Method of determining the deformation characteristics of an elastic foundation bed combining an elastic half-space and a winkler foundation bed

1971 ◽  
Vol 8 (4) ◽  
pp. 234-238 ◽  
Author(s):  
S. Rakhimov ◽  
L. N. Repnikov
Keyword(s):  
Half Space ◽  
Elastic Foundation ◽  
Elastic Half Space ◽  
Winkler Foundation ◽  
Deformation Characteristics

Moving Load on a Plate Resting on an Elastic Half Space

1967 ◽  
Vol 34 (4) ◽  
pp. 910-914 ◽  
Author(s):  
J. D. Achenbach ◽  
S. P. Keshava ◽  
G. Herrmann
Keyword(s):  
Half Space ◽  
Moving Load ◽  
Elastic Half Space ◽  
Winkler Foundation ◽  
Bending Moments ◽  
Line Load ◽  
Resonance Effects ◽  
Small Load ◽  
Smooth Contact ◽  
Time Invariant

An elastic plate supported by a semi-infinite elastic continuum is subjected to a moving line load. Both welded and smooth contact between plate and foundation are considered. Dynamic solutions for the bending moments in the plate are presented that are time-invariant relative to a coordinate system moving with the load. Resonance effects at certain critical velocities are discussed. The response of the system depends significantly on the relative stiffness of plate and half space and on the type of contact. For the relatively stiff plate certain resonances occur for smooth contact but not for welded contact. For subcritical load velocities the bending moments are calculated and compared with corresponding bending moments for a plate on a Winkler foundation. The Winkler foundation is adequate for smooth contact and small load velocities.

A concave indenter on a piezoelectromagneto-elastic substrate or a layer elastically supported

2012 ◽  
Vol 47 (6) ◽  
pp. 362-378 ◽  
Author(s):  
Bogdan Rogowski
Keyword(s):  
Half Space ◽  
Elastic Foundation ◽  
Contact Region ◽  
Approximate Solutions ◽  
Elastic Half Space ◽  
Solution Technique ◽  
Elementary Functions ◽  
Full Field ◽  
Full Contact ◽  
Two Parameter

Indentation of piezoelectromagneto-elastic half-space or a layer on a two-parameter elastic foundation by a cylindrical indenter with a slightly concave base is considered. Full-field magnetoelectro-elastic solutions in elementary functions are obtained for the case of full contact and half-space. If the axial load is small, the contact area will be an annulus the outer circumference of which coincides with the edge of the punch. The inner circumference will shrink with increasing load and there will be a critical load above which the stratum makes contact with the entire punch base. The contact problem for high loads can therefore be treated by classical methods. The more interested case in which the load is less the critical value and the contact region is annulus remains. By use the methods of triple integral equations and series solution technique the solution for an indentured substrate over an annular contact region is also given. For parabolic and conical concave punches the exact or approximate solutions are obtained for full contact or annular contact region, respectively. For the layer on two-parameter elastic foundation and concave punch approximate solution is established.

Unbonded Contact of a Square Plate on an Elastic Half-Space or a Winkler Foundation

1988 ◽  
Vol 55 (2) ◽  
pp. 430-436 ◽  
Author(s):  
Hui Li ◽  
J. P. Dempsey
Keyword(s):  
Contact Problem ◽  
Half Space ◽  
Contact Region ◽  
Elastic Half Space ◽  
Unilateral Contact ◽  
Winkler Foundation ◽  
Vertical Loading ◽  
Centrally Symmetric ◽  
Receding Contact ◽  
Square Plate

The unbonded frictionless receding contact problem of a thin plate placed under centrally symmetric vertical loading while resting on an elastic half-space or a Winkler foundation is solved in this paper. The problem is transformed into the solution of two-coupled integral-series equations over an unknown contact region. The problem is nonlinear by virtue of unilateral contact and therefore needs to be solved iteratively. Special attention is given to the edge and corner contact pressure singularities for the plate on the elastic half-space. Comparison is made with other relevant numerical results available.

Problems in calculating the flexure of beams on elastic foundation

1987 ◽  
Vol 14 (4) ◽  
pp. 581-584 ◽  
Author(s):  
Dajun Ding
Keyword(s):  
Half Space ◽  
Elastic Foundation ◽  
Elastic Characteristic ◽  
Elastic Half Space ◽  
Algebraic Equations ◽  
Improved Method ◽  
Concentrated Loads ◽  
Dimensionless Coefficient ◽  
Loading Case ◽  
Beams On Elastic Foundation

This paper deals with some problems concerning the flexure of beams on an elastic half space. Based on the link method of Zemochkin, the author gives an improved method by which the number of simultaneous algebraic equations can be reduced by 2. Following the author's proposal, the universal tables of reaction coefficients for any loading case are compiled. The author has obtained dimensionless coefficients of reaction, shear, and moment between the infinite and semi-infinite beams subjected to concentrated loads and those under moments, so the coefficient tables of long beams under concentrated loads can be used for calculating those under moments. Key words: elastic foundation, settlement, half-plane and half-space, link method, pressure, segment, typical equation, matrix, dimensionless coefficient, long (infinite and semi-infinite) beam, finite beam (beam with finite length), elastic characteristic value.

The efficiency of application of virtual cross-sections method and hypotheses MELS in problems of wave signal propagation in elastic waveguides with rough surfaces

2016 ◽  
pp. 3564-3575 ◽  
Author(s):  
Ara Sergey Avetisyan
Keyword(s):  
Half Space ◽  
Cross Sections ◽  
Classical Method ◽  
Signal Propagation ◽  
Elastic Half Space ◽  
Layered Systems ◽  
Surface Layers ◽  
Inhomogeneous Surface ◽  
Wave Signal ◽  
The Impact

The efficiency of virtual cross sections method and MELS (Magneto Elastic Layered Systems) hypotheses application is shown on model problem about distribution of wave field in thin surface layers of waveguide when plane wave signal is propagating in it. The impact of surface non-smoothness on characteristics of propagation of high-frequency horizontally polarized wave signal in isotropic elastic half-space is studied. It is shown that the non-smoothness leads to strong distortion of the wave signal over the waveguide thickness and along wave signal propagation direction as well.  Numerical comparative analysis of change in amplitude and phase characteristics of obtained wave fields against roughness of weakly inhomogeneous surface of homogeneous elastic half-space surface is done by classical method and by proposed approach for different kind of non-smoothness.

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