Computation of Coefficients of Crack-Tip Asymptotic Fields Using the Weak Form Quadrature Element Method

Abstract

Coefficients of crack-tip asymptotic fields are computed using a recently developed weak form quadrature element method (QEM), combined with the subregion generalized variational principle. The variational description of a crack is established by dividing the domain into two regions, the potential energy region and the complementary energy region. Then the weak form QEM is employed to derive a system of algebraic equations. The coefficients are extracted directly from solving the equations. The accuracy, efficiency, and parameter sensitivity of the proposed method are discussed by solving a number of benchmark examples. The computed results are in very good agreement with available analytical or numerical results. The involved parameters can be adjusted according to convergence requirements. Thus, the method enjoys the advantages of straightforwardness and self-adaptivity.