Author(s)

WILBER VELEZ, THIAGO ARAUJO, ARTUR PORTELA

Abstract

The Meshfree Method with reduced integration (ILMF) is derived through the work theorem of structures theory. In the formulation of the ILMF, the kinematically-admissible strain field is an arbitrary rigid-body displacement; as a consequence, the domain term is canceled out and the work theorem is reduced to regular local boundary terms only. The moving least squares (MLS) approximation of the elastic field is used to construct the trial function in this local meshfree formulation. ILMF has a high performance in problems with irregular nodal arrangement leading to accurate numerical results. This paper presents the size effect of the irregularity nodal arrangement parameter (c_n) on three different nodal discretization to solve the Timoshenko cantilever beam using values fixed for the local support domain (α_s) and the local quadrature domain (α_q). Results obtained are optimal for 2D plane stress problems when compared with the exact solution.

Keywords

work theorem, reduced integration, local meshless method