Contact between a curved viscoelastic beam and a rigid plane

1973 ◽  
Vol 8 (1) ◽  
pp. 58-64 ◽  
Author(s):  
I Granstam
Keyword(s):  
Horizontal Plane ◽  
Contact Point ◽  
Critical Time ◽  
Contact Problems ◽  
Critical Value ◽  
Curved Beam ◽  
Viscoelastic Beam ◽  
Elastic Bodies ◽  
Concentrated Forces ◽  
Rigid Plane

The following problem has been analysed by the theory of small deflections of bending. A circularly curved beam of Maxwell material is pressed against a rigid horizontal plane by two constant and concentrated forces P, each acting on one end of the beam. Before loading there is contact only at the mid-point of the beam. As load is applied the Maxwellian beam behaves like a Hookean beam. If the load P is below a critical value Pc, there is contact only at the mid-point, but if the load exceeds this value, linear contact is formed along a certain length 2λ° of the beam. At the time t the beam will rise from the support over a distance of 2λ° ( t) if the load P exceeds Pc, while if P is less than Pc there will be a similar deflection only after a critical time tc. The contact pressure is two concentrated forces, acting on each contact point. Expressions for the deflections w(O, t) and w( L, t) of the centre and the ends of the beam are also derived and are compared with corresponding expressions for a Hookean beam. The paper shows that essential differences can exist between contact problems with similar viscoelastic or elastic bodies.

scholarly journals Analytical calculation of time of reaching specific values based on visibility loss during a fire

2018 ◽  
Vol 193 ◽  
pp. 03007 ◽  
Author(s):  
Sergei Kolodyazhniy ◽  
Vladimir Kozlov
Keyword(s):  
Mathematical Model ◽  
Analytical Solutions ◽  
Ventilation System ◽  
Analytical Calculation ◽  
Critical Time ◽  
Original Data ◽  
Critical Value ◽  
Time Intervals ◽  
Evacuation Time ◽  
Analytical Formulas

Using an integral mathematical model of a fire considering the assumptions typical of a starting stage of a fire, analytical dependencies were obtained for determining the time of reaching a critical value of the density of a smoke screen in a premises with a fire epicenter and adjoining premises. By means of analytical formulas for determining critical evacuation time intervals based on visibility loss, table values for different parameters that are included in the original equations were obtained. Simple engineering analytical solutions that describe the dynamics of smoke formation in premises in case of a fire when used in a certain combination are presented. The obtained dependencies allow one to identify the critical time of evacuation with no use of special PC software as well as to obtain original data without calculating an anti-smoke ventilation system.

Contact Analysis of Functionally Graded Materials Using Smoothed Finite Element Methods

2019 ◽  
Vol 17 (05) ◽  
pp. 1940012 ◽  
Author(s):  
Y. F. Zhang ◽  
J. H. Yue ◽  
M. Li ◽  
R. P. Niu
Keyword(s):  
Finite Element ◽  
Functionally Graded Materials ◽  
Contact Point ◽  
Linear Complementarity Problems ◽  
Contact Problems ◽  
Contact Analysis ◽  
Functionally Graded ◽  
Numerical Results ◽  
Graded Materials ◽  
Stiffness Matrices

In the paper, the smoothed finite element method (S-FEM) based on linear triangular elements is used to solve 2D solid contact problems for functionally graded materials. Both conforming and nonconforming contacts algorithms are developed using modified Coulomb friction contact models including tangential strength and normal adhesion. Based on the smoothed Galerkin weak form, the system stiffness matrices are created using the formulation procedures of node-based S-FEM (NS-FEM) and edge-based S-FEM (ES-FEM), and the contact interface equations are discretized by contact point-pairs. Then these discretized system equations are converted into a form of linear complementarity problems (LCPs), which can be further solved efficiently using the Lemke method. The singular value decomposition method is used to deal with the singularity of the stiffness matrices in the procedure constructing the standard LCP, which can greatly improve the stability and accuracy of the numerical results. Numerical examples are presented to investigate the effects of the various parameters of functionally graded materials and comparisons have been made with reference solutions and the standard FEM. The numerical results demonstrate that the strain energy solutions of ES-FEM have higher convergence rate and accuracy compared with that of NS-FEM and FEM for functionally graded materials through the present contact analysis approach.

The method of caustics for the determination of normal loads acting on surfaces of elastic bodies

1980 ◽  
Vol 15 (1) ◽  
pp. 37-41 ◽  
Author(s):  
P S Theocaris ◽  
N I Ioakimidis
Keyword(s):  
Three Dimensional ◽  
Contact Problems ◽  
Two Dimensional ◽  
Concentrated Force ◽  
Elastic Bodies ◽  
Plate And Shell ◽  
Elasticity Problems ◽  
Three Dimensional Elasticity ◽  
Quantities Of Interest

The optical method of caustics constitutes an efficient experimental technique for the determination of quantities of interest in elasticity problems. Up to now, this method has been applied only to two-dimensional elasticity problems (including plate and shell problems). In this paper, the method of caustics is extended to the case of three-dimensional elasticity problems. The particular problems of a concentrated force and a uniformly distributed loading acting normally on a half-space (on a circular region) are treated in detail. Experimentally obtained caustics for the first of these problems were seen to be in satisfactory agreement with the corresponding theoretical forms. The treatment of various, more complicated, three-dimensional elasticity problems, including contact problems, by the method of caustics is also possible.

Contact Problems in Wire Ropes

1979 ◽  
Vol 101 (4) ◽  
pp. 702-710 ◽  
Author(s):  
S. D. S. R. Karamchetty ◽  
W. Y. Yuen
Keyword(s):  
Contact Point ◽  
Contact Problems ◽  
Wire Rope ◽  
Computer Method ◽  
Wire Ropes ◽  
Basic Model ◽  
Contact Points ◽  
Double Helices

Forces are transmitted across the contact points in a wire rope. Wires tend to bend in between the contact points and they tend to nick and cut at the contact points. A computer method is discussed to determine the contact points in a wire rope. In a geometrically perfect wire rope with the wires laid as double-helices no contact point occurs. But in an actual rope, the geometry changes while laying and due to loading, thus permitting contacts at a number of points. The paper discusses such contact points. Some refinements of the basic model were considered and results presented.

A Modified Conjugate Gradient Method for Frictionless Contact Problems

1983 ◽  
Vol 105 (2) ◽  
pp. 242-246 ◽  
Author(s):  
W. R. Marks ◽  
N. J. Salamon
Keyword(s):  
Finite Element ◽  
Conjugate Gradient ◽  
Solution Method ◽  
Contact Region ◽  
Contact Problems ◽  
Computer Code ◽  
Frictionless Contact ◽  
Elastic Bodies ◽  
Gradient Technique ◽  
Modified Conjugate Gradient Method

The solution of elastic bodies in contact through the application of a conjugate gradient technique integrated with a finite element computer code is discussed. This approach is general, easily applied, and reasonably efficient. Furthermore the solution method is compatible with existing finite element computer programs. The necessary algorithm for use of the technique is described in detail. Numerical examples of two-dimensional frictionless contact problems are presented. It is found that the extent of the contact region and the displacements and stresses throughout the contacting bodies can be economically computed with precision.

scholarly journals Unilateral Contact of Elastic Bodies (Moment Theory)

2001 ◽  
Vol 8 (4) ◽  
pp. 753-766
Author(s):  
R. Gachechiladze
Keyword(s):  
Contact Zone ◽  
Couple Stress Theory ◽  
Contact Problems ◽  
Theory Of Elasticity ◽  
Unilateral Contact ◽  
Stress Theory ◽  
Nonhomogeneous Media ◽  
Elastic Bodies ◽  
The Moment ◽  
Boundary Contact

Abstract Boundary contact problems of statics of the moment (couple-stress) theory of elasticity are studied in the case of a unilateral contact of two elastic anisotropic nonhomogeneous media. A problem, in which during deformation the contact zone lies within the boundaries of some domain, and a problem, in which the contact zone can extend, are given a separate treatment. Concrete problems suitable for numerical realizations are considered.

A simple node-to-segment contact technique of finite element models of elastic bodies to attain the node-to-node contact accuracy

2013 ◽  
Vol 228 (7) ◽  
pp. 1089-1093 ◽  
Author(s):  
Kisu Lee
Keyword(s):  
Numerical Simulation ◽  
Finite Element ◽  
Contact Point ◽  
Finite Element Models ◽  
Elastic Bodies ◽  
Contact Constraint

By modifying the contact point displacement with a simple and systematic way, it has been explained that the node-to-segment contact solution can become as accurate as that of the node-to-node contact constraint. The accuracy of the solution is demonstrated by the numerical simulation using a punch sliding on the slab.

On perturbations of Jeffery-Hamel flow

1988 ◽  
Vol 186 ◽  
pp. 559-581 ◽  
Author(s):  
W. H. H. Banks ◽  
P. G. Drazin ◽  
M. B. Zaturska
Keyword(s):  
Stokes Equations ◽  
Temporal Stability ◽  
Pitchfork Bifurcation ◽  
Critical Value ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Nonlinear Perturbations ◽  
Navier Stokes Equations ◽  
Weakly Nonlinear ◽  
Rigid Plane

We examine various perturbations of Jeffery-Hamel flows, the exact solutions of the Navier-Stokes equations governing the steady two-dimensional motions of an incompressible viscous fluid from a line source at the intersection of two rigid plane walls. First a pitchfork bifurcation of the Jeffery-Hamel flows themselves is described by perturbation theory. This description is then used as a basis to investigate the spatial development of arbitrary small steady two-dimensional perturbations of a Jeffery-Hamel flow; both linear and weakly nonlinear perturbations are treated for plane and nearly plane walls. It is found that there is strong interaction of the disturbances up- and downstream if the angle between the planes exceeds a critical value 2α2, which depends on the value of the Reynolds number. Finally, the problem of linear temporal stability of Jeffery-Hamel flows is broached and again the importance of specifying conditions up- and downstream is revealed. All these results are used to interpret the development of flow along a channel with walls of small curvature. Fraenkel's (1962) approximation of channel flow locally by Jeffery-Hamel flows is supported with the added proviso that the angle between the two walls at each station is less than 2α2.

scholarly journals THE NON-VISCOUS BURGERS EQUATION ASSOCIATED WITH RANDOM POSITION IN COORDINATE SPACE: A THRESHOLD FOR BLOW UP BEHAVIOUR

2009 ◽  
Vol 19 (05) ◽  
pp. 749-767 ◽  
Author(s):  
SERGIO ALBEVERIO ◽  
OLGA ROZANOVA
Keyword(s):  
Burgers Equation ◽  
Blow Up ◽  
Critical Time ◽  
Threshold Effect ◽  
Critical Value ◽  
Initial Distribution ◽  
Coordinate Space ◽  
Random Position ◽  
The Mean ◽  
Particle Paths

It is well known that the solutions to the non-viscous Burgers equation develop a gradient catastrophe at a critical time provided the initial data have a negative derivative in certain points. We consider this equation assuming that the particle paths in the medium are governed by a random process with a variance which depends in a polynomial way on the velocity. Given an initial distribution of the particles which is uniform in space and with the initial velocity linearly depending on the position, we show both analytically and numerically that there exists a threshold effect: if the power in the above variance is less than 1, then the noise does not influence the solution behavior, in the following sense: the mean of the velocity when we keep the value of position fixed goes to infinity outside the origin. If, however, the power is larger or equal to 1, then this mean decays to zero as the time tends to a critical value.

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