Some inequalities concerning the characteristic frequencies of elastic continuum

1977 ◽  
Vol 112 (1) ◽  
pp. 273-283
Author(s):  
Ludvik Janos
Keyword(s):  
Elastic Continuum ◽  
Characteristic Frequencies

THE GLASS AS AN ELASTIC CONTINUUM

1982 ◽  
Vol 43 (C9) ◽  
pp. C9-475-C9-479 ◽  
Author(s):  
D. M. Duffy ◽  
N. Rivier
Keyword(s):  
Elastic Continuum

Elastic continuum stiffness of contractile tail sheaths from molecular dynamics simulations

2019 ◽  
Vol 151 (18) ◽  
pp. 185103
Author(s):  
A. Chatterjee ◽  
A. Maghsoodi ◽  
N. C. Perkins ◽  
I. Andricioaei
Keyword(s):  
Molecular Dynamics ◽  
Molecular Dynamics Simulations ◽  
Elastic Continuum ◽  
Contractile Tail ◽  
Dynamics Simulations

scholarly journals Electrically turning periodic structures in cholesteric layer with conical–planar boundary conditions

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Oxana Prishchepa ◽  
Mikhail Krakhalev ◽  
Vladimir Rudyak ◽  
Vitaly Sutormin ◽  
Victor Zyryanov
Keyword(s):  
Boundary Conditions ◽  
Periodic Structures ◽  
Cholesteric Liquid Crystal ◽  
Growth Direction ◽  
Smooth Transition ◽  
Defect Structures ◽  
Optical Cell ◽  
Elastic Continuum ◽  
The One ◽  
Experimental Findings

AbstractElectro-optical cell based on the cholesteric liquid crystal is studied with unique combination of the boundary conditions: conical anchoring on the one substrate and planar anchoring on another one. Periodic structures in cholesteric layer and their transformation under applied electric field are considered by polarizing optical microscopy, the experimental findings are supported by the data of the calculations performed using the extended Frank elastic continuum approach. Such structures are the set of alternating over- and under-twisted defect lines whose azimuthal director angles differ by $$180^\circ$$ 180 ∘ . The $$U^+$$ U + and $$U^-$$ U - -defects of periodicity, which are the smooth transition between the defect lines, are observed at the edge of electrode area. The growth direction of defect lines forming a diffraction grating can be controlled by applying a voltage in the range of $$0\le \, V \le 1.3$$ 0 ≤ V ≤ 1.3  V during the process. Resulting orientation and distance between the lines don’t change under voltage. However, at $$V>1.3$$ V > 1.3  V $$U^+$$ U + -defects move along the defect lines away from the electrode edges, and, finally, the grating lines collapse at the cell’s center. These results open a way for the use of such cholesteric material in applications with periodic defect structures where a periodicity, orientation, and configuration of defects should be adjusted.

scholarly journals Buckling of Continuously Supported Beams

1973 ◽  
Vol 40 (2) ◽  
pp. 546-552 ◽  
Author(s):  
G. K. N. Murthy
Keyword(s):  
Two Dimensional ◽  
Elastic Continuum ◽  
Buckling Loads

The buckling of infinite beams continuously supported by a semi-infinite elastic continuum is investigated. The buckling loads were determined when the beam rests on a two-dimensional elastic continuum and also when the foundation extends beyond the width of the beam. The effect of the outside foundation is shown by comparing the obtained buckling loads.

Bending of an Infinite Beam on an Elastic Foundation

1937 ◽  
Vol 4 (1) ◽  
pp. A1-A7 ◽  
Author(s):  
M. A. Biot
Keyword(s):  
Elastic Foundation ◽  
Poisson Ratio ◽  
Elementary Theory ◽  
Three Dimensional ◽  
Bending Moment ◽  
Two Dimensional ◽  
Concentrated Load ◽  
Elastic Continuum ◽  
Infinite Beam ◽  
A Value

Abstract The elementary theory of the bending of a beam on an elastic foundation is based on the assumption that the beam is resting on a continuously distributed set of springs the stiffness of which is defined by a “modulus of the foundation” k. Very seldom, however, does it happen that the foundation is actually constituted this way. Generally, the foundation is an elastic continuum characterized by two elastic constants, a modulus of elasticity E, and a Poisson ratio ν. The problem of the bending of a beam resting on such a foundation has been approached already by various authors. The author attempts to give in this paper a more exact solution of one aspect of this problem, i.e., the case of an infinite beam under a concentrated load. A notable difference exists between the results obtained from the assumptions of a two-dimensional foundation and of a three-dimensional foundation. Bending-moment and deflection curves for the two-dimensional case are shown in Figs. 4 and 5. A value of the modulus k is given for both cases by which the elementary theory can be used and leads to results which are fairly acceptable. These values depend on the stiffness of the beam and on the elasticity of the foundation.

Mechanical Modeling of Thin Films and Cover Plates Bonded to Graded Substrates

2008 ◽  
Vol 75 (5) ◽  
Author(s):  
Mehmet A. Guler
Keyword(s):  
Thin Films ◽  
Stress Intensity ◽  
Interfacial Shear Stress ◽  
Contact Problems ◽  
Stress Concentrations ◽  
Elastic Continuum ◽  
Temperature Changes ◽  
Initiation And Propagation ◽  
Axial Normal Stress ◽  
Cover Plates

In this study, the contact problems of thin films and cover plates are considered. In these problems, the loading consists of any one or combination of stresses caused by uniform temperature changes and temperature excursions, far field mechanical loading, and residual stresses resulting from film processing or welding. The primary interest in this study is in examining stress concentrations or singularities near the film ends for the purpose of addressing the question of crack initiation and propagation in the substrate or along the interface. The underlying contact mechanics problem is formulated by assuming that the film is a “membrane” and the substrate a graded elastic continuum, and is solved analytically by reducing it to an integral equation. The calculated results are the interfacial shear stress between the film and the graded substrate, the Mode II stress intensity factor at the end of the film, and the axial normal stress in the film. The results indicate that grading the material properties of the substrate helps to decrease the film stresses and the stress intensity factors at the free edges and to lower the axial normal stresses at the midsection where the film is most likely to crack.

A CUBIC ARRANGED SPHERICAL DISCRETE ELEMENT MODEL

2014 ◽  
Vol 11 (05) ◽  
pp. 1350102 ◽  
Author(s):  
WEI GAO ◽  
YUANQIANG TAN ◽  
MENGYAN ZANG
Keyword(s):  
Strain Energy ◽  
Element Model ◽  
Discrete Element ◽  
Discrete Element Model ◽  
Laminated Plate ◽  
Discrete Elements ◽  
Elastic Continuum ◽  
Vibration Process ◽  
Spring Constants ◽  
Dem Model

A 3D discrete element model (DEM model) named cubic arranged discrete element model is proposed. The model treats the interaction between two connective discrete elements as an equivalent "beam" element. The spring constants between two connective elements are obtained based on the equivalence of strain energy stored in a unit volume of elastic continuum. Following that, the discrete element model proposed and its algorithm are implemented into the in-house developed code. To test the accuracy of the DEM model and its algorithm, the vibration process of the block, a homogeneous plate and laminated plate under impact loading are simulated in elastic range. By comparing the results with that calculated by using LS-DYNA, it is found that they agree with each other very well. The accuracy of the DEM model and its algorithm proposed in this paper is proved.

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