A shakedown oriented topology optimization algorithm utilizing second-order cone programming (SOCP) and its application in spacecraft structure design

Mechanical components are often subjected to time-varied loading during their service. One of the key objectives for designing these parts is to reduce the weight while maintaining the load-bearing capacity. To this end, we propose a second-order cone programming (SOCP) based technique that allows the topology of elastoplastic structures to be optimized with respect to the shakedown limit. The method established consists of nested loops, in the inner loop the shakedown limit is calculated by solving a SOCP problem formulated according to Melan’s theorem, while in the outer loop, the topology optimization is realized by a gradient-based algorithm in which the sensitivity of each element is evaluated using solutions of the shakedown problem as inputs. To enhance the numerical efficiency, inequality constraints in the shakedown problem are converted to Euclidean ball constraints, while a slack variable-based tactic is employed to facilitate the sensitivity calculation. Applying the method to two classical examples and a 3D spacecraft bracket emerged from engineering practice, the capability of the method in dealing with real engineering structures and complicated load cases is demonstrated, and the benefits of conducting shakedown-based design are discussed in comparison to conventional compliance and stress-based designs.