ABSTRACT
It is required to find the displacements under the loads and the stresses in the plate.
The steps in a finite element analysis are as follows: (a) Divide the plate up into a number of elements of finite dimensions, for example triangles, joined together at their corners or nodes, so that the corners of adjacent elements have common displacements. This process is referred to as discretization. An example of a very coarse division is shown in the figure: the more elements taken, the better would be the results. (b) Assume a state of strain in each element and express it in terms of the nodal displacements. Then use the stress/strain relations to obtain the stresses in the element and find a set of fictitious nodal forces on each element, which would be in equilibrium with the internal stresses. These fictitious nodal forces are thus expressed in terms of the nodal displacements. The most common assumption for a state of strain in an element is that of uniform strain, i.e. the same state of strain at all points in an element but differnt from element to element. (c) Apply the conditions for equilibrium of each node under the forces applied to it from adjacent elements, together with any external forces applied at the node. This gives a set of equations for the unknown nodal displacements. For the crude subdivisions into triangular elements shown in the figure, there would be 6 unknown nodal displacements; uA, v A, u0 , v 0 , uE, VE and 6 equations of equilibrium for the 3 nodes A, D and E ( uB = v B = Uc = v c == 0 ). When all the
nodal displacements have been determined, the stresses in each element can be evaluated.
