A thesis submitted in partial fulfillment of the requirements for the degree of Master of Engineering, School of Civil Engineering

Thesis (M.Eng.) - Asian Institute of Technology, 2001

A meshless local Petrov-Galerkin method that employs polygonal nodal sub-domains constructed from several triangular patches rather than the typically used circular sub-domains is presented. Moving least-squares approximation is used as the trial functions while linear Lagrange interpolation functions are used as the test functions. In the MLPG method, redescritization of the problem domain is relatively simple as compared to the finite element methods, and therefore an adaptive technique to improve the accuracy of approximate solutions with a minimum of extra computational cost is developed. The adaptive MLPG method, which considers with local error assessment and placement of additional nodes, is the focus of this study. Two refinement indicators, a local L2-norm of displacement error and an approximate effective stress gradient are introduced. Additional nodes are placed at the middle of each of the edges of the patch which exceeds the prescribed error level. A method to vary the domain of influence (DOI) adaptively is also proposed in this study. Numerical examples show that the adaptive MLPG method performs well. The combination of the effective stress gradient error indicator and the variable DOI was found to provide exceptional accuracy at a highly reduced computational cost.