ABSTRACT
In this chapter finite element equations are developed for analysis of linear elastic bodies under static conditions. In elastostatic finite element analyses employing irreducible elements, the only permissible form of loading is through suitable concentrated nodal forces. Thus body forces, forces due to initial stresses and/or strains, and forces due prescribed surface tractions (pressures) must thus be converted to equivalent nodal loads. Traction normal to an edge is assumed to be positive if, in conjunction with a counterclockwise node number specification, it is directed into the element. A tangential load is assumed to be positive if it acts in a counterclockwise direction with respect to the loaded element. The integral statement necessary for deriving element equations associated with linear elastostatics was obtained using a variational approach. In this note the same equations will be derived using the method of weighted residuals. The result will be shown to be a statement of the principle of virtual work.
