7.6. Fundamentals

Structural analysis involves the determination of the forces and deflections within a structure or its members. The earliest demands for structural analysis led to a host of so-called classical methods. The specialization of the classical methods was replaced by generalities of the modern matrix methods. The presentation of this chapter is limited to the most widely used of these techniques: the finite element stiffness or displacement method. Unless otherwise specified, we shall refer to it as the finite element method (FEM). The finite element analysis (FEA) is a numerical approach and well suited to digital computers. The method relies on the formulations of a simultaneous set of algebraic equations relating forces to corresponding displacements at discrete preselected points (called nodes) on the structure. These governing algebraic equations, also called the force–displacement relations, are expressed in matrix notations.

The powerful finite element method had its beginnings in the 1980s, and with the advent of high-speed, large-storage-capacity digital computers, it has gained great prominence throughout the industries in the solution of practical analysis and design problems of high complexity. The FEA offers many advantages. The structural geometry can be readily described, and combined load conditions can be easily handled. It offers the ability to treat discontinuities, to handle composite and anisotropic materials, to handle unlimited numbers and kinds of boundary conditions, to handle dynamic and thermal loadings, and to treat nonlinear structural problems. It also has the capacity for complete automation. The literature related to the FEA is extensive. See, for example, Refs. 7.2 through 7.20. Numerous commercial FEA software programs are available, as described in Section 7.16, including some directed at the learning process.