Multiple stiffness topology optimizations of continuum structures

This paper presents a new multi-objective topology optimization algorithm for continuum structures under multiple loading cases. An expert evaluation method of weights based on grey system theory is proposed to calculate the objective weights when the compromise programming approach is employed as a multi-objective optimization scheme converting the multi-objective problem to a single objective problem. A modified updating scheme with a self-adaptive move limit for design variables is also suggested, SIMP is regarded as density-stiffness interpolation scheme and the optimality criteria method is used as the optimizer. Numerical instabilities, such as checkerboards and mesh dependencies, are also discussed. The validities of these methods in this paper are demonstrated by some numerical applications.