ABSTRACT
This chapter shows how to extend the finite element method to fields of study other than solid mechanics. It considers finite elements for heat conduction. The chapter introduces the method of weighted residuals and the method of Galerkin for the entire domain. It shows the link between variational principles and finite elements, and explains how to extrapolate the method to fields of study other than solid mechanics. In the finite element method, the domain is broken down to many small contiguous simple elements connected at the nodal points. The nodal displacements are then adjusted for each element so as to minimize the total potential energy in each small element. For finite elements, the boundary conditions will not be homogeneous for each element. Homogeneity occurs only at the left of the first element and at the right of the last element. Hence one will form a quadratic functional here by manipulation.
