A nested algorithm of truss topology optimization for maximum plastic shakedown loading capacity

Abstract

Abstract This paper proposes a nested algorithm for truss topology optimization under plastic shakedown theory, which aims at maximizing the shakedown loading capacity. The nested algorithm consists of shakedown analysis and sensitivity-based optimization. Analytical sensitivity of shakedown load with respect to the design variables is derived in a concise form for the first time in conjunction with the adjoint variable scheme. A primal-dual shakedown algorithm is implemented for the determination of the shakedown load limit of structures and adjoint variables needed in the sensitivity analysis. The ground structure approach is applied to formulate the optimization problem for determining the optimized topology and cross-sections of the truss structure. Based on the analytical sensitivity above, the nested algorithm of truss structure topology optimization can be done efficiently by a gradient-based mathematical programming algorithm. Through independent shakedown analysis and optimization processes, the proposed approach facilitates the computation scale and efficiency for large-scale structure optimization design. Several numerical examples involving two- and three-dimensional truss illustrate the effectiveness of the proposed approach.