Meshless formulation and parameters study for an elastic bar problem

A recent strong interest in computational methods is in developing and exploring Mesh less Methods as an alternative numerical technique to other grid based methods like Finite Element Method. Meshfree methods are expected to be more adaptive and flexible in solving fracture mechanics and large deformation problems where Finite Element Method (FEM) is not suitable. Meshless Local Petrov Galerkin (MLPG) method is one of the popular meshfree technique based on a local weak form of the governing differential equation and employs shape functions derived from Moving Least Square (MLS) approximants. Present work demonstrates application of MLPG to an elastic bar problem with linear body force and investigates effect of some significant parameters on solution accuracy in MLPG formulation. These parameters include order of monomial basis function and weight function selection while constructing MLS shape functions, number of nodes in the problem domain (uniform and non-uniform distribution), size of support domain and sub-domain and different Gauss quadrature integration schemes. Axially loaded elastic bar problem is selected for clarity and unambiguous presentation. MLPG results are compared and validated with exact solution and FEM. It is also shown that MLPG stress results are continuous in the domain while FEM stress results are discontinuous at element boundary.