Evaluation Of Numerical Quadratures For The Element Stiffness Matrix of Finite elements

Abstract

The finite element method is a numerical technique for solving engineering newlineproblems. Solving problems in finite element analysis needs more computational newlineefforts because of handling large varying data. The element stiffness matrix newlineembodies the primary properties of a finite element. For a structural finite element, newlinethe stiffness matrix contains the geometric and material behavior information that newlineindicates the resistance of the element to deform when subjected to loading. newlineSampling points and weighting factor play a key role in the calculation of element newlinestiffness matrix because it needs to deal with large varying data with more accuracy. newlineThe expressions for the integration of element stiffness matrices and load vectors newlinefor the general case of finite elements cannot be done analytically. Instead, load newlinevectors and element stiffness matrices are numerically evaluated using some newlineintegration rule. For different types of finite elements, numerical integration newlinemethods are used to estimate element matrices and vectors. The present research newlinework proposes four simple quadrature methods for evaluating the element stiffness newlinematrix of finite elements such as triangular, quadrilateral, hexahedral, and newlinetetrahedral elements. The corner center point method (CCPM) is the first quadrature method proposed, newlinewith sampling points are located at the corners and center of the assumed interior newlineelement. The edge center point method (ECPM) is the second proposed quadrature method, with sampling points are located at the assumed interior element edges and newlinecenter. The corner edge point method (CEPM) is the third proposed quadrature newlinemethod, with sampling points are located at the assumed interior element edges and newlinecorners. The corner face center point method (CFCPM) is the fourth proposed newlinequadrature method, with sampling points are located at the assumed interior newlineelement edges and face center.