Refined Interior Shell Equations

1969 ◽  
pp. 1-14 ◽  
Author(s):  
F. John
Keyword(s):  
Shell Equations

DIMENSIONING OF ORTHOTROPICALLY STIFFENED CFRP SHELLS OF LARGE LAUNCH VEHICLES FOR LOAD INTRODUCTION AND STABILITY

2010 ◽  
Vol 10 (04) ◽  
pp. 601-621 ◽  
Author(s):  
ANDREAS RITTWEGER ◽  
SUSANNE CHRISTIANSON ◽  
HUBA ÖRY
Keyword(s):  
Analytical Methods ◽  
Flux Distribution ◽  
Fe Analysis ◽  
Launch Vehicles ◽  
Local Instability ◽  
Axial Loads ◽  
Ring Frame ◽  
Final Design ◽  
Shell Equations ◽  
Analytical Approaches

The dimensioning of an orthotropically stiffened cylindrical CFRP shell subjected to the introduction of concentrated axial loads using rapid analytical methods is presented. For stress calculation the shell equations are simplified by applying the semibending theory and integrated by employing the transfer matrix method. Analytical approaches are used for stability verification. The dimensioning considers required constraints in the force flux distribution, strength of the laminate, general instability, panel instability (from ring frame to ring frame) and local instability. The rapid analytical methods allow mass optimization. The final design is confirmed by detailed FE analysis. A comparison of the FE analysis with the analytical results is shown.

Buckling of a Circular Cylindrical Web-Stiffened Sandwich Shell Under Axial Compression

1974 ◽  
Vol 18 (01) ◽  
pp. 55-61
Author(s):  
Vincent Volpe ◽  
Youl-Nan Chen ◽  
Joseph Kempner
Keyword(s):  
Axial Compression ◽  
Large Deflection ◽  
Single Layer ◽  
Subsequent Development ◽  
Buckling Load ◽  
Sandwich Shell ◽  
Cylindrical Sandwich Shell ◽  
Axisymmetric Mode ◽  
Shell Equations ◽  
The Mathematical Model

A stability analysis of an infinitely long web-stiffened, circular cylindrical sandwich shell under uniform axial compression is presented. The formulation begins with the establishment of a set of suitable large-deflection shell equations that forms the basis for the subsequent development of the buckling equations. The mathematical model corresponds to two face layers that are considered as thin shells and a thick core that is capable of resisting both transverse shear and circumferential extension. The associated eigenvalue problem is solved. Results show that the lowest buckling load is associated with the axisymmetric mode and is less than one half the buckling load of an equivalent single-layer shell.

Cylindrical Shells Under Line Load

1957 ◽  
Vol 24 (4) ◽  
pp. 553-558
Author(s):  
R. M. Cooper
Keyword(s):  
Cylindrical Shell ◽  
Radial Displacement ◽  
Circular Cylindrical Shell ◽  
Transverse Shear Deformation ◽  
System Of Equations ◽  
Principle Of Superposition ◽  
Line Load ◽  
Simply Supported ◽  
Shell Equations ◽  
Shell Geometry

Abstract The problem of a line load along a segment of a generator of a simply supported circular cylindrical shell is treated using shallow cylindrical shell equations which include the effect of transverse-shear deformation. The line load is first treated as a sinusoidally-varying edge load over the length of the shell, with boundary conditions prescribed along the loaded generator such that the continuity of the shell is maintained. The solution for the problem of a uniform line load over a segment of a generator is obtained from the preceding solution, using the principle of superposition. By means of a numerical example it is shown that the results predicted by the Donnell equations for the stresses are in excellent agreement with those obtained from the system of equations employed here. However, the radial displacement predicted by the Donnell equations is in error by as much as 20 per cent in the range of shell geometry considered.

Blocking in the Rotating Axial Flow in a Corotating Flexible Shell

2008 ◽  
Vol 76 (1) ◽  
Author(s):  
F. Gosselin ◽  
M. P. Païdoussis
Keyword(s):  
Traveling Waves ◽  
Physical Phenomenon ◽  
Axial Flow ◽  
Critical Value ◽  
Inviscid Fluid ◽  
Shell Wall ◽  
Stagnation Region ◽  
Linear Dynamics ◽  
Shell Equations ◽  
Rotating Cylindrical Shell

By coupling the Donnell–Mushtari shell equations to an analytical inviscid fluid solution, the linear dynamics of a rotating cylindrical shell with a corotating axial fluid flow is studied. Previously discovered mathematical singularities in the flow solution are explained here by the physical phenomenon of blocking. From a reference frame moving with the traveling waves in the shell wall, the flow is identical to the flow in a rigid varicose tube. When the ratio of rotation rate to flow velocity approaches a critical value, the phenomenon of blocking creates a stagnation region between the humps of the wall. Since the linear model cannot account for this phenomenon, the solution blows up.

Effet des imperfections géométriques sur la stabilité des coques élastiques cylindriques

2004 ◽  
Vol 31 (1) ◽  
pp. 27-32 ◽  
Author(s):  
Abdellatif Khamlichi ◽  
Mohammed Bezzazi ◽  
Larbi Elbakkali ◽  
Ali Limam
Keyword(s):  
Critical Load ◽  
Axial Symmetry ◽  
A Priori ◽  
Severe Case ◽  
Thin Shells ◽  
Geometrical Imperfections ◽  
Localized Defects ◽  
Shell Equations ◽  
Selection Of ◽  
Numerical Approaches

The effects of geometrical imperfections on the critical load of elastic cylindrical shells when subjected to axial compression are studied through analytical modelling. In addition to distributed defects of both axisymmetric or asymmetric forms, emphasis is put on the more severe case of localized defects satisfying the axial symmetry. The Von Kármán – Donnell shell equations were used. The obtained results show that shell strength at buckling varies very much with the defect amplitude. These variations are not monotonic in general. They indicate however a clear reduction of the shell critical load for some defects revealed as the most dangerous ones. The proposed method does not consider the complete coupled situation that may arise from interactions between several localized defects. It facilitates nevertheless straightforward initializing of closer analyses if such couplings are to be taken into account by means of special numerical approaches, because it enables fast a priori selection of the most hazardous isolated defects.Key words: stability, buckling, imperfections, thin shells, silos, localized defects.

Pressurized Cylindrical Shell With a Rigid Circular Inclusion

1978 ◽  
Vol 100 (2) ◽  
pp. 158-163 ◽  
Author(s):  
D. H. Bonde ◽  
K. P. Rao
Keyword(s):  
Differential Equation ◽  
Cylindrical Shell ◽  
Shallow Shell ◽  
Circular Inclusion ◽  
Hankel Functions ◽  
Curvature Parameter ◽  
Shell Equations ◽  
Limiting Case ◽  
Rigid Circular Inclusion ◽  
Good Agreement

The effect of a rigid circular inclusion on stresses in a cylindrical shell subjected to internal pressure has been studied. The two linear shallow shell equations governing the behavior of a cylindrical shell are converted into a single differential equation involving a curvature parameter and a potential function in nondimensionalized form. The solution in terms of Hankel functions is used to find membrane and bending stressses. Boundary conditions at the inclusion shell junction are expressed in a simple form involving the in-plane strains and change of curvature. Good agreement has been obtained for the limiting case of a flat plate. The shell results are plotted in nondimensional form for ready use.

A Review of Tubular Conical Transition Strength Design Equations

2020 ◽  
Author(s):  
Albert Ku ◽  
Jieyan Chen ◽  
Bernard Cyprian
Keyword(s):  
Thin Shell ◽  
Shell Theory ◽  
Yield Criterion ◽  
Plasticity Theory ◽  
Transition Strength ◽  
Ultimate Capacity ◽  
Design Standards ◽  
Fem Simulations ◽  
Column Type ◽  
Shell Equations

Abstract This paper consists of two parts. Part one presents a thin-shell analytical solution for calculating the conical transition junction loads. Design equations as contained in the current offshore standards are based on Boardman’s 1940s papers with beam-column type of solutions. Recently, Lotsberg presented a solution based on shell theory, in which both the tubular and the cone were treated with cylindrical shell equations. The new solution as presented in this paper is based on both cylindrical and conical shell theories. Accuracies of these various derivations will be compared and checked against FEM simulations. Part 2 of this paper is concerned with the ultimate capacity equations of conical transitions. This is motivated by the authors’ desire to unify the apparent differences among the API 2A, ISO 19902 and NORSOK design standards. It will be shown that the NORSOK provisions are equivalent to the Tresca yield criterion as derived from shell plasticity theory. API 2A provisions are demonstrated to piecewise-linearly approximate this Tresca yield surface with reasonable consistency. The 2007 edition of ISO 19902 will be shown to be too conservative when compared to these other two design standards.

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