A Local Coordinate Approach in the MLPG Method for Beam Problems

System matrices for Euler-Bernoulli beam problems for the meshless local Petrov-Galerkin (MLPG) method deteriorate as the number of nodes in the beam models are consistently increased. The reason for this behavior is explained. To overcome this difficulty and improve the accuracy of the solutions, a local coordinate approach for the evaluation of the generalized moving least squares shape functions and their derivatives is proposed. The proposed approach retains the accuracy of the MLPG methods.