APPLICATION OF SINGULAR VALUE DECOMPOSITION IN SYMMETRIC STRUCTURES BY FORCE METHOD

Different methods are used for the formation of the null basis matrix of a structure followed by calculating the element forces when the force method of structural analysis is utilized. Singular value decomposition (SVD) method is one of the algebraic methods in force method that uses equilibrium matrix in its computation of finding element forces. By increasing the dimensions of the equilibrium matrix in large scale structures, the time needed for making orthogonal matrices grows. In recent decades many researchers have worked on block-diagonalization of structural matrices such as stiffness matrix in symmetric structures to reduce the computational time and simplify the equations. Block-diagonalization of equilibrium matrix can also reduce the computational time in algebraic force methods. In this paper block-diagonalization of equilibrium matrices of circulant structure is performed using Kronocker product and SVD method is utilized to calculate the block-diagonalization null basis matrix. Finally the results are compared to those of the method without block-diagonalization and other algebraic methods.