Analysis of 2D Problems Resorting to a New Meshless Method

A new tmly meshless method is presented. The interntion backgound mesh is entirely constructed based on the nodal mesh, which discretize the problem domain. The method guaranties the nodal connectivity by searching the closest nodes for each interest point as in the Natural Neighbour Methods [1, 2]. The basic equations of the 2-Dimensional plane stress problem theory represented and a description of the shape functions to be used in the variational form of the equilibrium equations is made. The shape functions are constructed based in Euclidean norms, taking into account simple geometrical considerations. It is shown that the presented shape functions respect the delta Kronecker propelty. In order to enforce the boundq conditions the Lagange Multiplier method is applied. A computational cost comparison is made between the new meshless method, the Finite Element Method and the Radial Point Interpolation Method [3], which is another meshless method that uses interpolation functions. The results show the low computational cost of the new meshless method. Optimization tests and several examples of well-known solid mechanics problems are solved and compared with the fmite element method in order to prove the high accuracy and convergence rate of the method. Results show that the new meshless method is a good alternative to the fmite element method.