2D Solids. Linear Triangular and Rectangular Elements

This chapter initiates the application of the FEM to structures which satisfy the assumptions of two-dimensional (2D) elasticity (i.e. plane stress or plane strain). Many of the concepts here studied will be useful when dealing with other structural problems in the subsequent chapters. Therefore, this chapter is introductory to the application of the FEM to continuous 2D and 3D structures.

There are a wide number of structures of practical interest which can be analyzed following the assumptions of 2D elasticity. All these structures have a sort of prismatic geometry. Depending on the relative dimensions of the prism and the loading type, the following two categories can be distinguished: Plane stress problems. A prismatic structure is under plane stress if one of its dimensions (thickness) is much smaller than the other two and all the loads are contained in the middle plane of the structure. The analysis domain is the middle section (Figure 4.1). Amongst the structural problems that can be included in the plane stress category we find the analysis of deep beams, plates and walls under in-plane loading, buttress dams, etc.