6th World Congresses of Structural and Multidisciplinary Optimization

1. Abstract A novel boundary method for implementing design sensitivity analysis (DSA) by FEM is developed in shape optimization problems of an elastic body. A sensitivity formula is derived based on the continuum formulation in a boundary integral form, which consists of the boundary solutions and shape variation vectors. Though the boundary element method (BEM) has mainly been used to obtain the boundary solution, the FEM is used in this paper with greater advantage because it is much more popular and has improved meshing and computing power recently. The advantage of the boundary DSA is that the shape variation vectors, which are also known as design velocity fields, are needed only on the boundary. As such, the step used to determine the design velocity field over the whole domain, which was necessary in the domain-based DSA, is eliminated, thereby making the process easy to implement and efficient. Problem of fillet design is chosen to illustrate the efficiency of the proposed method. Excellent accuracy is achieved for the sensitivities using the boundary method even when employing free mesh in the FEM. 2.