ABSTRACT
There are a number of reasons for including the consideration of the subject of calculus of variations in the study of the finite element method. This chapter presents eight steps of finite element analysis and the basic knowledge of variational calculus. These steps include discretizing and selecting element configuration, selecting approximation models or functions, defining strain-displacement and stress-strain relationships, and deriving element equations. The steps also include assembling element equations to obtain global or assemblage equations and introducing boundary conditions, solving the primary unknowns, solving derived or secondary quantities, and providing interpretation of results. A number of functionals are obtained in some examples from the governing equations and natural boundary conditions for both one-dimensional and two-dimensional problems. The area integrals are associated with the governing equation in the two-dimensional domain of the problem and the line integrals are associated with the boundary of the problem.
