Topology Optimization Using Ellipsoidal Frame Elements : for Maximization of Eigen-values

Abstract

This paper presents the,outcome of research concerning the development of a structural topology optimization methodology which can be used at the conceptual design phase of mechanical products. This optimization method is constructed based on beam elements with ellipsoidal cross-section and its cross-sectional area and rotational angle denoting the principal direction of second moment of inertia. First, the optimization problem is formulated for the eivenvalue maximization problem, and its algorithm is constructed based on the ground structure approach and the convex approximation method. The update procedure of the rotational angle denoting the principal direction of second moment of inertia in ellipsoidal cross-section is derived form KKT-conditions. In addition, several examples are provided to show the utility of the methodology presented here.