Canonical Forms for Symmetric and Regular Structures

Matrices associated with symmetric and regular structures can be arranged into certain block patterns known as Canonical forms. Using such forms, the decomposition of structural matrices into block diagonal forms, is considerably simplified. In this paper the main canonical forms are reviewed; and symmetric/regular structural configurations that can be explained with such forms are investigated. The invariant subspaces are formulated and the closed form solutions for the block‐diagonalized stiffness matrices are provided in each case. Utility and robustness of the canonical forms in the analysis of structures exhibiting decomposable matrix patterns are demonstrated by numerous examples. Furthermore, a numerical method is proposed to extend the computational advantages of the matrix canonical forms to other nonconforming regular structures.