Kiyohiro Ikeda

Bifurcation analysis of symmetric structures using block-diagonalization

Abstract A group-theoretic method to trace bifurcation behavior of truss structures with regular-polygonal symmetry is proposed. By means of a suitable ‘local’ coordinate transformation, the present method decomposes the tangent-stiffness matrix into a block-diagonal form with possible occurrences of twice-repeated matrices. An efficient way to compute the block-diagonal form is described in view of the sparseness of the local transformation matrix. This achieves computational efficiency and moreover leads to systematic categorization of critical points. The present method is applied to a series of regular-polygonal truss domes to demonstrate its usefulness.

Block-diagonalization analysis of symmetric plates

Abstract This paper presents a block-diagonalization method to solve stiffness equations of isotropic symmetric plates. By means of a suitable “local” coordinate transformation, chosen based on group theory, the stiffness matrix is decomposed into a block-diagonal form. The stiffness equation in the local coordinate is solved block by block, thus realizing numerical efficiency and greatly reducing the requisite amount of computer memory. The efficiency has been further upgraded with the aid of the concept of augmented orbit. This method is applied to a square isotropic plate subject to “asymmetric” loads to show its usefulness.