The Buckling of Cylindrical Shells Under Longitudinally Varying Loads

1962 ◽  
Vol 29 (1) ◽  
pp. 81-85 ◽  
Author(s):  
V. I. Weingarten
Keyword(s):  
Compressive Stress ◽  
Solid Propellant ◽  
Cylindrical Shells ◽  
Longitudinal Direction ◽  
External Pressure ◽  
Circular Cylinders ◽  
Shear Load ◽  
Curvature Parameter ◽  
Axial Compressive Stress ◽  
The Stability

Two problems illustrating the effect of nonuniformity of loading on the buckling characteristics of circular cylinders are investigated. The first problem deals with the effect of linearly varying axial compressive stress, such as would be produced by the weight of the propellant in a solid-propellant engine case. The results indicate that the ratio of the maximum critical compressive stress induced by the shear load to the critical uniform compressive stress varies from 1.9 for the curvature parameter Z equal to 0 to 1.0 as Z becomes infinite. In particular, the increase in stress is less than 20 per cent for Z greater than 100. The stability of thin cylinders loaded by lateral external pressure, varying linearly in the longitudinal direction, is also investigated. The results indicate that for Z greater than 100, the buckling coefficients are proportional to Z1/2.

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.

Stability Analysis of Cylindrical Shells Resting on Winkler Elastic Foundation Using Semi-Analytical Quadrature Element Method

2019 ◽  
Vol 821 ◽  
pp. 459-464
Author(s):  
Qi Gao Hu ◽  
Xu Dong Hu ◽  
Zhi Qiang Shen ◽  
Liang Yun Tao ◽  
Ze Tan
Keyword(s):  
Elastic Foundation ◽  
Cylindrical Shells ◽  
Longitudinal Direction ◽  
External Pressure ◽  
Element Formulation ◽  
Quadrature Element Method ◽  
Advanced Composite Materials ◽  
Winkler Elastic Foundation ◽  
Parametric Studies ◽  
Element Method

The buried pipelines or vessels and other similar structures made of homogeneous or advanced composite materials are commonly used in civil engineering and biotechnology. The radial stability problem of these structures was widely studied using the cylindrical shell model over the past years. In this paper, the linear stability of cylindrical shells resting on Winkler elastic foundation under uniformly distributed external pressure was analyzed with semi-analytical quadrature element method (QEM). As for the longitudinal direction, the radial deflection of shell was approximated by the quadrature element formulation. While the analytic trigonometric function was adopted for description of radial deflection in circumferential direction. The Numerical results of critical buckling load were compared with the semi-analytical FEM. It is found that the semi-analytical QEM possesses higher computational efficiency and applicability than semi-analytical FEM. Then, the effects of the shell length, radius, and thickness on the critical buckling pressures are systematically investigated through the parametric studies.

On the Buckling of Circular Cylindrical Shells Under Pure Bending

1961 ◽  
Vol 28 (1) ◽  
pp. 112-116 ◽  
Author(s):  
Paul Seide ◽  
V. I. Weingarten
Keyword(s):  
Galerkin Method ◽  
Compressive Stress ◽  
Cylindrical Shells ◽  
Bending Stress ◽  
Pure Bending ◽  
Circular Cylindrical Shells ◽  
The Stability ◽  
The Galerkin Method

The stability of circular cylindrical shells under pure bending is investigated by means of Batdorf’s modified Donnell’s equation and the Galerkin method. The results of this investigation have shown that, contrary to the commonly accepted value, the maximum critical bending stress is for all practical purposes equal to the critical compressive stress.

On the Linear Buckling of Circular Cylindrical Shells Under Asymmetric Axial Compressive Stress Distributions

1966 ◽  
Vol 70 (672) ◽  
pp. 1095-1097 ◽  
Author(s):  
D. J. Johns
Keyword(s):  
Compressive Stress ◽  
Cylindrical Shells ◽  
Bending Moment ◽  
Transverse Load ◽  
Stress Distributions ◽  
Pure Bending ◽  
Linear Buckling ◽  
Circular Cylindrical Shells ◽  
Axial Compressive Stress

The linear buckling of circular cylindrical shells is considered with particular attention to the cantilever shell subjected to either a pure bending moment (M) or transverse load (P)—see Fig. 1. It is believed that the conclusions reached have wider application to more general loading cases.

Buckling of Locally Loaded Isotropic, Orthotropic, and Composite Cylindrical Shells

1988 ◽  
Vol 55 (2) ◽  
pp. 425-429
Author(s):  
Wei Xiao ◽  
Shun Cheng
Keyword(s):  
Differential Equation ◽  
Critical Loads ◽  
Cylindrical Shells ◽  
External Pressure ◽  
Local Loading ◽  
Eighth Order ◽  
Governing Differential Equation ◽  
The Stability ◽  
First Time ◽  
Composite Cylindrical Shells

This paper incorporates an analysis of the stability of orthotropic or isotropic cylindrical shells subjected to external pressure applied over all or part of their surfaces. An eighth-order governing equation for buckling of orthotropic, isotropic, and composite cylindrical shells is deduced. This governing differential equation can facilitate the analysis and enable us to resolve the buckling problem. The formulas and results, deduced for the first time in this paper, may be readily applied in determining critical loads for local loading of orthotropic, isotropic, and composite cylindrical shells.

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