Efficient solution of differential equations for linear and non-linear analysis of structures

In this paper using the eigenvalues and eigenvectors of symmetric and asymmetric of tridiagonal matrices with infinite dimension, inverse of these matrices are found. Moreover numerical method of finite difference is used for numerical modeling of engineering problems. Many engineering problems modeled by numerical methods result in solution of linear systems. Many of these linear systems are in tri-diagonal form. The inverse of this kinds of matrices have many applications. In this paper, response of linear and nonlinear structures resulting from different types of arbitrary dynamics and statics analyses are presented. The method of this paper provides closed form solutions for the analysis of structures under different static and seismic loadings.