Fig-2.1: A three dimensional body As mentioned earlier in section 1.1, that the FEM analysis of the structural problem involves three major steps - the tasks involved in each step require a good understanding of the sequential aggregation of the modeling of the structure, evaluation of Global stiffness matrix and load vector and the handling of specified displacement boundary conditions. Since this study mainly focuses on the two-dimensional problem concerning the analysis of a plate with a hole, the approach towards most of the conceptual review would be to cover only the twodimensional aspects of finite element analysis.
2.1 Finite Element Modeling The Finite Element Method is the dominant discretization technique in structural mechanics. The basic concept in FEM is the subdivision of a region into disjoint (non-overlapping) components of simple geometry called finite element or element for short. For 2-D modeling the most commonly employed elements are linear or quadratic triangles and quadrilaterals. In two-dimensional problem, each node is permitted to displace in the two directions. Thus, each node has two degrees of freedom. So, the displacement components of node j are taken as Q2j-1 in the x direction and Q2j in the y direction. And the global displacement vector can be represented as Q = [Q1 , Q2 ,.........., Q N ] ………………….. (2.2) T
And global load vector,