Axial tension of nonlinear elastic composite shells of zero Gaussian curvature with a rectangular hole

Abstract

The formulation of physically nonlinear problems for composite shells of zero Gaussian curvature weakened by a rectangular hole under the action of axial loading is given. The initial equations are the equations of the theory of non-sloping shells, in which the Kirchhoff–Love hypotheses take place. Geometric relationships are written in vector form, and physical relationships are based on the deformation theory of plasticity for anisotropic materials. The system of resolving equations is obtained from the Lagrange variational principle. A technique has been developed for the numerical solution of two-dimensional physically nonlinear problems for orthotropic composite shells of this type, based on the use of the method of additional stresses and the method of finite elements. A variant of the finite element method is proposed, the peculiarity of which lies in the vector approximation of the sought values and the discrete execution of the geometric part of the Kirchhoff–Love hypotheses (at the nodes of finite elements). Using the developed technique, the nonlinear elastic state of an organoplastic conical shell with a rectangular hole, which at the ends is reinforced with frames and loaded with uniformly distributed tensile forces, has been investigated.