A MESH FREE METHOD BASED ON AN OPTIMIZATION TECHNIQUE AND THE MOVING LEAST SQUARES APPROXIMATION
A mesh free method based on an optimization technique and the moving least-squares approximation is presented. In this method, the problem domain is modelled by a set of properly scattered points. Approximation functions are used to represent field variables and their derivatives. Like other mesh free methods, no mesh of elements is required. The other advantages are: prescribed displacements and tractions are imposed directly as a result of the minimization procedure, and there is no need to integrate the governing equations. The theory is developed for two-dimensional problems. As numerical examples of the proposed scheme, a cantilever beam and a Poisson equation are considered. The numerical results compare very well with the analytical solutions for these examples.
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