Novel weight function approach for plane elasticity crack problem

摘要

A novel weight function approach for the plane elasticity crack problem is suggested in this paper. In the case of boundary traction being in equilibrium, the obtained weight function for evaluating the stress intensity factors does not depend on the elastic constant in its appearance. To complete derivation, a singular field called the β_1-field is introduced, which has an order of O (r~-1/2) for the displacements and O(r~-3/2) for the stresses at the vicinity of the crack tip. We also introduce a complementary regular field, called the β_2-field, in which the applied boundary tractions are opposite to those derived from the β_1-field.