MATLAB Code Implementation for Finite Element Analysis

This documentation presents an introduction to the MATLAB finite element analysis program. Designed for fundamental finite element computations, the program employs sparse matrix storage techniques to efficiently manage large-scale matrices, significantly enhancing performance and memory utilization. Users can leverage this implementation for structural and mechanical design analysis, enabling deeper insights into design characteristics and potential limitations. The implementation features key algorithms including stiffness matrix assembly using nodal connectivity data, boundary condition application through matrix modification techniques, and displacement solution via direct solvers like backslash operator (\) for linear systems. Additionally, the program finds applications in diverse domains such as power system design, electronic device development, and materials science research. Across these fields, the MATLAB FEA program delivers accurate, reliable analytical results through robust numerical methods including shape function calculations for various element types (e.g., quadrilaterals, tetrahedrons) and Gaussian quadrature integration for element matrix formulations, ultimately supporting comprehensive problem understanding and resolution.