A Numerical Method for the Solution of the Bi-Dimensional Continuous with No-Tension Material

Abstract

The present work proposes an efficient numerical method, based on the use of projection operators, for solving boundary problems of the elastic equilibrium of two-dimensional body not withstanding tension.Due to their high non-linearity, boundary problems involving materials with no resistance to tension, known as no-tension materials, are quite exacting to solve. Although a number of solution methods have been proposed in the literature, the approach presented herein has the advantage of circumventing the computational difficulties due to such non-linearity by resolving a sequence of linear problems, the solution to each of which is guaranteed by efficient use of the projection operator. In other words, what is proposed is an iterative procedure that, while satisfying the equilibrium conditions, makes appropriate corrections to the linear-elastic solution in order to make it converge on a final result congruent with the defined conditions of the material's lack of tensile resistance.The two-dimensional problems are studied under the hypothesis of a plane stress state, and the method applied to body discretized via three-node finite elements under constant stress. The effectiveness of the method is then demonstrated by resolving some simple example problems.