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 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 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.

Nonconservative Components of Follower Forces in the Classical Shell Theory

1989 ◽  
Vol 42 (11S) ◽  
pp. S13-S19
Author(s):  
Wolf Altman ◽  
Luiz Bevilacqua
Keyword(s):  
Dynamic Stability ◽  
Shell Theory ◽  
Shell Structures ◽  
Small Strains ◽  
Generalized Displacements ◽  
Order Of Magnitude ◽  
Classical Shell Theory ◽  
Follower Forces

An analysis of follower forces acting on shell structures is presented. Attention is focussed on the expressions of such forces as functions of the generalized displacements. Specific expressions for the follower forces are obtained, according to the order of magnitude of the strains and angles of rotation. For small strains the follower forces allow a decomposition into conservative and non-conservative components. This leads to the equations of dynamic stability of shell problems subjected to follower loads. The dynamic counterparts of Donnell-Mushtari-Vlasov stability equations are presented, by either retaining or omitting the prebuckling rotations.

Exact Analysis of a Thick Sandwich Conical Shell by Forward Integration

1972 ◽  
Vol 39 (2) ◽  
pp. 495-500 ◽  
Author(s):  
D. H. Seitz
Keyword(s):  
Numerical Method ◽  
Shell Theory ◽  
Elasticity Analysis ◽  
The Core ◽  
Transverse Normal Stress ◽  
Arbitrary Thickness ◽  
Sandwich Plates And Shells ◽  
Classical Shell Theory ◽  
Plates And Shells ◽  
Forward Integration

A numerical method for stress analysis of three-layered, honeycomb-type sandwich plates and shells of arbitrary thickness is illustrated by application to a thick conical frustum. Results are demonstrated in a numerical example. The method features an exact elasticity analysis of the core including transverse shear and transverse normal stress. The facings are treated by classical shell theory. The numerical method used is forward integration.

A Bending Theory for Multi-layer Anisotropic Conical Shells

1969 ◽  
Vol 20 (1) ◽  
pp. 61-74 ◽  
Author(s):  
Boen-Dar Liaw
Keyword(s):  
Shell Theory ◽  
Energy Functional ◽  
System Of Equations ◽  
Neutral Surface ◽  
Governing Equations ◽  
Conical Shells ◽  
Independent Variables ◽  
Dependent Variables ◽  
Classical Shell Theory ◽  
Definition Of

SummaryThe governing equations for bending of truncated conical shells with multi-layer anisotropic construction are developed by a variational method. The shell is considered to consist of an arbitrary number of alternating soft and hard layers. It is assumed further that the n hard membrane layers are isotropic and may possess different elastic properties, while the (n-1) soft core layers are orthotropic in general and may take transverse shear only. The variations of stresses across the membranes are neglected, as are the surface-parallel stresses in the cores. These assumptions are consistent with those usually employed in single-core sandwich shells. The energy functional is formulated with the stresses considered as independent variables. The stresses are also dependent variables defined in the set of two curvilinear co-ordinates defining the surface of the shell. The stress resultants are introduced as constraint conditions utilising Lagrange multipliers. Successful definition of an elastic neutral surface ensures the uniqueness of shell constants and the equations obtained may be in a form comparable to that of classical shell theory. The system of equations is reduced to a form where Galerkin’s method can be applied directly.

Sign in / Sign up

Export Citation Format

Share Document