A. T. Vasilenko

Some Approaches to the Solution of Problems on Thin Shells with Variable Geometrical and Mechanical Parameters

A number of approaches to the solution of stress problems for anisotropic inhomogeneous shells in the classical formulation are discussed. A review is made of approaches to the solution of one- and two-dimensional static problems for thin shells with variable parameters and to the solution of stress–strain problems for anisotropic shells of revolution under axisymmetric and non-axisymmetric loading, shallow convexo-convex shells, noncircular cylindrical shells, plates of various shapes, and shells of complex geometry

Elastic Equilibrium of Circumferentially Inhomogeneous Orthotropic Cylindrical Shells of Arbitrary Thickness

An approach is proposed to determine the three-dimensional stress–strain state of hollow orthotropic cylinders with elastic characteristics variable in the circumferential direction. The solution of the problem is represented as a double Fourier series in the axial and circumferential coordinates. A resolving system of ordinary differential equations of high order is derived. An analysis is made of the stress state of a cylinder made of a composite with reinforcement density variable in the circumferential direction

Solving stress problems for elastic systems of anisotropic shells of revolution with regard for transverse shear and reduction

An approach is proposed for refined solution of stress problems for elastic systems consisting of coaxial shells of revolution. Transverse shear and reduction are taken into account. Multivariant calculations made for orthotropic cylindrical shells with elliptical end-plates allow us to analyze the influence of the semiaxis ratio and intermediate supports on the stress–strain state of the shell systems under consideration

Stress analysis of laminated shells of revolution with an imperfect interlayer contact

An approach is proposed to solve problems on the contact interaction of layers in structurally inhomogeneous shells of revolution with allowance for both the normal and tangential stresses in the contact zones. A system of algebraic equations is constructed by using a method for solution of static problems for arbitrary shells of revolution. From this system, the contact zones and contact stresses are determined by the iteration method. The restricted behavior of the adhesion layer in cleavage and shear is taken into account. As an example, the stress state of a two-layer cylindrical shell under a concentrated load is determined

Solving problems on the stress state of thin shells of revolution under local loads

An approach to the solution of problems on the deformation of locally loaded orthotropic shells of revolution is proposed. Some analytical transformations are carried out to reduce the initial resolving system of partial differential equations to the form where the constant terms representing the surface loads are continuous functions of the circumferential coordinate. This allows us to accelerate the convergence of the trigonometric series that represent the desired solution. One-dimensional boundary-value problems are solved by a stable numerical method. Examples of solving problems on the stress state of a cylindrical shell are presented.

Bending of an anisotropic elliptic plate on an elastic foundation

An approach is proposed to solve a stress–strain problem for anisotropic rigidly fixed plates on an elastic foundation. The problem is solved by the method of successive approximations. At each approximation, the deflection is represented as polynomials whose coefficients are determined from a system of linear algebraic equations. Study is made of the influence of the reinforcement angle and the modulus of subgrade reaction on the deflections and the bending moments in an orthotropic plate.

The Stress State of Stiffened Shallow Orthotropic Shells

An approach is proposed for stress analysis of elastic systems consisting of shallow shells having a rectangular planform and stiffened with rods in one direction. The shell curvature varying in the direction perpendicular to the ribs and piecewise-constant in another direction is taken into account. A system of ordinary differential equations and shell–rib conjugation conditions are derived after separation of variables for two simply supported opposite contours. A one-dimensional boundary-value problem is solved by a stable numerical method. The results of a stress–strain analysis of shipbuilding structural elements are presented as an example

Determination of the stressed state of three-layer cylindrical shells with allowance for layer separation

An approach is proposed for investigation of the stressed state of three-layer orthotropic cylindrical shells with allowance for possible layer separation. The regions of layer contact and separation and the contact-pressure distribution are found.

Stress Analysis of Anisotropic Inhomogeneous Shells of Revolution Subjected to Centrifugal Forces

An approach is proposed to analyze the stress state of thin shells of revolution under centrifugal loads with regard for anisotropy, the meridional variability of geometrical and mechanical parameters, and the eccentricity of the axis of revolution relative to the axis of geometric symmetry. Allowance is also made for the change in the dimensions of the shell due to deformation, which results in a nonaxisymmetric distribution of stresses and strains and their nonlinear dependence on the squared frequency of rotation. By separating variables, the problem is made one-dimensional and then solved numerically. The stress state of an ellipsoidal filament-winded composite shell is analyzed

Determination of the stress-strain state of anisotropic thermosensitive cylinders

In the three-dimensional formulation we study a class of problems involving the stressed state of an axisymmetrically heated anisotropic cylinder arbitrarily inhomogeneous over the thickness taking account of the dependence of mechanical characteristics on the temperature. The solution of the boundary-value problems is carried out numerically. We study the temperature and mechanical fields in composite cylinders.