Development of computer program for the numerical surface integration over 3D solids by applying finite element concepts

Abstract

Numerical surface integration is an important technique used in various engineering and scientific applications, such as finite element analysis, computational fluid dynamics, and electromagnetic simulations. The technique involves the computation of surface integrals over a 3D solid geometry, which is often a complex and challenging task.

The purpose of this Final Year Project (FYP) is to develop a computer program for the numerical surface integration over 3D solids using finite element concepts. The program is designed to automate the process of surface integration, which is essential in many engineering simulations and analysis tasks.

To achieve the goal, the computer program developed in MATLAB utilizes the finite element method, a powerful numerical technique widely used in engineering and physics. The finite element method allows solid geometry to be discretized into smaller elements forming a mesh. The elements are then converted to a similar element shape in the reference coordinate system using shape functions and isoparametric mapping. The finite element mesh composed of these similar elements is then used by the computer program to perform numerical surface integration over the mesh’s solid.

The developed computer program is tested and validated through several benchmark problems, which demonstrated its accuracy and efficiency compared to existing analytical integration methods. Overall, the developed computer program provides a powerful tool for the numerical surface integration over 3D solids, which has numerous applications in various engineering fields such as structural analysis, heat transfer, fluid mechanics, and electromagnetics.