Optimal structural design considering flexibility

A topology optimization method based on the homogenization method (the homogenization design method) has been successfully applied to a variety of optimization problems such as the stiffness maximization problem and the eigen-frequency maximization problem. In this study, a methodology to obtain the optimal structure design considering flexibility is developed as a new extension of the homogenization design method. First, flexibility is formulated using the mutual energy concept. Second, a new multi-objective function is proposed to obtain optimal solutions incorporating flexibility and stiffness. Next, the topology optimization procedure is constructed using the homogenization method and sequential linear programming (SLP). Finally, some examples are presented to confirm that the methodology presented here can provide flexible structures satisfying the problem specifications.