Influence of Shear Loading on the Shapes of Optimal Holes in a Quasi-Orthotropic Plate

We develop an analytic-numerical algorithm for the determination of the optimal shape of smooth holes (with minimum stress concentration) in quasiorthotropic plates subjected to biaxial tension and shear at infinity. We solved the inverse problems of the theory of elasticity for quasiorthotropic bodies with unknown boundaries. To do this, we use the effective solutions of the corresponding direct problems obtained by the method of singular integral equations. The solution of the inverse problem with unknown shape of the hole is reduced to the minimization of the multiparameter functional of standard deviations of tensile stresses along the contour of the hole from their averaged values. We determine the shapes of optimal holes in quasiorthotropic plate for different types of biaxial tensions and shears at infinity and the degree of its orthotropy.