Development of Nonlinear Transfer Matrix Method for Inelastic Analyses of Beams

The objective of this study is to develop a material-nonlinear-analysis algorithm based on the transfer matrix method (TMM). This newly developed algorithm can be used to perform nonlinear analyses of continuous beam systems. The nonlinear transfer matrix is derived from the general frame stiffness matrix and the Gauss-Lobatto integration scheme is employed for numerical integration. In the TMM, the system equation has a constant number of system unknowns regardless of the total degree-of-freedom number in the structure and the system response (either linear or nonlinear). As a result, TMM can be used efficiently both for linear and nonlinear structural analyses. In this study, a secant nonlinear algorithm required in nonlinear TMM is employed due to its good compromise between the convergence rate and numerical stability. To verify accuracy and efficiency of the developed TMM, four numerical examples are selected and analyzed. The analysis results are compared with those obtained by the highly accurate flexibility-based frame model in terms of global and local responses.