A Computationally Efficient Meshless Local Petrov-Galerkin Method for Axisymmetric Problems

The Meshless Local Petrov-Galerkin (MLPG) method is one of the recently developed element-free methods. The method is convenient and can produce accurate results with continuous secondary variables, but is more computationally expensive than the finite element method. To overcome this disadvantage, a simple Heaviside test function is chosen. The computational effort is significantly reduced by eliminating the domain integral for the axisymmetric potential problems and by simplifying the domain integral for the axisymmetric elasticity problems. The method is evaluated through several patch tests for axisymmetric problems and example problems for which the exact solutions are available. The present method yielded very accurate solutions. The sensitivity of several parameters of the method is also studied.