scholarly journals Asymptotic theory for thin two-ply shells

2020 ◽  
Vol 42 (3) ◽  
pp. 269-282
Author(s):  
David J. Steigmann
Keyword(s):  
Shell Theory ◽  
Asymptotic Theory ◽  
A Priori ◽  
Small Strain ◽  
Asymptotic Model ◽  
Strain Response ◽  
Pure Bending ◽  
Laminated Shells ◽  
Limit Model ◽  
Interfacial Surface

We develop an asymptotic model for the finite-deformation, small-strain response of thin laminated shells composed of two perfectly bonded laminae that exhibit reflection symmetry of the material properties with respect to an interfacial surface. No a priori hypotheses are made concerning the kinematics of deformation. The asymptotic procedure culminates in a generalization of Koiter's well-known shell theory to accommodate the laminated structure, and incorporates a rigorous limit model for pure bending.

CHARACTERIZATION OF THE MEMBRANE THEORY OF A CLAMPED SHELL.

1994 ◽  
Vol 04 (02) ◽  
pp. 147-177 ◽  
Author(s):  
JYRKI PIILA
Keyword(s):  
3D Model ◽  
Asymptotic Theory ◽  
Convergence Result ◽  
Elastic Model ◽  
Asymptotic Model ◽  
Membrane Theory ◽  
Limit Model ◽  
Deformation State ◽  
Mathematical Characteristics

We study the membrane-dominated deformation state of a thin shell, the mid-surface of which is located on a surface of revolution with positive principal radii of curvature. The lateral shape of the shell is assumed to be that of a curvilinear polygon. The shell is loaded by a smooth surface traction acting on its outer surface and rigidly supported throughout its edge. Proceeding from the 3D elastic model, an asymptotic model is constructed to describe the limit behavior of the shell as the thickness tends to zero. The limit model is referred to as membrane theory. A convergence result relating the 3D model and the asymptotic model is proved and the mathematical characteristics of the asymptotic theory are analyzed. Energy methods are used throughout the work.

Collapse of Thin Orthotropic Elliptical Cylindrical Shells Under Combined Bending and Pressure Loads

1979 ◽  
Vol 46 (2) ◽  
pp. 363-371 ◽  
Author(s):  
J. Spence ◽  
S. L. Toh
Keyword(s):  
Shell Theory ◽  
Nonlinear Boundary ◽  
Cylindrical Shells ◽  
Normal Pressure ◽  
Nonlinear Ordinary Differential Equations ◽  
Pure Bending ◽  
Finite Deflection ◽  
Shooting Technique ◽  
Theoretical Predictions ◽  
Thin Shell Theory

The elastic collapse of thin orthotropic elliptical cylindrical shells subject to pure bending alone or combined bending and uniform normal pressure loads has been studied. Nonlinear finite deflection thin shell theory is employed and this reduces the problem to a set of nonlinear ordinary differential equations. The resulting two-point nonlinear boundary-value problem is then linearized, using quasi-linearization, and solved numerically by the “shooting technique.” Some experimental work has been carried out and the results are compared with the theoretical predictions.

Asymptotic Energy Behavior of Two Classical Intermediate Benchmark Shell Problems

2003 ◽  
Vol 13 (09) ◽  
pp. 1279-1302 ◽  
Author(s):  
L. Beirão da Veiga
Keyword(s):  
Numerical Methods ◽  
Boundary Conditions ◽  
Shell Theory ◽  
A Priori ◽  
Energy Norm ◽  
Numerical Comparison ◽  
Benchmark Tests ◽  
Energy Behavior ◽  
Interpolation Techniques ◽  
Asymptotic Energy

We consider two classical problems which are widely used as benchmark tests for shell numerical methods: the Scordelis–Lo roof and the pinched roof. Due to the particular load and boundary conditions applied, neither belongs to the well-known classes of purely bending or purely membrane dominated shells. Consequently the asymptotic energy norm behavior, which is useful not only because it represents the structure stiffness, but also for numerical comparison purposes, is not a priori known. In this work, using space interpolation techniques and a recently developed "intermediate" shell theory, the asymptotic energy behavior of both problems is found analytically. The results are in agreement with the numerical estimates obtained in other papers.

An obstacle problem for Koiter’s shells

2019 ◽  
Vol 24 (10) ◽  
pp. 3061-3079 ◽  
Author(s):  
Philippe G Ciarlet ◽  
Paolo Piersanti
Keyword(s):  
Asymptotic Analysis ◽  
A Priori ◽  
Elastic Shell ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Three Dimensional Model ◽  
Limit Model ◽  
Membrane Shells ◽  
Point Of Departure ◽  
Confinement Condition

In this paper, we define, a priori, a natural two-dimensional Koiter’s model of a ‘general’ linearly elastic shell subject to a confinement condition. As expected, this model takes the form of variational inequalities posed over a non-empty closed convex subset of the function space used for the ‘unconstrained’ Koiter’s model. We then perform a rigorous asymptotic analysis as the thickness of the shell, considered a ‘small’ parameter, approaches zero, when the shell belongs to one of the three main classes of linearly elastic shells, namely elliptic membrane shells, generalized membrane shells and flexural shells. To illustrate the soundness of this model, we consider elliptic membrane shells to fix ideas. We then show that, in this case, the ‘limit’ model obtained in this fashion coincides with the two-dimensional ‘limit’ model obtained by means of another rigorous asymptotic analysis, but this time with the three-dimensional model of a ‘general’ linearly elastic shell subject to a confinement condition as a point of departure. In this fashion, our proposed Koiter’s model of a linearly elastic shell subject to a confinement condition is fully justified in this case, even though it is not itself a ‘limit’ 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.

Laminated shells in nonlinear six-parameter shell theory

2009 ◽  
pp. 229-232
Author(s):  
A Sabik ◽  
J Chróscielewski ◽  
I Kreja ◽  
W Witkowski
Keyword(s):  
Shell Theory ◽  
Laminated Shells

scholarly journals Size-Dependent Properties of Magnetosensitive Polymersomes: Computer Modelling

Sensors ◽  
2019 ◽  
Vol 19 (23) ◽  
pp. 5266
Author(s):  
Aleksandr Ryzhkov ◽  
Yuriy Raikher
Keyword(s):  
Material Parameter ◽  
Computer Modelling ◽  
Single Cells ◽  
A Priori ◽  
Amphiphilic Polymer ◽  
Dynamics Simulation ◽  
Strain Response ◽  
Qualitative Explanation ◽  
Size Dependent ◽  
Nanoscale Object

Magnetosensitive polymersomes, which are amphiphilic polymer capsules whose membranes are filled with magnetic nanoparticles, are prospective objects for drug delivery and manipulations with single cells. A molecular dynamics simulation model that is able to render a detailed account on the structure and shape response of a polymersome to an external magnetic field is used to study a dimensional effect: the dependence of the field-induced deformation on the size of this nanoscale object. It is shown that in the material parameter range that resembles realistic conditions, the strain response of smaller polymersomes, against a priori expectations, exceeds that of larger ones. A qualitative explanation for this behavior is proposed.

Sign in / Sign up

Export Citation Format

Share Document