BOUNDARY PROBLEMS OF THE THEORY OF THIN AND NONTHIN ORTHOTROPIC SHELLS WITH ACCOUNT OF NONLINEAR ELASTIC PROPERTIES AND LOW SHEAR RIGIDITY OF COMPOSITE MATERIALS

摘要

The basic geometric and physical relations and resolving equations of the theory of thin and nonthin orthotropic composite shells with account of nonlinear properties and low shear rigidity of their materials are presented. These are derived based on two theories, namely the theory of anisotropic shells, which employs the Timoshenko or Kirchhoff-Love hypotheses, and the nonlinear theory of elasticity and plasticity of anisotropic media and the Lagrangian variational principle. The procedure and algorithm for a numerical solution of the nonlinear (linear) problems are based on the successive approximation method, difference-variational method, and Lagrangian multiplier method. Calculations of the stress-strain state for a spherical shell with a circular hole loaded by internal pressure are presented. The effect of transverse shear strains and physical nonlinearity of the material on the distribution of maximum deflections and circumferential stresses in the shell, obtained according to two variants of the shell theories, is studied. A comparison of the results of the problem solution in linear and nonlinear statements with and without account of the shell shear strains is given. The numeric data obtained for the thin and nonthin (of average thickness) composite shells are analyzed.