Finite Element Analysis - Essay Example

n into "series of smaller regions in which the differential equations are approximately solved; by assembling the set of equations for each region, the behaviour over the entire problem domain is determined". Considering a three-dimensional body (as shown in the figure), assume that force F is acting on the body, whereas the body is under gravitational pull by the virtue of its weight represented. The distributed load T is also acting of the body. The part of the body is segmented, and single specific outer surface is considered.

The body is under stress, as result of the application of the external force, the distributed load and the gravitational force. The external force acts on surface of the body, and is regarded as the surface forces, whereas the weight is acting on the entire volume of the body and is regarded as the body forces. By the virtue of its material characteristic, the body will tend to deform upon application of the external force. The body initially behaves within the elastic limits, and will therefore retain its shape after the surface forces are withdrawn.

This tentative deformation with the body in terms of length, area and volume is regarded as the strain. As per Cartesian system, the developed strain can be explained as, This entire set of differential equations is configured on the element of volume. Further calculations are pursued to obtain the energy change in the entire system due to the application of the forces. The node is the critical point for the specific surface. The location of this point is based upon the value of the known field variable.

In specific cases, the net displacement at support node is amounted to be zero, in similar manner the temperature values are prescribed at nodes. The nodes are considered to the points at the boundaries of the finite element mesh. The mesh is the marking of regions on the surface area, and therefore in the case of continuous regions no gaps are evident during finite element mesh. The