Stress–Strain State of Flexible Orthotropic Cylindrical Shells with a Reinforced Circular Hole

Abstract

The stress-strain state of flexible orthotropic cylindrical shells with a reinforced circular hole under static loading is analyzed numerically. The incremental-loading procedure, modified Newton-Kantorovich method, and finite-element method are used. The effect of geometrical nonlinearity, the orthotropy of the material, and the stiffness of the reinforcement in a shell subject to uniform internal pressure on the distribution of stresses, strains, and displacements along the hole edge and in the zone of their concentration is studied Keywords: flexible orthotropic cylindrical shell, geometrical nonlinearity, stress concentration, reinforced circular hole, finite deflections, internal pressureIntroduction. Traditionally, a shell with a reinforced hole is considered as a structure that consists of the shell proper and a one-dimensional thin rod reinforcing it. The stress-strain state (SSS) of each of these components is described by an applied theory and has its peculiarities. Therefore, the development of a theory that describes the SSS of shells with reinforced holes involves difficulties associated with the necessity of describing the combined action of components with different dimensionality and satisfying the interface conditions [4,7]. Note that the same difficulties are encountered in studying the SSS of ribbed shells [3,6,12,17].Most results on stress concentration in isotropic and anisotropic shells with reinforced holes were obtained by solving linear elastic problems with analytic, variational, and numerical methods and are reviewed in [4,7,11,16].Much fewer studies are concerned with nonlinear boundary-value problems of stress concentration, but mainly for shells of revolution under an axisymmetric load [4, 10, 13].Very few publications report on solution of nonlinear two-dimensional problems for shells with reinforced holes. For example, the effect of plastic strains and finite deflections on the SSS of isotropic shells with a reinforced curved hole was analyzed in [7,20]. A nonclassical approach to the design of thin composite shells with reinforced curved holes that employs the same formulas for the shell and the reinforcement was proposed in [14], where some numerical results on the nonlinear deformation of a flexible orthotropic cylindrical shell with a reinforced circular hole under uniform internal pressure are presented.It is of considerable interest to study the effect of a reinforced hole on the stability of composite shells [9,18,19].In what follows, we will use the approach described in [14] to formulate geometrically nonlinear problems for thin orthotropic cylindrical shells with a reinforced circular hole, outline a numerical method for solving this class of problems, and study the effect of geometrical nonlinearity, the orthotropy of the material, and the stiffness of the reinforcement on the distribution of displacements, strains, and stresses in the zone of their concentration.1. Problem Formulation. Basic Nonlinear Equations. Consider a thin cylindrical shell of radius R and thicknes...