Buckling of a spherical shell embedded in an elastic medium loaded by a far-field hydrostatic pressure

2001 ◽  
Vol 36 (6) ◽  
pp. 535-544 ◽  
Author(s):  
S-L Fok ◽  
D. J Allwright
Keyword(s):  
Hydrostatic Pressure ◽  
Spherical Shell ◽  
Critical Load ◽  
Elastic Medium ◽  
Upper Bound ◽  
Mode Number ◽  
Elastic Buckling ◽  
Far Field ◽  
Buckling Mode ◽  
Geometric Constants

Elastic buckling of a spherical shell, embedded in an elastic material and loaded by a far-field hydrostatic pressure is analysed using the energy method together with a Rayleigh—Ritz trial function. For simplicity, only axisymmetric deformations are considered and inextensional buckling is assumed. The strains within the structure that are pre-critical are assumed to be small for the linear theory to be applicable. An expression is derived relating the pressure load to the buckling mode number, from which the upper-bound critical load can be determined. It is found that the presence of the surrounding elastic medium increases the critical load of the shell and the corresponding buckling mode number. However, the results also show that the strain of the shell at the point of instability may not be small for typical values of material and geometric constants.

Analysis of the buckling of long cylindrical shells embedded in an elastic medium using the energy method

2002 ◽  
Vol 37 (5) ◽  
pp. 375-383 ◽  
Author(s):  
S. L Fok
Keyword(s):  
Cylindrical Shell ◽  
Hydrostatic Pressure ◽  
Linear Elasticity ◽  
Energy Method ◽  
Surrounding Medium ◽  
Far Field ◽  
Buckling Mode ◽  
Linear Elasticity Theory ◽  
Present Solution ◽  
Long Cylindrical Shell

Buckling of a long cylindrical shell, embedded in an elastic material and loaded by a far-field hydrostatic pressure, is reanalysed using the energy method together with a Rayleigh-Ritz trial function. For simplicity, linear elasticity theory is employed and inextensional buckling is assumed. An expression is derived relating the pressure load to the buckling mode number, from which the critical load can be determined. The solution is similar to that given by Forrestal and Hermann using a more elaborate approach. However, the present solution predicts lower buckling load if Poisson's ratio of the surrounding medium is less than 0.5 and hence seems to provide better agreement with experiments.

Dynamic Buckling of Cylindrical Shells under Axial Impact in Hamiltonian System

2012 ◽  
Vol 13 (1) ◽  
Author(s):  
Jia-Bin Sun ◽  
Xin-Sheng Xu ◽  
Chee-Wah Lim
Keyword(s):  
Hamiltonian System ◽  
Critical Load ◽  
Impact Load ◽  
Dynamic Buckling ◽  
Inertia Force ◽  
Elastic Cylindrical Shell ◽  
Symplectic Method ◽  
Buckling Mode ◽  
Axial Impact ◽  
Dual Variables

AbstractIn this paper, the dynamic buckling of an elastic cylindrical shell subjected to an axial impact load is analyzed in Hamiltonian system. By employing a symplectic method, the traditional governing equations are transformed into Hamiltonian canonical equations in dual variables. In this system, the critical load and buckling mode are reduced to solving symplectic eigenvalues and eigensolutions respectively. The result shows that the critical load relates with boundary conditions, thickness of the shell and radial inertia force. And the corresponding buckling modes present some local shapes. Besides, the process of dynamic buckling is related to the stress wave, the critical load and buckling mode depend upon the impacted time. This paper gives analytically and numerically some new rules of the buckling problem, which is useful for designing shell structures.

On the elastic buckling of cross-ply composite closed cylindrical shell under hydrostatic pressure

2021 ◽  
Vol 227 ◽  
pp. 108633
Author(s):  
Muhammad Imran ◽  
Dongyan Shi ◽  
Lili Tong ◽  
Ahsan Elahi ◽  
Muqeem Uddin
Keyword(s):  
Cylindrical Shell ◽  
Hydrostatic Pressure ◽  
Elastic Buckling ◽  
Closed Cylindrical Shell

Buckling of Multiple-Bay Ring-Reinforced Cylindrical Shells Subject to Hydrostatic Pressure

1953 ◽  
Vol 20 (4) ◽  
pp. 469-474
Author(s):  
W. A. Nash
Keyword(s):  
Cylindrical Shell ◽  
Hydrostatic Pressure ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Middle Surface ◽  
Elastic Buckling ◽  
Elastic Instability ◽  
Total Potential ◽  
External Forces ◽  
Work Done

Abstract An analytical solution is presented for the problem of the elastic instability of a multiple-bay ring-reinforced cylindrical shell subject to hydrostatic pressure applied in both the radial and axial directions. The method used is that of minimization of the total potential. Expressions for the elastic strain energy in the shell and also in the rings are written in terms of displacement components of a point in the middle surface of the shell. Expressions for the work done by the external forces acting on the cylinder likewise are written in terms of these displacement components. A displacement configuration for the buckled shell is introduced which is in agreement with experimental evidence, in contrast to the arbitrary patterns assumed by previous investigators. The total potential is expressed in terms of these displacement components and is then minimized. As a result of this minimization a set of linear homogeneous equations is obtained. In order that a nontrivial solution to this system of equations exists, it is necessary that the determinant of the coefficients vanish. This condition determines the critical pressure at which elastic buckling of the cylindrical shell will occur.

scholarly journals OPTIMUM BUCKLING DESIGN OF CYLINDRICAL STIFFENER SHELL UNDER EXTERNAL HYDROSTATIC PRESSURE

2018 ◽  
Vol 18 (2) ◽  
pp. 239-252 ◽  
Author(s):  
Rawa Hamed M. Al-Kalali
Keyword(s):  
Hydrostatic Pressure ◽  
Numerical Optimization ◽  
Collapse Load ◽  
Ansys Software ◽  
External Hydrostatic Pressure ◽  
Buckling Mode ◽  
Design Elements ◽  
Design Variables ◽  
Thick Cylinder ◽  
Strength Constraints

This paper present an investigation of the collapse load in cylinder shell under uniformexternal hydrostatic pressure with optimum design using finite element method viaANSYS software. Twenty cases are studied inclusive stiffeners in longitudinal and ringstiffeners. Buckling mode shape is evaluated. This paper studied the optimum designgenerated by ANSYS for thick cylinder with external hydrostatic pressure. The primarygoal of this paper was to identify the improvement in the design of cylindrical shell underhydrostatic pressure with and without Stiffeners (longitudinal and ring) with incorporativetechnique of an optimization into ANSYS software. The design elements in this researchwas: critical load, design variable (thickness of shell (TH), stiffener’s width (B) andstiffener’s height (HF). The results obtained illustrated that the objective is minimizedusing technique of numerical optimization in ANSYS with optimum shell thickness andstiffener’s sizes. In all cases the design variables (thickness of shell) was thicker than themonocoque due to a shell’s thicker is essential to achieve the strength constraints. It can beconcluded that cases (17,18,19, and 20) have more than 90% of un-stiffened critical load.The ring stiffeners causes increasing buckling load than un-stiffened and longitudinalstiffened cylinder.

Dynamic Buckling of Cylindrical Shells under Axial Impact in Hamiltonian System

2012 ◽  
Vol 13 (1) ◽  
Author(s):  
Jia-Bin Sun ◽  
Xin-Sheng Xu ◽  
Chee-Wah Lim
Keyword(s):  
Hamiltonian System ◽  
Critical Load ◽  
Impact Load ◽  
Dynamic Buckling ◽  
Inertia Force ◽  
Elastic Cylindrical Shell ◽  
Symplectic Method ◽  
Buckling Mode ◽  
Axial Impact ◽  
Dual Variables

AbstractIn this paper, the dynamic buckling of an elastic cylindrical shell subjected to an axial impact load is analyzed in Hamiltonian system. By employing a symplectic method, the traditional governing equations are transformed into Hamiltonian canonical equations in dual variables. In this system, the critical load and buckling mode are reduced to solving symplectic eigenvalues and eigensolutions respectively. The result shows that the critical load relates with boundary conditions, thickness of the shell and radial inertia force. And the corresponding buckling modes present some local shapes. Besides, the process of dynamic buckling is related to the stress wave, the critical load and buckling mode depend upon the impacted time. This paper gives analytically and numerically some new rules of the buckling problem, which is useful for designing shell structures.

A comprehensive time-domain elasto-acoustics study of a fluid-filled spherical shell embedded in an elastic medium

2020 ◽  
Vol 132 ◽  
pp. 106002
Author(s):  
Ako Bahari ◽  
Gaëlle Lefeuve-Mesgouez ◽  
Arnaud Mesgouez ◽  
Neil Popplewell
Keyword(s):  
Spherical Shell ◽  
Elastic Medium ◽  
Time Domain

scholarly journals Elastic buckling of thin plate with circular holes in bending

2019 ◽  
Vol 136 ◽  
pp. 04043
Author(s):  
Guo Yanli ◽  
Song Xiaoqing ◽  
Li Xiao ◽  
Yao Xingyou ◽  
Xia Zhifan ◽  
...  
Keyword(s):  
Finite Element ◽  
Perforated Plate ◽  
Thickness Ratio ◽  
Thin Plates ◽  
Elastic Buckling ◽  
Buckling Mode ◽  
Element Analysis ◽  
Short Side ◽  
Finite Element Software ◽  
Circular Holes

Stress redistribution will occur around the hole for the perforated plate under bending, and the buckling mode of bending plate is changed, which makes the design of bending plate more complicated. The finite element software ABAQUS is used to establish the perforated plate under bending model, analyze the degree of influence of the plate aspect ratio, width-thickness ratio, size and position of the holes, meanwhile, the distance between holes is also discussed. The results show that the thickness of the plate size and width-thickness ratio have little influence on the elastic buckling performance of thin plates with holes in bending. As the size of the holes increase, the influence is greater, and there is a certain regularity. The opening position is closer to the short side of the plate, the buckling coefficient of plate will be significantly decreased. The effect is greater with the increase of opening size, the distance between holes have a safe value, the position of the opening is more obvious for the buckling of the bending plate. Finally, based on the data from finite element analysis, the proposed formula of buckling stability coefficient k for the bending perforated plate is given.

Sign in / Sign up

Export Citation Format

Share Document