Chapter 2 - Discretization of the Domain

Abstract

This chapter presents the details of discretization or modeling methods used to represent a continuous region or body using a finite number of smaller pieces or elements. The considerations in selecting the shape, size, number, and configurations (or orientations) of the elements are explained. Bar and beam elements for one-dimensional problems; triangle, rectangle, and quadrilateral elements for two-dimensional problems; tetrahedron, hexahedron, and rectangular prism elements for three-dimensional problems; and curved bar, curve-sided triangle, curved-faced tetrahedron, curve-faced hexahedron, axisymmetric triangular ring element, and curved shell elements for modeling curved domains are shown along with their use in practical engineering problems. The discretization process that involves selection of type, size, and number of elements to be used; location of nodes; and node numbering schemes are presented. Finite representation of infinite bodies, node numbering schemes to reduce the bandwidth of the resulting matrices, and automatic mesh generation methods are also discussed.