Optimization of Meshless Local Petrov-Galerkin Parameters using Genetic Algorithm for 3D Elasto-static Problems (TECHNICAL NOTE)

A truly Meshless Local Petrov-Galerkin (MLPG) method is developed for solving 3D elasto-static problems. Using the general MLPG concept, this method is derived through the local weak forms of the equilibrium equations, by using a test function, namely, the Heaviside step function. The Moving Least Squares (MLS) are chosen to construct the shape functions. The penalty approach is used to impose essential boundary conditions. The complete study of the effects of radius of support domain on the accuracy and efficiency of the solution is performed. The values of this parameter leave a great effect on runtime and accuracy. The Genetic Algorithm (GA) is used to determine the optimum values of this MLPG parameter to minimize the runtime and maximize the accuracy. Several numerical examples are included to demonstrate that the present method is very promising for solving the elasto-elastic problems.