A direct approach for continuous topology optimization subject to admissible loading

Abstract

In the present paper, a method is proposed for topology optimization of continuum structures subject to static and plastic admissibility conditions relative to a prescribed load.A key feature of the method is that, using a finite-element discretization, the form of the resulting topology optimization problem is similar to that of the direct static approach of the limit analysis problem. The proposed method is formulated in plane strain using Tresca materials and is illustrated on example problems taken from the literature.

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.…”

“…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. It was considered for smooth topology design in [11][12][13][14] and extended to discrete (i.e., 0-1) design in [16,17,20].…”

“…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. It was considered for smooth topology design in [11][12][13][14] and extended to discrete (i.e., 0-1) design in [16,17,20]. Although the discrete design is generally the primary goal, the smooth design problem is worthy of study as it is a component in many solution strategies for discrete design [16,21].…”

Strength-based topology optimisation of plastic isotropic von Mises materials

“…The formulation is similar to finite element limit analysis (FELA) [1,33,17] and the set of feasible stress states are governed by the yield function assuming a rigid plastic behaviour. Kammoun and Smaoui [18] presented a formulation for topology optimisation based on FELA for plane strain Tresca materials. A lower bound approach was taken, which ensures a statically admissible stress field, whereas in this paper, we consider four different elements including the upper bound element, which ensures a kinematically feasible solution.…”

“…A lower bound approach was taken, which ensures a statically admissible stress field, whereas in this paper, we consider four different elements including the upper bound element, which ensures a kinematically feasible solution. Identically to [18], the scope is to minimise the volume of the structure for a given load case while the stress field satisfies the yield function in the chosen stress interpolation points. In many ways, the present formulation is identical to sizing optimisation, where e.g.…”