An antiplane crack problem for some kinds of regions

Abstract An antiplane crack problem for some kinds of regions is duscussed, while the regions consist of several rectangular subregions (Figs. 3, 5). When solving the Neumann problems of the Laplace equation, we divide the original considered region into several rectangular subregions. In addition, using a theorem of continuation of harmonic function, the solution on original region can be found. The procedure used here has a different form in place of that mentioned in our previous papers[1,2]. Using the energy release method, the K 3 values can be obtained. All numerical results are shown in Figs. 4, 6 and Tables 1 and 2 respectively. A format for deriving all basic relations is presented, which is of great importance to get all results cited below.