Abstract
In this chapter, the interpolation formula will be developed for one-dimensional (1D), two-dimensional (2D), three-dimensional (3D) and the numerical integration for the matrices involved in the determination of stiffness, mass matrices, and load vectors. The polynomial assumption was used to derive the shape functions for the 2-, 3-, and 4-node elements. The Lagrangian interpolation was also used to derive the shape functions for 1D, 2D, and 3D cases. The 3- and 6-node triangular elements shape functions were derived in terms of polynomial, intrinsic, and area coordinates. The quadrilateral elements 8- and 9-node isoparametric shape functions were derived. The serendipity elements shape functions were derived, such as the 20-node, 4-node tetrahedral element, and higher-order elements in terms of volume coordinates. The numerical integration for the determination of the element stiffness matrix in addition, to some selected problems was included in this chapter.
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