5. Numerical Integration

This chapter provides a brief account of numerical integration schemes used to approximately evaluate definite integrals of arbitrary functions. Numerical integration schemes are required to evaluate the integrals that appear in the Galerkin weak forms presented in the preceding chapter for both mesh-based and meshfree methods. First, the classical Gauss quadrature scheme is explained before the more modern stabilized conforming nodal integration (SCNI) scheme is derived. Stabilized conforming nodal integration is a more advanced domain integration scheme that relies on a modification of the Galerkin weak form. A firm theoretical foundation for the modification of the Galerkin weak form used in stabilized conforming nodal integration is provided by the enhanced assumed strain (EAS) method. This method was originally introduced to alleviate volumetric locking in the finite element method. In this chapter, it is demonstrated how the enhanced assumed strain method can be used as a basis for a nodal integration scheme that can be applied to both Galerkin mesh-based and meshfree methods.