TABLE OF CONTENTS It was noted in Section 2.3 that solution of a set of nonlinear equations for structural analysis can be carried out by different methods (e.g. [1]). In general, no matter what method is used, a set of updated linear equations must be repeatedly solved during the solution process. In addition, the structure stiffness matrix is often decomposed into upper and lower triangular matrices. As a result, the CA method is also most suitable for nonlinear analysis, as is shown in this chapter. The solution steps of geometric nonlinear analysis problems are summarized in Section 11.1. Application of the CA method in geometric nonlinear analysis is demonstrated in Section 11.2, and nonlinear reanalysis by the method is presented in Section 11.3.
[1]Crisfield, M. A. Nonlinear Finite Element Analysis of Solids and Structures, Vol. 1: essentials, John Wiley & Sons, Chichester, 1997.
Geometric nonlinear analysis described in Section 2.3.1 involves the following steps. Starting with linear analysis, we first calculate the initial displacements r 0 by the linear analysis equations [Eq. (2.41)]
where K 0 is the elastic stiffness matrix and R 0 is the external force vector. In the solution process the following calculations are repeated until convergence occurs:
Calculate the member forces N, which are functions of the displacements r [see Eq. (2.43)]
Calculate the corresponding internal force vector R I by Eq. (2.44)
where the elements of matrix C(r) depend on the deformed geometry.
