Stress concentration in the region of a rec tangular hole on the side surface of a nonlinearly elastic orthotropic conical shell

Abstract

The formulation and development of a numerical method for solving physically nonlinear static problems for a composite conical shell weakened by a rectangular hole is given. Geometric relationships are written in the vector form according to the theory of non-stray shells, in which Kirchhoff-Love’s hypotheses take place, and physical ones are based on the deformation theory of plasticity of anisotropic media. The inversion of physical relations with respect to stresses is performed numerically — by the Newton method. The system of resolving equations in displacements is obtained from the Lagrange variational equation using the method of additional stresses and the modified finite element method. A feature of the proposed version of the finite-element method is the implementation of the vector form of approximations of the unknown quantities and the implementation of the geometric part of the Kirchhoff—Love hypotheses at the nodes of the final element. Using the developed technique, the effect of nonlinear elasticity of the material and the location of a rectangular hole relative to the ends on the stress concentration in an orthotropic conical shell loaded with axial tensile forces is investigated.