Evaluation of Coefficients of Mode III Crack-Tip Asymptotic Fields Using Weak Form Quadrature Elements

A weak form quadrature element formulation is established to obtain the coefficients of Mode III crack-tip asymptotic fields. The problem domain is divided into circular subdomains near the crack tips and several integrable normal subdomains elsewhere. The total potential energy of the crack problem is given using the displacement expressions in circular subdomains and nodal displacements in normal subdomains. Accordingly, the minimum potential energy principle is employed to establish algebraic equations. Coefficients of any order, which are part of the unknowns of the algebraic equations, are solved for from the equations. Several benchmark examples are examined to validate the present formulation, showing high effectiveness in evaluation of coefficients of Mode III eigenfunction expansion.