Finite Element Method

Introductory Course on Finite Element Method is written with a unique objective of presenting the subject in a systematic approach by classifying the topics into three groups such as: Direct Stiffness Method, the Variational method, and Galerkin Weighted Residual Methods. The scope and application of each method has been unique for specific type of problems due to the underlying principle behind its formulation. It is shown that each method can yield the same result certain problems. Simple elements like, bar, truss and beam are dealt in the direct stiffness method in which the element stiffness equations are derived using equations of static equilibrium. Similar equations are derived using variational method by applying the principle of minimum potential energy while the Weighted residual method is based on error minimization principle. The Galerkin Weighted Residual Method is applied for bar and beam and for heat transfer problems. The shape functions are derived for two-and three-dimensional basic elements as well as for isoparametric elements using linear algebra, Lagrange interpolation formulas and serendipity method.