Adaptive Newton-Raphson Method for Analysis of Structures with Material Nonlinearity Using Stiffness-Equivalent Load

This paper presents a new material nonlinear analysis algorithm which utilizes equivalent load for stiffness. The proposed algorithm requires calculation of the inverse of the global stiffness matrix only once regardless of the loading steps and provides the same results as those by the conventional method. The efficiency of the proposed algorithm depends on the ratio of the boundary DOFs - the DOFs directly connected to the elements where stiffness changed - to the total DOFs. If the number of boundary DOFs is less than about 1/8 of the band width of the global stiffness matrix the proposed algorithm is more efficient than the conventional method. The analysis results of the model structure showed that the linear analysis of a structure using the proposed algorithm produced identical responses as those by conventional plastic hinge analysis method.