In this research a new meshless method is proposed to solve linear two dimensional elasticity and steady state heat conduction as well as materially nonlinear solid problems. The new method is based on a subdomain collocation approach. The governing equations are weakly satisfied on the boundaries of the subdomains. The integrals are calculated analytically to reduce the calculation time. The method in one hand is based on a weak formulation, leading to more accuracy, and on the other hand avoids numerical integrations (which decreases the computational costs). The subdomains do not necessary cover the whole domain. The optimum size of the subdomains is determined through an optimization technique. However, by further reducing the size of the subdomains the governing equations are satisfied in small zones in a manner similar to Finite Point Method (FPM). Therefore the method is named as the “Generalized Finite Point Method (GFPM)”. The method has been further extended to solve nonlinear plasticity problems. Regarding storing the history dependent state variables and computing the required integrals, two different strategies are proposed. In the first one which uses Gauss points, the integrant values in all integration points are calculated using only one cloud constructed around the central point of the subdomain. The second method utilizes the stress components at the nodes where other state variables are also stored. One of the important features of the latter method is that a set of closed form integrals are obtainable for boundary integrals. This leads to significant reduction of the computational cost in comparison with other integral based meshless methods. Since the accuracy of the two procedures depends on the size of the subdomains, the optimal sizes are found by a series of patch tests. In linear elastic and heat problems, the results of the numerical solution of some benchmark problems show that the method can compete with the finite element method in terms of robustness and computational cost. In nonlinear problems, both proposed strategies show similar accuracies in prediction of displacement field but the first strategy with numerical integration gives slightly more accurate results for stress field. Key words: finite point method, subdomain collocation, steady state heat conduction, materially nonlinear, plane strain, patch test.
