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CHAPTER 1 |

** What Is FEM**
?

In the field of Engineering Design we come across many complex problems, the Mathematical Formulation of which is tedious and usually not possible by analytical methods. At such instants we resort to the use of Numerical techniques. Here lies the importance of FEM, which is a very powerful tool for getting the Numerical solution of a wide range of Engineering problems. The basic concept is that a body or structure may be divided into smaller elements of finite dimensions called as “Finite Elements”. The original body or structure is then considered as an assemblage of these elements connected at a finite number of joints called as “Nodes” or “Nodal Points”. The properties of the elements are formulated and combined top obtain the properties of the entire body.

The equations of equilibrium for the entire structure or body are then obtained by combining the equilibrium equation of each element such that the continuity is ensured at each node. The necessary boundary conditions are then imposed and the equations of equilibrium are the solved to obtain the required variables such as Stress, Strain, Temperature Distribution or Velocity Flow depending on the application.

Thus instead of solving the problem for the entire structure or body in one operation, in the method attention is mainly devoted to the formulation of properties of the constituent elements. A common procedure is adopted for combining the elements, solution of equations and evaluation of the required variables in all fields. Thus the modular structure of the method is well exploited in various disciplines of Engineering.