Elastic, Plastic, and Creep Buckling of Imperfect Cylinders Under Mechanical and Thermal Loading

1997 ◽  
Vol 119 (1) ◽  
pp. 27-36 ◽  
Author(s):  
M. R. Eslami ◽  
M. Shariyat

Based on the concept of secant and tangent modulus, the nonlinear equilibrium and stability equations of thin cylindrical shells under axial compression, external pressure, or external fluid pressure are derived. The resulting equations are applicable to shells without length limitation as the rotations and transverse shears are included in the derivations. The reduction factors for plastic and creep buckling are then obtained. A procedure for determining secant and tangent modulus in the very general case of elastic, plastic, or creep stress in the presence of temperature gradient is proposed. Then, using Donnell’s nonlinear theory of shells, the effect of initial imperfection on the strength of the elastic shell is discussed. The foregoing results are extended to plastic and creep buckling of cylindrical shells of arbitrary length and temperature gradient. Some design curves are proposed using the obtained equations. Finally, the present results are compared with available results in the literature and the accuracy of the method is examined.

2004 ◽  
Vol 10 (4) ◽  
pp. 343-349 ◽  
Author(s):  
X. W. Zhao ◽  
J. H. Luo ◽  
M. Zheng ◽  
H. L. Li ◽  
M. X. Lu

1974 ◽  
Vol 96 (3) ◽  
pp. 155-161 ◽  
Author(s):  
I. Berman ◽  
J. M. Chern ◽  
G. D. Gupta

The elastic-plastic-creep buckling of a long thin cylindrical shell with initial out-of-roundness subjected to uniform external pressure is herein studied. The work is carried out by means of an economical computer program which consistently accounts for the effects of load changes and plastic strains and which has a calculation procedure based on direct integration. The ratio of the sustained load to the initial buckling load is discovered to be a parameter which relates the sustained load to the buckling time without explicit reference to the geometric parameters for the conditions considered. Other results are uncovered concerning the effect of: the shape of the imperfection, the temperature variations and the choice of creep relations on initial buckling load and buckling time. Alternatives to the expensive and time consuming calculations to meet the requirements of the time factor of safety on Code Case 1331 of the ASME Boiler and Pressure Vessel Code for Class 1 nuclear components are explored. Recommendations are made.


1976 ◽  
Vol 98 (1) ◽  
pp. 75-80 ◽  
Author(s):  
I. Berman ◽  
A. C. Gangadharan ◽  
G. H. Jaisingh ◽  
G. D. Gupta

The effects of variation of elastic-plastic and creep properties of type 304 stainless steel on solutions of two specific inelastic problems are studied in this paper. The problems considered are: 1 – elastic-plastic-creep buckling of a thin cylindrical shell with initial imperfection and sustained external pressure at high temperature; and 2 – creep and fatigue damage in a thin cylindrical shell subjected to cyclic thermal load and constant internal pressure. Some conclusions are drawn as to the relative importance of variations of different material parameters on initial buckling load, creep buckling time and creep and fatigue damage factors.


Author(s):  
Andre´ Turbat ◽  
Bernard Drubay

In the case of structures operating at high temperature in normal or accidental conditions, the influence of creep has to be considered at the design stage because this phenomenon may reduce the lifetime significantly. This is true in particular for buckling analysis : in creep conditions, the buckling sometimes occurs after a long period under a compressive load which is lower than the critical load assessed when considering an instantaneous buckling. The main reason is that creep deformations induce an amplification of the initial geometrical imperfections and consequently a reduction of the buckling load. Some Design Codes incorporate special rules and/or methods to take creep buckling into account. Creep buckling analysis methods aim at evaluating critical loading for a given hold period with creep or alternatively critical creep time for a given loading. The Codes where creep buckling is considered also define margins with respect to critical loading : it shall be demonstrated that creep instability will not occur during the whole lifetime when multiplying the specified loading by a coefficient (design factor) depending on the situation level. For the design of NPP, specific creep buckling rules exist in the US, France and Russia. In the US, ASME, Section III, Subsection NH, which is dedicated to high temperature components design, provides limits which are applicable to general geometrical configurations and loading conditions that may cause buckling due to creep behaviour of the material. For load-controlled time-dependent creep buckling, the design factors to apply to the specified loadings are 1.5 for levels A, B or C service loadings and 1.25 for level D service loadings. A design factor is not required in the case of purely strain-controlled buckling. No specific method is provided to obtain critical loading or critical time for creep instability. In France, creep buckling rules included in RCC-MR, Chapter RB or RC 3200 are similar to those of ASME, Subsection NH. In addition, a new simplified method has been developed recently to assess critical creep loading/time for a shell under mechanical loading. Diagrams, presently valid for 316 austenitic steel, have been established from a ring model with perfect plasticity. Creep buckling load is determined applying a reduction factor to Euler instantaneous buckling load, depending on temperature, hold time, thinness of the structure and geometrical imperfection amplitude. This method has been validated by experimental tests and finite element results. It will be included in Appendix A7 of RCC-MR, Edition 2000. In Russia, the document PNAE G-7-002-86 applicable to NPP equipment and pipeline strength analysis, presents stability check analytical calculations to be performed to determine the allowable loading or allowable operation lifetime for typical geometries (cylindrical shells, dished ends) and loadings (external pressure, axial force). In the case of stability analysis under creep, creep deformation is assessed using a Norton law. In Germany, a KTA project including an analytical method for creep buckling analysis had also been proposed at the beginning of 90th to be used in HTR development. Finally, in India, a creep buckling analysis method has been proposed in the framework of PFBR project. As per this approach, elastic-plastic analysis should be performed replacing the instantaneous stress-strain curve at the design temperature by the isochronous curve for the time corresponding to the lifetime of the component and the same temperature. These methods are applied in the case of cylindrical shells under external pressure and comparative results are provided. The RCC-MR method appears to be reasonably conservative and applicable with several creep law types.


2018 ◽  
Vol 85 (9) ◽  
Author(s):  
S. Gerasimidis ◽  
E. Virot ◽  
J. W. Hutchinson ◽  
S. M. Rubinstein

This paper investigates issues that have arisen in recent efforts to revise long-standing knockdown factors for elastic shell buckling, which are widely regarded as being overly conservative for well-constructed shells. In particular, this paper focuses on cylindrical shells under axial compression with emphasis on the role of local geometric dimple imperfections and the use of lateral force probes as surrogate imperfections. Local and global buckling loads are identified and related for the two kinds of imperfections. Buckling loads are computed for four sets of relevant boundary conditions revealing a strong dependence of the global buckling load on overall end-rotation constraint when local buckling precedes global buckling. A reasonably complete picture emerges, which should be useful for informing decisions on establishing knockdown factors. Experiments are performed using a lateral probe to study the stability landscape for a cylindrical shell with overall end rotation constrained in the first set of tests and then unconstrained in the second set of tests. The nonlinear buckling behavior of spherical shells under external pressure is also examined for both types of imperfections. The buckling behavior of spherical shells is different in a number of important respects from that of the cylindrical shells, particularly regarding the interplay between local and global buckling and the post-buckling load-carrying capacity. These behavioral differences have bearing on efforts to revise buckling design rules. The present study raises questions about the perspicacity of using probe force imperfections as surrogates for geometric dimple imperfections.


1974 ◽  
Vol 96 (4) ◽  
pp. 1322-1327
Author(s):  
Shun Cheng ◽  
C. K. Chang

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.


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