Exact solutions for anti-plane deformation of a cylindrically monoclinic wedge under concentrated loads

摘要

This article studies anti-plane deformation of a cylindrically monoclinic wedge under concentrated loads. To the best of the author's knowledge, exact solutions to this type of wedge problem under concentrated loads are not available in the literature. By applying a newly defined argument to the displacements in terms of a holomorphic function in cooperation with a complex analogous Mellin transform, the exact solutions for the considered problems are obtained. The novel arrangements greatly simplify the formulation and result in concise complex shear stress equations that can be solved. With prescribed boundary settings, the closed-form solutions for Green's functions can be derived conveniently. Exact solutions are obtained for two kinds of boundary conditions. The stress fields obtained from the two cases are presented and discussed for certain combinations of anisotropic parameters. Contours of the generalized stress intensity factor, which is related to the direction of approach to the wedge apex and the material properties, are also shown. In addition, the results of a problem with distributed loads agree well with numerical solutions. The proposed method clarifies and simplifies the analysis and solution of related wedge problems. In determining the reduced orthotropic and isotropic cases to solutions under anti-plane deformation, the results are generated naturally.