Finite element analysis of a continuum undergoing large plastic deformation

In today's society there is a need for engineers to design to the limit of materials, with which they are working, because of industrial demands for more competative designs. This thesis describes the work carried out to investigate the concept of the finite element method, to gain insight into the theory behind it and to apply this knowledge in developing a computer program to simulate the load mechanisms and boundary conditions, particularly to the ring structure under large elasticplastic deformation. Finite element is a method of mathematically modelling a component for stress analysis. It requires large quantities of data which are manipulated by matrix techniques to obtain results. The use of the computer is therefore essential to save time on a complex component. The finite element program developed in this work is based on a twodimensional plane elasticity analysis using constant strain triangular elements. Yield is based on Von-Mises' criterion, plastic flow on Prandtl-Reuss relationship and the formulation includes linear strain hardening. The formulation of the elasticplastic matrix is based on the initial stress method. The equipment for the experimental work was designed and this included the modification of the hydraulic system of the press machine, the base of testing and the measurement system. Experimental work was carried out on the ring structure under three different types of loading conditions: 1. between two knife-edges; 2. between two rigid parallel surfaces; 3. between two rigid parallel surfaces and two lateral walls with a gap. A comparison was made between the output data from the E.P. Program, which was developed in the current work, and the commercial packages. The results of this comparison are in reasonable agreement with each other. A comparison was also carried out between the experimental results and the theoretically predicted results, and reasonable agreement was obtained