STABILITY NON-THIN ANISOTROPIC CONICAL SHELLS UNDER AXIAL COMPRESSION

Abstract

Cone structures in the form of cones are widely used in shipbuilding, aircraft construction, instrument making, rocket technology, construction, engineering, and many other industries. The use of laminated composite materials can enhance one of their main advantages - a combination of ease with high durability. When designing thin-walled shell designs one of the main steps is to calculate the stability.

The paper presents an approach to calculations for the stability of non-thin conical anisotropic membranes made from a material having a plane of elastic symmetry based on a refined theory of the Tymoshenko-Midline type. The material of which the shell is made has one plane of elastic symmetry, which is due to the rotation of the principal directions of elasticity of the output orthotropic material.

To construct equations that help determine the critical state of the shells associated with the phenomenon of bifurcation, we use the canonical system of equations for nonlinear deformation of symmetrically loaded non-thin anisotropic shells.

The problem of static stability of a symmetrically loaded elastic anisotropic rotation shell is reduced to a system of ten ordinary homogeneous differential equations in normal form with variable coefficients and homogeneous boundary conditions.

The method of solving the boundary value problem under consideration is based on the numerical method of discrete orthogonalization. The numerical methodology for calculating the task is implemented as a software package for the PC.

To represent the proposed method, we consider the problem of calculating the stability of a hinged conic shell made from boron plastic. Axial compression is applied to the shell. The results of the calculations are presented in the form of graphs illustrating the dependence of the magnitude of the critical value of the axial compression on the change in the angle of the composite winding and the angle of the shell conic. The obtained critical loads are compared with numerous calculations for the stability of anisotropic shells, using a technique that relies on the Kirchhoff-Love hypothesis.