An approach to solution of three-dimensional physically nonlinear problems in the statics of noncircular elastic cylinders

Abstract

physically nonlinear problems in elasticity theory for canonical domains. Some questions concerning its practical convergence have been investigated in [15]. The paper [10] is devoted to combined application of the first variant of the method of perturbation of the shape of a boundary [2,7] and the approach in [91 for solving three-dimensional physically nonlinear boundary-value problems for bodies of revolution with a closed contour for the meridional cross section which is nearly circular. In this paper, we consider three-dimensional nonlinear botmdary-value problems for elastic bodies with noncircular cylindrical bounding surfaces (in particular, continuous and composite noncircular cylinders, and also a layer with a free and reinforced noneircular cylindrical cavity or rigid inclusion). We assume that the contour of the transverse cross section of the surface of the cylinder is sufficiently smooth and nearly circular. 1. Formulation of the Problem and Initial Equations. We assume that as the intensity of the external load and the temperature T increase, the stress-strain diagram deviates from the linear behavior described by Hooke's law. For an active load, such mechanical behavior may be satisfactorily described by nonlinear relationships between the stresses oij and the small strains e# in the form in [51, which we represent as