A COMPARISON BETWEEN NUMERICAL INTEGRATION TECHNIQUES IN MLPG-1 APPLIED TO 2D ELASTICITY PROBLEMS

JOAO PEDRO FRANCO DE MELLO¹; JOSE ANTONIO FONTES SANTIAGO¹

¹ COPPE/UFRJ

doi:10.20906/CPS/CILAMCE2017-0188

Resumo

Numerical integration in the local subdomains is the most complex process in the solution of problems by a truly meshless method, especially if the boundary of the local subdomain surpasses the global boundary of the problem. This paper proposes an alternative integration method and a comparison with the commonly used integration methods. The development of a new integration technique aims an increase in effectiveness, precision, and a reduction in the computational cost of the integration process. Numerical integration in MLPG is performed by quadrature techniques applied over local subdomains. One of the mostly used techniques is the Gauss quadrature. Traditionally, in order to apply the gaussian quadrature, Gauss points are created over the domain and the boundary of the local subdomains. Subsequently, new subdomains are created using the Gauss points as their central point, which are used as the quadrature's domain. Nonetheless, the traditional technique enforces some restrictions on the positioning of subdomains, avoiding the intersection of the subdomain boundary and the global problem boundary. These restrictions are necessary because the traditional method do not embrace subdomains with a circular segment geometry. This paper proposes a technique which adopts the subdomains created by the Moving Least Squares (MLS) method, used to find the shape functions, as the integration domain of the quadrature. Moreover, this technique can be applied to subdomains with a circular segment geometry.

Palavras-chave: MESHLESS; MLPG; NUMERICAL INTEGRATION