In this chapter, we discuss the general finite element analysis procedure for linear vector field problems. A vector field problem is a problem whose primary unknown physical quantity is a vector quantity at any spatial location in the computational domain. As solid mechanics and fluid dynamics are representatives of vector field problems, this chapter demonstrates the solutions of a set of solid mechanics and fluid dynamics problems. The chapter contains four sections. The first section briefly reviews the theory of linear elasticity. The second section introduces the FEA procedure for structural analysis of a 2-D elasticity problem. The third section discusses a 3-D elasticity problem and illustrates the FEA steps. The fourth section discusses the FEA procedure for 2-D steady state incompressible viscous flow problems. At the end of each section, MATLAB codes for solving these problems are presented.
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