Elastic-plastic analysis of some trusses with large deformations

The importance of geometric and material nonlinear analysis in trusses is not deniable. Furthermore, everyone knows the importance of closed-form solution to the behavior of structures. However, the solution volumes make this type of analysis impossible or very difficult for most structures. Closed-form solution only for a few simple trusses, with geometric and material nonlinearities, can be obtained. Elastic analysis of trusses is widely performed by the methods, such as, the finite element scheme. So far, researchers have proposed many approaches for truss nonlinear analysis. New techniques are validated by the benchmark problems. In this view, it is important to have an explicit solution for this purpose. In this paper, some simple two and three-dimensional trusses are analyzed analytically. This study considers both large deformations with elastic-plastic behavior simultaneously. The behavior of material is assumed to have a bilinear diagram. The strain energy function is obtained in terms of the Green strain. Equilibrium equations are satisfied by minimizing total energy. At the point, in which determent of the tangent matrix becomes zero, structural instability is found. The load-displacement graph is obtained by analyzing the strain of the truss members in the stable range of the equilibrium path. It is important to know that the multi-relational function of the equilibrium path of each truss can be applied to test the accuracy of new nonlinear analysis techniques.