This paper deals with the shape optimization of symmetric truss structures from the viewpoint of maximization of linear buckling load. Multiple eigenvalues appear very often in structural optimizations dealing with buckling loads, and they are the causes of the difficulty in solving those kinds of problems. In this paper, the stiffness matrices are diagonalized according to symmetricity of the structures by using the group theory, so that the eigenvalues are classified according to irreducible representations. This classification is useful to understand the characteristics of multiple eigenvalue. It is shown that multiple eigenvalues obtained in the optimization problems are mainly caused from the coincidence between different irreducible representations, and the problems canbe formulated as a ordinary nonlinear programming problem by using the block-diagonalization.
