Meshless MLPG Method Source Code for Cantilever Beam with Concentrated Load

This article presents a novel meshless MLPG (Meshless Local Petrov-Galerkin) method for solving concentrated load problems in cantilever beam structures. The core methodology utilizes mass-point based discretization coupled with material point motion equations to simulate stress and strain distributions in beams. Key implementation aspects include node generation algorithms that eliminate traditional mesh dependencies, and local weak form formulations that use radial basis functions for field approximations. The primary advantage lies in significant reduction of grid elements, thereby enhancing computational efficiency while minimizing meshing constraints. The MLPG framework employs numerical integration techniques over local subdomains and implements penalty methods for essential boundary conditions. This meshless approach demonstrates broad applicability across engineering domains including seismic engineering, aerodynamics, and combustion engineering. The methodology's flexibility in handling large deformations and complex geometries makes it particularly suitable for multi-physics simulations, indicating substantial potential for addressing diverse engineering challenges.