Single parameter accelerated modified Newton–Raphson methods for rigid/plastic FE analysis

This paper presents applications of the single parameter accelerated modified Newton–Raphson (mN–R) methods (often referred to as the acceleration techniques in this paper) to the solution of nonlinear rigid–plastic finite element equations. A new formulation procedure used to derive acceleration techniques for the mN–R method is first described. Two new single parameter acceleration techniques of secant properties are obtained by using the modified BFGS and DFP quasi-Newton updates. Evaluation of the accelerators does not involve additional residual force calculation and requires little extra computational effort as compared to the standard mN–R method. The single parameter acceleration techniques are used to solve rigid–plastic finite element equations. Numerical performance of the techniques is compared with those of the standard N–R method (sN–R), standard mN–R method and other existing single parameter acceleration techniques. It is shown that the newly proposed techniques are more robust and efficient than the existing techniques.