ABSTRACT
This chapter considers engineering problems idealized as one-dimensional. The appropriate functional for solving the one-dimensional stress-deformation problem can be obtained in two ways: from the total potential energy expression and directly from the governing equation and natural boundary conditions using the variational calculus principles. For stress-deformation problems, the actions or causes are forces, and the effects or responses become strains, deformations, and stresses. The link connecting the action and response is the stress-strain or constitutive law of the material. The strain energy can be interpreted as the area under the stress-strain curve. In the mixed approach, both the element displacements and stresses are assumed to be unknowns. The formulation results in coupled sets of equations in which nodal displacements and stresses appear as unknowns. The equilibrium and the stress-strain displacement equation can be used for formulating the mixed approach with Galerkin's method. The stress approach yields a discontinuous distribution of displacement.
