A Direct Method Formulation for Topology Plastic Design of Continua

Large-scale smooth plastic topology optimization using domain decomposition

“…However, decomposition schemes for plastic topology design of continua are yet to be developed. This is understandable since design methods that efficiently solve plastic topology optimization problems for continuum structures have appeared only recently [11][12][13][14][15][16][17]. The key idea in these methods, which was introduced and detailed in [11], consists of formulating the plastic analysis problem using direct methods to limit analysis [18,19] and to integrate the analysis and design problems into a single mathematical problem.…”

Topology Optimization Considering Limit Analysis

“…The result of standard topology optimization for this problem found by [66] is shown in 4.12. The result found by Kammoun Z. and Smaoui H. [61] is represented in 4.13. And the resulting topology using the presented formulation is illustrated in 4.14.…”

“…The work of Kammoun and Smaoui [61] presents a similar formulation. However, the penalization approach adopted in that work has not succeeded in providing good black-and-white results.…”

“…In addition, the elastic formulation for topology optimization of trusses [59] and the plastic formulation considering equal stress limits in compression and tension are equivalent [60]. Although the plastic formulation for topology optimization on truss structures has been widely covered in the literature, this formulation has only recently been explored to continuum structures [61].…”

“…The long cantilever beam problem, shown in Figure 4.11, is addressed in the work of Kammoun and Smaoui [61] and, therefore, it is considered herein for comparison purposes. The structural domain has H = 1 m and L =4 m; the material adopted follows the von Mises yield criterion with yield stress σ y = 1kPa; and a 0.1 kN load is applied.…”