Investigation of the stress state of thick-walled cylindrical shells with nonuniform boundary conditions

1983 ◽  
Vol 19 (6) ◽  
pp. 494-498
Author(s):  
Ya. M. Grigorenko ◽  
N. D. Pankratova ◽  
L. D. Chupakha
Keyword(s):  
Stress State ◽  
Boundary Conditions ◽  
Cylindrical Shells

A Method for Obtaining Stresses and Displacements in Thick Cylindrical Shells Under Arbitrary Boundary Conditions

1973 ◽  
Vol 40 (1) ◽  
pp. 221-226 ◽  
Author(s):  
E. B. Golub ◽  
F. Romano
Keyword(s):  
Stress State ◽  
Variational Principle ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Cylindrical Shells ◽  
Present Theory ◽  
Bending Stress ◽  
Arbitrary Boundary ◽  
Elasticity Solutions ◽  
Circular Cylindrical Shells

This paper presents a means for obtaining both the stress and displacement states which appear in thick, circular, cylindrical shells under arbitrary load and boundary conditions. The governing differential equations and the associated boundary conditions are obtained by utilizing Reissner’s variational principle [6], the assumed form of the stress state containing, in addition to terms corresponding to conventional membrane and bending stress resultants, supplementary sets of self-equilibrating stress resultants. Comparison of results obtained from known elasticity solutions shows that the present theory accurately yields solutions for shells with radius-thickness ratios of the order of 3.0. Numerically computed here, for comparison purposes, is the axisymmetric, periodically spaced, band load problem of Klosner and Levine.

Buckling of Circular Cylindrical Shells Using a Displacement Function

1974 ◽  
Vol 96 (4) ◽  
pp. 1322-1327
Author(s):  
Shun Cheng ◽  
C. K. Chang
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
External Pressure ◽  
Displacement Function ◽  
Combined Loading ◽  
Trial Solution ◽  
Governing Differential Equation ◽  
Circular Cylindrical Shells ◽  
The Stability

The buckling problem of circular cylindrical shells under axial compression, external pressure, and torsion is investigated using a displacement function φ. A governing differential equation for the stability of thin cylindrical shells under combined loading of axial compression, external pressure, and torsion is derived. A method for the solutions of this equation is also presented. The advantage in using the present equation over the customary three differential equations for displacements is that only one trial solution is needed in solving the buckling problems as shown in the paper. Four possible combinations of boundary conditions for a simply supported edge are treated. The case of a cylinder under axial compression is carried out in detail. For two types of simple supported boundary conditions, SS1 and SS2, the minimum critical axial buckling stress is found to be 43.5 percent of the well-known classical value Eh/R3(1−ν2) against the 50 percent of the classical value presently known.

scholarly journals Vibration of rotating circular cylindrical shells with distributed springs

2021 ◽  
Vol 37 ◽  
pp. 346-358
Author(s):  
Fuchun Yang ◽  
Xiaofeng Jiang ◽  
Fuxin Du
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Shell Theory ◽  
Rotation Speed ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Governing Equations ◽  
Natural Response ◽  
Circular Cylindrical Shells ◽  
The Galerkin Method

Abstract Free vibrations of rotating cylindrical shells with distributed springs were studied. Based on the Flügge shell theory, the governing equations of rotating cylindrical shells with distributed springs were derived under typical boundary conditions. Multicomponent modal functions were used to satisfy the distributed springs around the circumference. The natural responses were analyzed using the Galerkin method. The effects of parameters, rotation speed, stiffness, and ratios of thickness/radius and length/radius, on natural response were also examined.

scholarly journals Узагальнення моделі Голанда і Рейсснера на випадок осьової симетрії

2021 ◽  
pp. 12-19
Author(s):  
Костянтин Петрович Барахов
Keyword(s):  
Stress State ◽  
Analytical Solution ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Bessel Functions ◽  
Classical Model ◽  
Adhesive Bond ◽  
Radial Coordinate ◽  
Round Hole ◽  
Normal Stresses

The purpose of this work is to create a mathematical model of the stress state of overlapped circular axisymmetric adhesive joints and to build an appropriate analytical solution to the problem. To solve the problem, a simplified model of the adhesive bond of two overlapped plates is proposed. The simplification is that the movement of the layers depends only on the radial coordinate and does not depend on the angular one. The model is a generalization of the classical model of the connection of Holland and Reissner in the case of axial symmetry. The stresses are considered to be evenly distributed over the thickness of the layers, and the adhesive layer works only on the shift. These simplifications allowed us to obtain an analytical solution to the studied problem. The problem of the stress state of the adhesive bond of two plates is solved, one of which is weakened by a round hole, and the other is a round plate concentric with the hole. A load is applied to the plate weakened by a round hole. The discussed area is divided into three parts: the area of bonding, as well as areas inside and outside the bonding. In the field of bonding, the problem is reduced to third- and fourth-order differential equations concerning tangent and normal stresses, respectively, the solutions of which are constructed as linear combinations of Bessel functions of the first and second genera and modified Bessel functions of the first and second genera. Using the found tangential and normal stresses, we obtain linear inhomogeneous Euler differential equations concerning longitudinal and transverse displacements. The solution of the obtained equations is also constructed using Bessel functions. Outside the area of bonding, displacements are described by the equations of bending of round plates in the absence of shear forces. Boundary conditions are met exactly. The satisfaction of marginal conditions, as well as boundary conditions, leads to a system of linear equations concerning the unknown coefficients of the obtained solutions. The model problem is solved and the numerical results are compared with the results of calculations performed by using the finite element method. It is shown that the proposed model has sufficient accuracy for engineering problems and can be used to solve problems of the design of aerospace structures.

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