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The main purpose of this paper is the nonlinear analysis of bending plates with the finite difference. Based on the variable damping, the dynamic relaxation technique will be utilized. In order to achieve proper convergence, the velocity, kinetic energy and two successive displacement ratio criteria are used. For various bending plate samples, the results of constant and variable damping are compared. Numerical examples show that the variable damping is better than the constant damping. However, author's scheme reduces the number of iterations and the time duration. The finite difference method is very sensitive to the choice of some factors. A slight change in the amount of these parameters will increase the number of iterations and the time duration. Moreover, sometimes the solution procedure is divergenced. Another goal of this article is presenting a brief review of the dynamic relaxation approach in solving the bending plates. [ABSTRACT FROM AUTHOR]

Dynamic relaxation method is an iterative procedure for solving the simultaneous system of equations. This technique is used in the static and dynamic nonlinear structural analysis. One of the most important parameters in this approach is fictitious damping factor. If this factor is selected more accurately, convergence rate will rise. In this paper, inverse vector iteration method is utilized to find the damping factor in the dynamic relaxation iterations, and a new formulation is proposed. The geometric nonlinear analysis of several plane and space trusses and also structural frames are performed using the suggested method. The numerical results indicate that the convergence rate improves compared with the conventional dynamic relaxation procedure so that the number of iterations and the analysis time decrease significantly. Consequently, the authors' technique makes the solving process faster and more capable.