MOTIVATION

Most of the real life objects are much too complex to be solved analytically for stresses. This is because the differential equations obtained in stress analysis, because of the complex geometry, cannot be solved without making use of numerical techniques. The Finite Elements Methods is a powerful and popular tool of analysis used by engineers. the first step in FEM is dividing the object into small elements which can be analysed individually using simple functions. This can be illustrated using following examples. The first example is "rod extension problem". This is essentially a 1-D problem and can easily be solved analytically for simple geometries (i.e. when the x-section area varies according to a simple function) and material properties. The next example is much more complex: gear tooth. A gear tooth is subjected to a complex loding pattern in course of its operation and it is impossible to study it analytically.