Strength-based topology optimisation of plastic isotropic von Mises materials

Abstract

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Large-scale smooth plastic topology optimization using domain decomposition

“…The commonly used Messerschmitt-Bolkow-Blohm (MBB) beam problem [14] illustrated in Figure 13 is considered with the geometric dimensions L = 6 m, H = 1 m. The beam is subjected to a single vertical load F = 0.25 MN at midspan and rests at its ends on two e = 0.1 m wide substrates. The prescribed load F is verified to be admissible by running the limit analysis for the fully solid beam using a mesh of 120 × 20 × 4 = 9600 finite elements.…”

“…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.…”

“…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].…”

“…As a result, the design problem preserves the bulk of the mathematical structure and properties of the LA problem, especially convexity, the conic quadratic programming form, and the rigorous lower (or upper) bound character of the solution. These properties were found to convey attractive characteristics to the solution process, such as mesh independence and near-linear time complexity [11,14]. Moreover, limit analysis does not require a behavior law, which weakens the coupling between subproblems in a decomposition context.…”

“…Moreover, limit analysis does not require a behavior law, which weakens the coupling between subproblems in a decomposition context. The concept of integrated limit analysis and design was pivotal to a number of subsequent studies dealing with smooth [12][13][14] and discrete [16,17,20] topology design of plastic continua.…”