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.

Two-dimensional elastic continuum model of enterocyte layer migration

2007 ◽  
Vol 22 (4) ◽  
pp. 350
Author(s):  
Qi Mi ◽  
David Swigon ◽  
Beatrice Riviere
Keyword(s):  
Continuum Model ◽  
Two Dimensional ◽  
Elastic Continuum

Elastic continuum analysis and diffraction properties of two-dimensional liquid crystalline grating cells

2009 ◽  
Vol 26 (6) ◽  
pp. 1151 ◽  
Author(s):  
Hiroshi Ono ◽  
Masakata Hishida ◽  
Akira Emoto ◽  
Tatsutoshi Shioda ◽  
Nobuhiro Kawatsuki
Keyword(s):  
Liquid Crystalline ◽  
Two Dimensional ◽  
Elastic Continuum ◽  
Continuum Analysis

Damping of Flexural Vibration by Low-Density Foams and Granular Materials

2003 ◽  
Author(s):  
Kripa K. Varanasi ◽  
Samir A. Nayfeh
Keyword(s):  
Standing Waves ◽  
Flexural Vibration ◽  
Low Density ◽  
Two Dimensional ◽  
Foam Layer ◽  
Elastic Continuum ◽  
Foam Filled ◽  
Aluminum Beam ◽  
Inviscid Compressible Fluid ◽  
Good Agreement

The damping of flexural vibration by introduction of a layer of low-density foam or powder into a structure is investigated. First, we report on experiments in which a layer of foam attached to an aluminum beam gives rise to significant damping at frequencies high enough to induce standing waves in the foam layer. Next, we provide a simple model for such vibration in which the foam is treated as a two-dimensional elastic continuum in which waves can propagate and find that the model is in good agreement with the experiments. Then the results of experiments in which aluminum beams are filled with a low-density powder are presented. The powder-filled beams exhibit behavior qualitatively like that of the foam-filled beams, but we find that the powder can be adequately modeled as an inviscid compressible fluid.

A two-dimensional source function for a dynamic brittle bilateral tensile crack

1970 ◽  
Vol 60 (4) ◽  
pp. 1209-1219 ◽  
Author(s):  
Merle E. Hanson ◽  
Allan R. Sanford
Keyword(s):  
Source Function ◽  
Near Field ◽  
Tensile Fracture ◽  
Two Dimensional ◽  
Tensile Crack ◽  
Elastic Continuum ◽  
Fracture Geometry ◽  
Velocity Function ◽  
Final Fracture ◽  
Fracture Velocity

abstract A numerical technic is used to simulate the two-dimensional elastic dynamic characteristics of a bilateral tensile fracture that accelerates, propagates and stops in an elastic continuum. The fracture-velocity function is specified for the calculation. Particle motion in the near field about the final fracture geometry is the result. Motion parallel to the fracture amounts to as much as 50 per cent of the perpendicular motion near the crack. The relaxation begins to occur after the fracture stops and the dynamic elastic radiation from both tips crosses the material.

scholarly journals Equilibrium of Two-Dimensional Cycloidal Pantographic Metamaterials in Three-Dimensional Deformations

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1523 ◽  
Author(s):  
Daria Scerrato ◽  
Ivan Giorgio
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Variational Formulation ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Element Analysis ◽  
Elastic Continuum ◽  
Bias Extension ◽  
Three Dimensional Space

A particular pantographic sheet, modeled as a two-dimensional elastic continuum consisting of an orthogonal lattice of continuously distributed fibers with a cycloidal texture, is introduced and investigated. These fibers conceived as embedded beams on the surface are allowed to be deformed in a three-dimensional space and are endowed with resistance to stretching, shearing, bending, and twisting. A finite element analysis directly derived from a variational formulation was performed for some explanatory tests to illustrate the behavior of the newly introduced material. Specifically, we considered tests on: (1) bias extension; (2) compressive; (3) shear; and (4) torsion. The numerical results are discussed to some extent. Finally, attention is drawn to a comparison with other kinds of orthogonal lattices, namely straight, parabolic, and oscillatory, to show the differences in the behavior of the samples due to the diverse arrangements of the fibers.

Critical state of a two-dimensional elastic continuum containing elliptical voids

1993 ◽  
Vol 46 (4) ◽  
pp. 553-570 ◽  
Author(s):  
Kaushik Mallick ◽  
Dusan Krajcinovic ◽  
Dragoslav Sumarac ◽  
Milena Vujosevic
Keyword(s):  
Critical State ◽  
Two Dimensional ◽  
Elastic Continuum

A Method for Investigating Certain Eigenvalue Problems of the Buckling and Vibration of Plates

1960 ◽  
Vol 27 (3) ◽  
pp. 557-558 ◽  
Author(s):  
H. D. Conway ◽  
A. W. Leissa
Keyword(s):  
Approximate Solution ◽  
Boundary Value Problems ◽  
Digital Computer ◽  
Eigenvalue Problems ◽  
Boundary Value ◽  
Thin Plates ◽  
Two Dimensional ◽  
Buckling Loads ◽  
Electronic Digital Computer ◽  
Hydrostatic Loading

In a recent investigation, a method was given for the approximate solution of certain boundary-value problems. This method lends itself well to the use of the electronic digital computer and is extended here to investigate the eigenvalue problems of the buckling under two-dimensional hydrostatic loading and the vibration of thin plates. The two-dimensional hydrostatic buckling loads of clamped square and equilateral-triangular plates are found by this method, the values agreeing well with the results obtainable by other methods where these results are known.

scholarly journals Mechanical interactions between adjacent airways in the lung

2014 ◽  
Vol 116 (6) ◽  
pp. 628-634 ◽  
Author(s):  
Baoshun Ma ◽  
Jason H. T. Bates
Keyword(s):  
Computational Model ◽  
Continuum Model ◽  
Network Models ◽  
The Other ◽  
Two Dimensional ◽  
Elastic Continuum ◽  
Spring Network Model ◽  
Triangular Network ◽  
One Airway ◽  
The Continuum

The forces of mechanical interdependence between the airways and the parenchyma in the lung are powerful modulators of airways responsiveness. Little is known, however, about the extent to which adjacent airways affect each other's ability to narrow due to distortional forces generated within the intervening parenchyma. We developed a two-dimensional computational model of two airways embedded in parenchyma. The parenchyma itself was modeled in three ways: 1) as a network of hexagonally arranged springs, 2) as a network of triangularly arranged springs, and 3) as an elastic continuum. In all cases, we determined how the narrowing of one airway was affected when the other airway was relaxed vs. when it narrowed to the same extent as the first airway. For the continuum and triangular network models, interactions between airways were negligible unless the airways lay within about two relaxed diameters of each other, but even at this distance the interactions were small. By contrast, the hexagonal spring network model predicted that airway-airway interactions mediated by the parenchyma can be substantial for any degree of airway separation at intermediate values of airway contraction forces. Evidence to date suggests that the parenchyma may be better represented by the continuum model, which suggests that the parenchyma does not mediate significant interactions between narrowing airways.

Sign in / Sign up

Export Citation Format

Share Document