On the Buckling Design of Spherical Shells

1981 ◽  
Vol 103 (3) ◽  
pp. 261-266 ◽  
Author(s):  
J. Morton ◽  
P. R. Murray ◽  
C. Ruiz
Keyword(s):  
Biaxial Tension ◽  
External Pressure ◽  
Design Codes ◽  
Safety Factors ◽  
Imperfection Sensitivity ◽  
Spherical Shells ◽  
State Of Stress ◽  
Biaxial Load ◽  
Loading Case ◽  
Selection Of

Experimental results are interpreted in the light of numerical analaysis, imperfection sensitivity and Design Codes. Two cases are discussed: spherical shells under uniform external pressure and partly filled spherical shells, supported on a continuous equatorial ring. The imperfection sensitivity associated with the first loading case leads to the selection of safety factors that depend on the actual shell stiffness. The second case, in which the load results in a biaxial tension-compression state of stress, is treated approximately in terms of a plate under biaxial load.

scholarly journals Nonlinear dynamics of spherical shells buckling under step pressure

2019 ◽  
Vol 475 (2223) ◽  
pp. 20180884 ◽  
Author(s):  
Jan Sieber ◽  
John W. Hutchinson ◽  
J. Michael T. Thompson
Keyword(s):  
Nonlinear Dynamics ◽  
External Pressure ◽  
Dynamic Buckling ◽  
Spherically Symmetric ◽  
Imperfection Sensitivity ◽  
Spherical Shells ◽  
Buckling Mode ◽  
Geometric Imperfections ◽  
Pressure Threshold ◽  
Initial Geometric Imperfections

Dynamic buckling is addressed for complete elastic spherical shells subject to a rapidly applied step in external pressure. Insights from the perspective of nonlinear dynamics reveal essential mathematical features of the buckling phenomena. To capture the strong buckling imperfection-sensitivity, initial geometric imperfections in the form of an axisymmetric dimple at each pole are introduced. Dynamic buckling under the step pressure is related to the quasi-static buckling pressure. Both loadings produce catastrophic collapse of the shell for conditions in which the pressure is prescribed. Damping plays an important role in dynamic buckling because of the time-dependent nonlinear interaction among modes, particularly the interaction between the spherically symmetric ‘breathing’ mode and the buckling mode. In general, there is not a unique step pressure threshold separating responses associated with buckling from those that do not buckle. Instead, there exists a cascade of buckling thresholds, dependent on the damping and level of imperfection, separating pressures for which buckling occurs from those for which it does not occur. For shells with small and moderately small imperfections, the dynamic step buckling pressure can be substantially below the quasi-static buckling pressure.

scholarly journals Buckling of spherical shells revisited

2016 ◽  
Vol 472 (2195) ◽  
pp. 20160577 ◽  
Author(s):  
John W. Hutchinson
Keyword(s):  
Middle Surface ◽  
External Pressure ◽  
Maximum Pressure ◽  
Imperfection Sensitivity ◽  
Spherical Shells ◽  
Mode Localization ◽  
Axisymmetric State ◽  
New Findings ◽  
Post Buckling ◽  
The 1960S

A study is presented of the post-buckling behaviour and imperfection sensitivity of complete spherical shells subject to uniform external pressure. The study builds on and extends the major contribution to spherical shell buckling by Koiter in the 1960s. Numerical results are presented for the axisymmetric large deflection behaviour of perfect spheres followed by an extensive analysis of the role axisymmetric imperfections play in reducing the buckling pressure. Several types of middle surface imperfections are considered including dimple-shaped undulations and sinusoidal-shaped equatorial undulations. Buckling occurs either as the attainment of a maximum pressure in the axisymmetric state or as a non-axisymmetric bifurcation from the axisymmetric state. Several new findings emerge: the abrupt mode localization that occurs immediately after the onset of buckling, the existence of an apparent lower limit to the buckling pressure for realistically large imperfections, and comparable reductions of the buckling pressure for dimple and sinusoidal equatorial imperfections.

scholarly journals Imperfection Sensitivity of Externally Pressurized Spherical Shells

1967 ◽  
Vol 34 (1) ◽  
pp. 49-55 ◽  
Author(s):  
J. W. Hutchinson
Keyword(s):  
General Theory ◽  
Shell Thickness ◽  
Middle Surface ◽  
External Pressure ◽  
Postbuckling Behavior ◽  
Imperfection Sensitivity ◽  
Spherical Shells ◽  
Small Deviations ◽  
Severe Effect ◽  
Shell Geometry

The initial postbuckling behavior of a shallow section of a spherical shell subject to external pressure is studied within the context of Koiter’s general theory of postbuckling behavior. Imperfections in the shell geometry are shown to have the same severe effect on the buckling strengths of spherical shells as has been demonstrated for axially compressed cylindrical shells. Large reductions in the buckling pressure result from small deviations, relative to the shell thickness, of the shell middle surface from the perfect configuration.

Imperfection sensitivity of unstiffened cylindrical shells under external pressure

ce/papers ◽  
2021 ◽  
Vol 4 (2-4) ◽  
pp. 1789-1796
Author(s):  
Esmaeil Azizi ◽  
Natalie Stranghöner
Keyword(s):  
Cylindrical Shells ◽  
External Pressure ◽  
Imperfection Sensitivity

Anisotropic Loading Functions for Combined Stresses in the Plastic Range

1955 ◽  
Vol 22 (1) ◽  
pp. 77-85
Author(s):  
L. W. Hu ◽  
Joseph Marin
Keyword(s):  
Plastic Flow ◽  
Biaxial Tension ◽  
Strain History ◽  
Test Results ◽  
Axial Tension ◽  
State Of Stress ◽  
Loading Function ◽  
Combined Stresses ◽  
Shift Of Origin ◽  
Tubular Specimens

Abstract A loading function is a relation between combined stresses for which the beginning of plastic flow takes place. The loading function for a given material is different depending upon the initial plastic strains produced. That is, the initial stress or strain history influences the subsequent loading function. This paper gives the results of an experimental investigation to determine the validity of certain loading functions proposed for anisotropic materials. The study reported was conducted for an aluminum alloy 24S-T and the state of stress covered was biaxial tension. These stresses were produced in the usual way by subjecting thin-walled tubular specimens to axial tension and internal pressure. The test results showed that none of the existing loading functions is adequate for interpreting the plastic stress-strain relations obtained. Tests also were made to determine the change in the loading function with increase in plastic flow. It was found that the loading function did not remain symmetrical with respect to the original function, nor was the new loading function the same as the original except for a shift of origin. However, the test results support in a qualitative way the concept of the so-called “yield corner.”

Calibration of reliability-based safety factors for sand boiling in excavations

2020 ◽  
Vol 57 (5) ◽  
pp. 742-753
Author(s):  
Ignatius Tommy Pratama ◽  
Chang-Yu Ou ◽  
Jianye Ching
Keyword(s):  
Factor Of Safety ◽  
Probability Of Failure ◽  
Reliability Theory ◽  
Design Codes ◽  
Test Results ◽  
Safety Factors ◽  
Target Probability ◽  
Analysis Methods ◽  
Actual Factor ◽  
The Relationship

This study calibrated the required factors of safety of five analysis methods for sand boiling using reliability theory. The factors of safety computed by the five analysis methods were compared with the results of a series of sand boiling model tests. The comparison shows that rigorous methods (Terzaghi’s and Harza’s methods) were more accurate in predicting the factors of safety compared to the simplified methods (Harr’s, simplified Terzaghi’s, and simplified Harza’s methods). The statistics of the model factor for each method, defined as the actual factor of safety divided by the computed one, was calibrated by the model test results. These statistics were then used to establish the relationship between the target probability of failure and the required factor of safety by reliability theory. Verification using a full-scale sand boiling case history shows that the required factor of safety calibrated by the reliability theory was more reasonable than the required factors of safety in references and design codes.

scholarly journals Non-linear buckling analysis of functionally graded shallow spherical shells

2009 ◽  
Vol 31 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Dao Huy Bich
Keyword(s):  
External Pressure ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Governing Equations ◽  
Spherical Shells ◽  
Buckling Loads ◽  
Linear Buckling ◽  
Non Linear ◽  
Linear Buckling Analysis

In the present paper the non-linear buckling analysis of functionally graded spherical shells subjected to external pressure is investigated. The material properties are graded in the thickness direction according to the power-law distribution in terms of volume fractions of the constituents of the material. In the formulation of governing equations geometric non-linearity in all strain-displacement relations of the shell is considered. Using Bubnov-Galerkin's method to solve the problem an approximated analytical expression of non-linear buckling loads of functionally graded spherical shells is obtained, that allows easily to investigate stability behaviors of the shell.

On the Nonlinear Analysis Methodologies for Thin Spherical Shells Under External Pressure with Different Finite-Element Codes

1989 ◽  
Vol 33 (04) ◽  
pp. 318-325
Author(s):  
Dario Boote ◽  
Donatella Mascia
Keyword(s):  
Finite Element ◽  
Numerical Procedure ◽  
External Pressure ◽  
Experimental Investigations ◽  
Nonlinear Analyses ◽  
Spherical Shells ◽  
Double Curvature ◽  
Load Carrying ◽  
Material Load ◽  
Structure Collapse

Submersible structures consist merely of simple and double curvature thin-walled shells. For this kind of structure, collapse occurs due to the combined nonlinear action of buckling and plasticity of material. Load-carrying capacity may then be assessed mainly by two approaches: experimental investigations and step-by-step numerical procedures. In nonlinear analyses, the results obtained are influenced by the magnitude of the load increment adopted. Solution procedures are then required in order to choose adequate parameters for material failure description as well as elastic nonlinearity. The aim of this paper is to carry out a suitable numerical procedure whose reliability does not depend on the finite-element code adopted.

Sign in / Sign up

Export Citation Format

Share Document