Two-dimensional finite elements can be used for two-dimensional stress analysis problems. A summary of pertinent equations from the theory of elasticity is presented below in order to better understand finite element formulation for two-dimensional stress analysis.
Three-Dimensional Elastic Body (Crandall et al., 1978)
Consider an elastic body in space. Any particle within the elastic body may experience displacements U, V, W in the X, Y, Z directions, respectively. For such displacement components, under the assumption of iso-tropic, elastic material properties, following expressions are well established.