Shell analysis by different methods of dynamic relaxation

Abstract

Shell analysis is a complex process. For this reason, so far, many equations and theories have been proposed. With the increasing processing power of computers, numerical and approximate solutions were developed. The dynamic relaxation scheme is one of these methods. The dynamic relaxation is an explicit technique for solving simultaneous equations. The fictitious mass and damping are added to the system of static structural equations in dynamic relaxation technique to obtain a fictitious dynamic system. In this article, twelve well-known dynamic relaxation processes were used for linear analysis of shells. It is found that so far, the ability of many solutions of dynamic relaxation in the linear analysis of shells has not been shown. In each approach, the mass, damping and time step matrices are obtained based on the researchers’ work. Twelve samples are analysed. Most of these are examples of well-known benchmarks in nonlinear analysis, whose linear solutions are not available. The number of iterations and the analysis time of each solution gives the score of each technique. Then, the final rank of each method was obtained. Numerical solutions show that MRE was the best process for linear shell analysis. Also, mdDR, Zhang, Qiang and RPS behaved very similar to each other.