A comparison between John's refined interior shell equations and classical shell theory

1969 ◽  
Vol 20 (5) ◽  
pp. 642-652 ◽  
Author(s):  
Warner T. Koiter
Keyword(s):  
Shell Theory ◽  
Classical Shell Theory ◽  
Shell Equations

scholarly journals Alternative derivation of the higher-order constitutive model for six-parameter elastic shells

2021 ◽  
Vol 72 (2) ◽  
Author(s):  
Mircea Bîrsan
Keyword(s):  
Energy Density ◽  
Constitutive Model ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Shell Theory ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Classical Shell Theory ◽  
Three Dimensional Elasticity ◽  
General Method

AbstractIn this paper, we present a general method to derive the explicit constitutive relations for isotropic elastic 6-parameter shells made from a Cosserat material. The dimensional reduction procedure extends the methods of the classical shell theory to the case of Cosserat shells. Starting from the three-dimensional Cosserat parent model, we perform the integration over the thickness and obtain a consistent shell model of order $$ O(h^5) $$ O ( h 5 ) with respect to the shell thickness h. We derive the explicit form of the strain energy density for 6-parameter (Cosserat) shells, in which the constitutive coefficients are expressed in terms of the three-dimensional elasticity constants and depend on the initial curvature of the shell. The obtained form of the shell strain energy density is compared with other previous variants from the literature, and the advantages of our constitutive model are discussed.

Effect of Accuracy Loss in Classical Shell Theory

1992 ◽  
Vol 59 (2S) ◽  
pp. S217-S223 ◽  
Author(s):  
V. Berdichevsky ◽  
V. Misyura
Keyword(s):  
Shell Theory ◽  
Underlying Causes ◽  
Classical Shell Theory

It is shown that classical shell theory does not yield correct values of displacements in some shell problems. Underlying causes of this effect are discussed.

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.

A Method to Estimate Deformation Strains in the Context of Coke Drum Life Assessments: Part 1

2019 ◽  
Author(s):  
John Huang ◽  
Kannan Subramanian ◽  
Patrick Boster ◽  
Julian J. Bedoya
Keyword(s):  
Theoretical Approach ◽  
Pressure Vessel ◽  
Analytical Method ◽  
Shell Theory ◽  
Theoretical Development ◽  
Strain Gages ◽  
Assessment Technique ◽  
Assessment Techniques ◽  
Classical Shell Theory ◽  
Comparison Of The Results

Abstract In this paper, an analytical method to estimate the deformation strains that can quantify the severity of bulges, as it applies to coke drums, is presented. The proposed method is based on classical shell theory and API 579-1/ASME FFS-1 (2016) procedures involving triaxiality limits. In this first part of the work, only the theoretical development is presented along with the comparison of the results from this theoretical approach with two case studies that emulate the bulging due to different loading scenarios. The developed approach is then applied to a deformed coke drum. In the next part of this paper, the application of this approach on selected in-service coke drums that are equipped with strain gages will be presented. The authors would like to emphasize the well-known fact that the coke drum is a complex pressure vessel for which any single simplified assessment technique may not be sufficient to quantify the life or fitness-for-service (FFS) of a coke drum due to the complexities associated with the various parameters that affect the mechanical integrity of the coke drum. This paper is an attempt to advance the assessment techniques that are currently utilized in the industry.

scholarly journals A Shell Description of Beams Incorporating Transverse Thickness Strain Energies for Receding Contact

2020 ◽  
Vol 87 (5) ◽  
Author(s):  
Adam R. Brink ◽  
Allen T. Mathis ◽  
D. Dane Quinn
Keyword(s):  
Shell Theory ◽  
Weak Form ◽  
Momentum Balance ◽  
Rigid Surface ◽  
Thickness Strain ◽  
Cambridge University ◽  
Receding Contact ◽  
Order Representation ◽  
Shell Equations ◽  
Geometrically Exact Shell

Abstract The geometrically exact nonlinear deflection of a beamshell is considered here as an extension of the formulation derived by Libai and Simmonds (1998, The Nonlinear Theory of Elastic Shells, Cambridge University Press, Cambridge, UK) to include deformation through the thickness of the beam, as might arise from transverse squeezing loads. In particular, this effect can lead to receding contact for a uniform beamshell resting on a smooth, flat, rigid surface; traditional shell theory cannot adequately such behavior. The formulation is developed from the weak form of the local equations for linear momentum balance, weighted by an appropriate tensor. Different choices for this tensor lead to both the traditional shell equations corresponding to linear and angular momentum balance, as well as the additional higher-order representation for the squeezing deformation. In addition, conjugate strains for the shell forces are derived from the deformation power, as presented by Libai and Simmonds. Finally, the predictions from this approach are compared against predictions from the finite element code abaqus for a uniform beam subject to transverse applied loads. The current geometrically exact shell model correctly predicts the transverse shell force through the thickness of the beamshell and is able to describe problems that admit receding contact.

Recommended Stress Formulae for Tubular Conical Transition Designs

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Albert Ku ◽  
Jieyan Chen
Keyword(s):  
Stress Concentration ◽  
Stress Concentration Factor ◽  
Shell Theory ◽  
Plate Thickness ◽  
Design Standards ◽  
Shell Equations ◽  
Offshore Industry ◽  
Hoop Stresses ◽  
Code Provisions

Abstract For the design of tubular conical transitions, the axial, bending, and hoop stresses at the junctions are required. Among the offshore design standards, API RP-2A, ISO 19902, and NORSOK N-004, various equations exist for the same stress quantity which may cause confusions. The quality of these existing stress formulae will be examined in this paper. The tubular conical stress equations used in the offshore industry started from Boardman’s studies in the 1940s. Recently, Lotsberg re-formulated this problem and applied the results to stress concentration factor (SCF) applications. This paper solves the same set of shell equations but the formulations are cast in a different form. This new format allows for an in-depth examination of existing code equations. In addition, the formulation as presented can be used for modifications to gain higher accuracy. Several recommended new stress formulae are provided. It is observed that the existing code provisions’ accuracy quickly deteriorates for cases where plate thickness in tubular and cone differ. The recommended approach is based on theoretical framework of shell mechanics, which better facilitate tubular/cone force balances when compared with existing equations. The sectional relationships among moment, shear, and hoop loads are also treated consistently using shell theory. The resulted improvements make the recommended formulae more accurate than the existing provisions.

scholarly journals Derivation of a refined six-parameter shell model: descent from the three-dimensional Cosserat elasticity using a method of classical shell theory

2020 ◽  
Vol 25 (6) ◽  
pp. 1318-1339 ◽  
Author(s):  
Mircea Bîrsan
Keyword(s):  
Shell Model ◽  
Shell Theory ◽  
Local Equilibrium ◽  
Three Dimensional ◽  
Simple Expression ◽  
Equilibrium Equations ◽  
Cosserat Elasticity ◽  
Shell Models ◽  
Classical Shell Theory ◽  
Derivation Method

Starting from the three-dimensional Cosserat elasticity, we derive a two-dimensional model for isotropic elastic shells. For the dimensional reduction, we employ a derivation method similar to that used in classical shell theory, as presented systematically by Steigmann (Koiter’s shell theory from the perspective of three-dimensional nonlinear elasticity. J Elast 2013; 111: 91–107). As a result, we obtain a geometrically nonlinear Cosserat shell model with a specific form of the strain energy density, which has a simple expression, with coefficients depending on the initial curvature tensor and on three-dimensional material constants. The explicit forms of the stress–strain relations and the local equilibrium equations are also recorded. Finally, we compare our results with other six-parameter shell models and discuss the relation to the classical Koiter shell model.

On Boundary Layers in a Pressurized Mooney Cylinder

1987 ◽  
Vol 54 (2) ◽  
pp. 280-286 ◽  
Author(s):  
L. A. Taber
Keyword(s):  
Boundary Layer ◽  
Shell Theory ◽  
Circular Cylindrical Shell ◽  
Small Strain ◽  
Axisymmetric Deformation ◽  
Transverse Shear Deformation ◽  
Edge Zone ◽  
Secondary Layer ◽  
Shell Equations ◽  
Pressurized Cylinder

Asymptotic expansions are developed for the equations governing large axisymmetric deformation of a circular cylindrical shell composed of a Mooney material. The shell equations allow large normal strains and thickness changes but ignore transverse shear deformation. For a pressurized cylinder with rigid end plugs, results are presented to illustrate the development of a primary and a secondary boundary layer as generalizations of those that occur in small-strain shell theory. The form of the WKB-type expansion divides the secondary layer into bending and stretching components, which lie within the wider primary boundary layer. While the bending component of the secondary layer can become significant when strains are still small, the stretching component emerges as a consequence of large geometry changes in the edge zone, becoming significant as strains grow large and material nonlinearity becomes important.

Sign in / Sign up

Export Citation Format

Share Document