scholarly journals A Constrained Cosserat Shell Model up to Order $O(h^{5})$: Modelling, Existence of Minimizers, Relations to Classical Shell Models and Scaling Invariance of the Bending Tensor

2021 ◽  
Author(s):  
Ionel-Dumitrel Ghiba ◽  
Mircea Bîrsan ◽  
Peter Lewintan ◽  
Patrizio Neff
Keyword(s):  
Shell Model ◽  
Scaling Invariance ◽  
Shell Models ◽  
Existence Of Minimizers

scholarly journals Lattice Dynamics of Simple Harmonic and Anharmonic Shell Models

1967 ◽  
Vol 20 (5) ◽  
pp. 495 ◽  
Author(s):  
J Oitmaa
Keyword(s):  
Dipole Moment ◽  
Shell Model ◽  
Lattice Dynamics ◽  
Higher Order ◽  
Force Constants ◽  
Dynamical Equations ◽  
Normal Coordinates ◽  
Shell Models ◽  
Rigid Ion Model ◽  
Explicit Expressions

The lattice dynamics of harmonic and anharmonic shell models are reviewed. It is shown that the various dynamical equations for the shell model can be expressed in the same form as those for the rigid ion model, but with modified force constants. The anharmonic shell model leads to higher order contributions to the dipole moment, quadratic and cubic in the normal coordinates, for which explicit expressions are obtained.

scholarly journals On the Adequacy of Shell Models for Predicting Stresses and Strains in Thick-Walled Tubes Subjected to Detonation Loading

2013 ◽  
Author(s):  
Neal P. Bitter ◽  
Joseph E. Shepherd
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Shell Model ◽  
Wall Thickness ◽  
Axial Strain ◽  
Nonlinear Behavior ◽  
Element Model ◽  
Shell Models ◽  
Axial Curvature ◽  
Detonation Loading

This paper analyzes the adequacy of shell models for predicting stresses and strains in thick-walled tubes subjected to detonation loads. Of particular interest are the large axial strains which are produced at the inner and outer surfaces of the tube due to bending along the tube axis. First, comparisons between simple shell theory and a static finite element model are used to show that the axial strain varies proportionally with wall thickness and inversely with the square of the axial wavelength. For small wavelengths, this comparison demonstrates nonlinear behavior and a breakdown of the shell model. Second, a dynamic finite element model is used to evaluate the performance of transient shell equations. This comparison is used to quantify the error of the shell model with increasing wall thickness and show that shell models can be inaccurate near the load front where the axial curvature is high. Finally, the results of these analyses are used to show that the large axial strains which are sometimes observed in experiments cannot be attributed to through-wall bending and appear to be caused instead by non-ideal conditions present in the experiments.

Pairing in shell models

1955 ◽  
Vol 232 (1188) ◽  
pp. 88-104 ◽  
Keyword(s):  
Group Theory ◽  
Shell Model ◽  
Magnetic Moments ◽  
Light Nuclei ◽  
Intermediate Coupling ◽  
Nuclear Magnetic Moments ◽  
Shell Models ◽  
Decomposition Procedure ◽  
Nuclear Magnetic

An L-S pairing shell model is proposed for light nuclei (§§2( b ) and 5). Three types of shell model, that is, super multiplet theory, j-j pairing scheme and the L-S pairing scheme are compared with respect to the decomposition procedure by group theory, and also are compared in connexion with nuclear magnetic moments (§§7, 3). It is very likely that in light nuclei the L-S pairing or an intermediate coupling between the L-S pairing and j-j pairing schemes is a very good approximation.

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.

scholarly journals The Isotropic Cosserat Shell Model Including Terms up to $O(h^{5})$. Part II: Existence of Minimizers

2020 ◽  
Vol 142 (2) ◽  
pp. 263-290 ◽  
Author(s):  
Ionel-Dumitrel Ghiba ◽  
Mircea Bîrsan ◽  
Peter Lewintan ◽  
Patrizio Neff
Keyword(s):  
Shell Model ◽  
Existence Of Minimizers

scholarly journals Interior and H-∞ feedback stabilization for sabra Shell model of turbulence

2021 ◽  
Author(s):  
Tania Biswas ◽  
Sheetal Dharmatti
Keyword(s):  
Control Problem ◽  
Shell Model ◽  
Turbulent Flows ◽  
Robust Stabilization ◽  
Feedback Stabilization ◽  
Algebraic Riccati Equation ◽  
Finite Dimensional ◽  
Shell Models ◽  
Linearized System ◽  
Unknown Disturbance

Shell models of turbulence are representation of turbulence equations in Fourier domain. Various shell models are studied for their mathematical relevance and the numerical simulations which exhibit at most resemblance with turbulent flows. One of the mathematically well studied shell model of turbulence is called sabra shell model. This work concerns with two important issues related to shell model namely feedback stabilization and robust stabilization. We first address stabilization problem related to sabra shell model of turbulence and prove that the system can be stabilized via finite dimensional controller. Thus only finitely many modes of the shell model would suffice to stabilize the system. Later we study robust stabilization in the presence of the unknown disturbance and corresponding control problem by solving an infinite time horizon max-min control problem. We first prove the $H^ \infty$ stabilization of the associated linearized system and characterize the optimal control in terms of a feedback operator by solving an algebraic riccati equation. Using the same riccati operator we establish asymptotic stability of the nonlinear system.

Approximate symmetries in atomic nuclei from a large-scale shell-model perspective

2015 ◽  
Vol 24 (05) ◽  
pp. 1530005 ◽  
Author(s):  
K. D. Launey ◽  
J. P. Draayer ◽  
T. Dytrych ◽  
G.-H. Sun ◽  
S.-H. Dong
Keyword(s):  
Shell Model ◽  
Large Scale ◽  
Interacting Particles ◽  
Approximate Symmetries ◽  
Atomic Nuclei ◽  
Shell Models ◽  
Model Spaces ◽  
Recent Developments ◽  
Particle Momentum ◽  
The Many

In this paper, we review recent developments that aim to achieve further understanding of the structure of atomic nuclei, by capitalizing on exact symmetries as well as approximate symmetries found to dominate low-lying nuclear states. The findings confirm the essential role played by the Sp(3, ℝ) symplectic symmetry to inform the interaction and the relevant model spaces in nuclear modeling. The significance of the Sp(3, ℝ) symmetry for a description of a quantum system of strongly interacting particles naturally emerges from the physical relevance of its generators, which directly relate to particle momentum and position coordinates, and represent important observables, such as, the many-particle kinetic energy, the monopole operator, the quadrupole moment and the angular momentum. We show that it is imperative that shell-model spaces be expanded well beyond the current limits to accommodate particle excitations that appear critical to enhanced collectivity in heavier systems and to highly-deformed spatial structures, exemplified by the second 0+ state in 12 C (the challenging Hoyle state) and 8 Be . While such states are presently inaccessible by large-scale no-core shell models, symmetry-based considerations are found to be essential.

A GEOMETRICALLY EXACT PLANAR COSSERAT SHELL-MODEL WITH MICROSTRUCTURE: EXISTENCE OF MINIMIZERS FOR ZERO COSSERAT COUPLE MODULUS

2007 ◽  
Vol 17 (03) ◽  
pp. 363-392 ◽  
Author(s):  
PATRIZIO NEFF
Keyword(s):  
Shell Model ◽  
Degrees Of Freedom ◽  
Equilibrium Solutions ◽  
Large Rotation ◽  
Curvature Term ◽  
Existence Of Minimizers ◽  
Cosserat Couple Modulus ◽  
Resistance Drilling ◽  
Shell Formulation ◽  
Transverse Shear Resistance

The existence of minimizers to a geometrically exact Cosserat planar shell model with microstructure is proven. The membrane energy is a quadratic, uniformly Legendre–Hadamard elliptic energy in contrast to traditional membrane energies. The bending contribution is augmented by a curvature term representing the interaction of the rotational microstructure in the Cosserat theory. The model includes non-classical size effects, transverse shear resistance, drilling degrees of freedom and accounts implicitly for thickness extension and asymmetric shift of the midsurface. Upon linearization with zero Cosserat couple modulus μc = 0, one recovers the infinitesimal-displacement Reissner–Mindlin model. It is shown that the Cosserat shell formulation admits minimizers even for μc = 0, in which case the drill-energy is absent. The midsurface deformation m is found in H1(ω, ℝ3). Since the existence of energy minimizers rather than equilibrium solutions is established, the proposed analysis includes the large deformation/large rotation buckling behaviour of thin shells.

scholarly journals 3D Numerical and Experimental Study on Paraffin Wax Melting in Thermal Storage for the Nozzle-and-Shell, Tube-and-Shell, and Reducer-and-Shell Models

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Agus Dwi Korawan ◽  
Sudjito Soeparman ◽  
Widya Wijayanti ◽  
Denny Widhiyanuriyawan
Keyword(s):  
Experimental Study ◽  
Temperature Distribution ◽  
Shell Model ◽  
Numerical Study ◽  
Liquid Fraction ◽  
Melting Process ◽  
Thermal Storage ◽  
Numerical Approach ◽  
Shell Models ◽  
Time Required

Paraffin melting experienced in the nozzle-and-shell, tube-and-shell, and reducer-and-shell models in thermal storage with 3D numerical and experimental approach has been studied. The numerical study aims to evaluate the melting process and discover temperature distribution, liquid-solid interface, liquid fraction, and the average surface Nusselt number, while the aim of this experimental study is to determine the distribution of melting temperature. The comparison of temperature distribution between the numerical approach and experimental one indicates a good agreement. The comparison result between the three models shows that the melting process of the nozzle-and-shell model is the best, followed by tube-and-shell and reducer-and-shell models, successively. To finish the melting process, the time required is 6130 s for the nozzle-and-shell model, while tube-and-shell model requires 8210 s and reducer-and-shell model requires 12280 s.

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