ABSTRACT
In this chapter, we learn about the procedure, algorithm, and technique used in the numerical analysis to obtain the solutions of the definite integral of the properties of a free-form surface. When the plate or shell element is not flat and rectangular, the solution of the problem becomes very difficult and tedious to be solved by hand calculation. By numerically integrating the geometrical features of a surface, we can evaluate the area, Jacobian operators, curvature, and gradient easily with accuracy[Q1][B2]. All of these properties are necessary for both the finite element formulation and the isogeometric approach formulation of a plate and shell element with a free-form surface. The famous Gauss–Legendre quadrature method is demonstrated by solving various calculations on the surface of a plate or shell element. All the numerical examples are accompanied by their relevant and complete MATLAB® codes.
