The aim of this work is to present a local meshless method (ILMF), developed at the Department of Civil and Environmental Engineering of the University of Brasilia, in the analysis of two-dimensional elastodynamic problems. Based on the weak formulation of weighted residue methods from the differential equations of dynamics, the approximation of the discretized elastic field is obtained through the method of moving least squares (MLS), generating a system of node-to-node equations in the local domain, globally compatible with the contribution of all nodes of the regular discretization adopted. The integration of the domain is computationally established in order to obtain the mass matrix, frequencies and eigenmodes of free vibration by solving the eigenvalue problem. Certified values in the literature are adopted, for the parameters used in determining the size of the compact support in the interpolation of the shape functions and integration domain. In time integration and forced vibration analysis, the Newmark method was adopted, comparing results obtained with the proposed formulations using routines programmed in MATLAB language. The influence of the dynamic response for various time intervals and the size of the influence domain a, is studied. Accuracy and efficiency of the method in elastodynamic problems is demonstrated through parametric analysis of a standard problem and comparing the responses obtained with a finite element model.
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