A LOCAL MESHLESS ANALYSIS OF DYNAMICS PROBLEMS

Resumo

This paper is concerned with new formulations of local meshfree numerical method, for the solution of
dynamic problems in linear elasticity, Integrated Local Mesh Free (ILMF) method. The key attribute of local
numerical methods is the use of a modeling paradigm based on a node-by-node calculation, to generate the rows
of the global system of equations of the body discretization. In the local domain, assigned to each node of a
discretization, the work theorem is kinematically formulated, leading thus to an equation of mechanical
equilibrium of the local node, that is used by local meshfree method as the starting point of the formulation. The
main feature of this paper is the use of a linearly integrated local form of the work theorem. The linear reduced
integration plays a key role in the behavior of local numerical methods, since it implies a reduction of the nodal
stiffness which, in turn, leads to an increase of the solution accuracy. As a consequence, the derived meshfree and
finite element numerical methods become fast and accurate, which is a feature of paramount importance, as far as
computational efficiency of numerical methods is concerned. The cantilever beam was analyzed with this
technique, in order to assess the accuracy and efficiency of the new local numerical method for dynamic problems
with regular and irregular nodal configuration. The results obtained in this work are in perfect agreement with
Mesh-Free Local Petrov-Galerkin (MLPG) and the Finite Element Method (FEM) solutions.