2D MATLAB EFG Code Implementation for Square Domains

This document discusses the application of 2D MATLAB EFG (Element-Free Galerkin) code for analyzing square domains. The implementation features node generation using uniform grid distribution and employs moving least squares (MLS) approximation functions for shape function computation. Key algorithms include numerical integration via Gaussian quadrature over background cells and imposition of essential boundary conditions using penalty methods. The code calculates various physical phenomena within square domains, including stress distribution analysis through derivative computation of displacement fields, strain rate evaluation using kinematic relationships, and temperature distribution modeling via heat transfer equations. The meshless nature of EFG method eliminates element connectivity issues, making it particularly effective for problems involving large deformations and crack propagation. This implementation provides researchers with robust numerical tools to study material behavior and performance under different loading conditions, offering valuable insights for future computational mechanics research. The use of 2D MATLAB EFG code for square domain analysis thus represents a significant and practical research methodology in computational solid mechanics.