Abdullah M. Al-Bagamy Master Theses
Theses Title : Elastic Plastic Analysis of Structures by Finite Element Method.
The main objective of the present work concerns the elastic-plastic analysis of structures by the finite element method. Combination of modern non-linear techniques with the finite element method has opened new and wide possibilities for the elastic-plastic analysis. It is now possible with modern computers and numerical techniques to relax limitations imposed in the classical theory of plasticity. Hardening behavior, load reversal and Bauschinger effects can all be accounted for. The thesis aims at mastering, implementing and using most modern numerical techniques associated with a finite element elastic plastic analysis. Various aspects of elastic plastic analysis are investigated. A Fortran open source program developed by the supervisor of the thesis was used. It deals with the plane stress and plane strain problems using isoparametric ٢D elements with four, eight or nine nodes. Manipulating an accessible source program is by far more efficient and useful for the investigator than using a black box executable program. Only a long experience with computer implementation can guarantee an appropriate modeling and good result interpretation with the use of black box software.
The main numerical algorithms and procedures (subroutines) are explained and after a validation, the program was used to study the effects of various parameters such as number of elements, type of element, plastic criterion, level of hardening, nonlinear methods. The gradual spread of plasticity was tracked with great accuracy and theoretical results were reproduced by numerical simulation with great accuracy. In stress concentration cases, elastic-plastic models caused stress redistribution which led to increased load capacity.
Nodal stress projection was also investigated and it was found that for postprocessing purposes, the use of projected nodal stresses was very important and that models using large numbers of simple elements were better than models with smaller number of higher order elements.