Finite Element Method for Solids and Structures A Concise Approach

In this chapter we first describe how to construct the element stiffness matrix and load vector in 2D domains. The mapping and shape functions derived in the previous chapter are introduced to express strain components in terms of nodal DOF. Extension of the finite element formulation to 3D domains is demonstrated using the eight-node hexahedron as an example. For dynamic problems, the element mass matrix can be formed by treating the inertia effect as a body force applied to the element. The global mass matrix is then assembled to construct the equation of motion for analyses of free vibration and forced vibration. In the last section, we briefly discuss important aspects of finite element modeling and analysis that often arise in 2D and 3D problems where the number of DOF can be large. We discuss issues, such as sparse matrices and mesh generation, which early students of the finite element method may find helpful for future reference.