimization methods and systems applied to material shaping of load-bearing structures are based on lower plastic limit analysis combined with material stress field decomposition.

Abstract

This invention proposes a method and system for optimizing topology for structures subjected to limit loads based on lower bound plastic limit analysis, combining stress field decomposition and second-order cone design (SOCP). The core of the solution is the decomposition of the total stress field into its elastic and self-balancing residual stress components σ = λ σE + σr, and the direct conversion of von Mises yield conditions into second-order cone constraints to optimize computation time and accuracy. To eliminate intermediate porous material and mesh-dependent errors, the system applies Gaussian density filtering and a stress penalty function g(ρ) = ep(1-ρ), thereby generating sharp black-and-white topology designs that absolutely guarantee the mechanical feasibility of the stress field. This solution offers high practical applicability for extreme load designs in fields such as steel structures, aerospace, mechanical engineering, automotive, and 3D printing technology.

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