Plane Contact of an Elastic Layer Supported by a Winkler Foundation

1990 ◽  
Vol 57 (4) ◽  
pp. 974-980 ◽  
Author(s):  
J. P. Dempsey ◽  
Z. G. Zhao ◽  
L. Minnetyan ◽  
H. Li
Keyword(s):  
Elastic Layer ◽  
Beam Theory ◽  
Contact Problems ◽  
Finite Depth ◽  
Winkler Foundation ◽  
Isotropic Layer ◽  
Line Load ◽  
Plane Contact ◽  
Pressure Distributions ◽  
Flexible Foundation

Plane contact problems of an elastic, homogeneous, and isotropic layer supported by a Winkler foundation are studied in this paper. The elastic layer has a finite depth and infinite in-plane dimensions. The upper surface of the layer is in plane contact with a rigid indenter. The particular applications studied in this paper are formulated by first providing the solution for a line load. For the case of a rigid cylinder, the upper portion of the load deflection response is modeled using beam theory with wrapping. The contact pressure distributions for the relatively flexible foundation cases can be accurately determined from the wrapping theory.

Vibration of infinite Timoshenko beam on Pasternak foundation under vehicular load

2017 ◽  
Vol 20 (5) ◽  
pp. 694-703
Author(s):  
Weili Luo ◽  
Yong Xia
Keyword(s):  
Timoshenko Beam ◽  
Current System ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Surface Irregularity ◽  
Radius Of Gyration ◽  
Winkler Foundation ◽  
Shear Rigidity ◽  
Maximum Displacement ◽  
Line Load

The vibration of beams on foundations under a vehicular load has attracted wide attention for decades. The problem has numerous applications in several fields such as highway structures. However, most of analytical or semi-analytical studies simplify the vehicular load as a concentrated point or distributed line load with the constant or harmonically varying amplitude, and neglect the presence of the vehicle and the road irregularity. This article carries out an analytical study of vibration on an infinite Pasternak-supported Timoshenko beam under vehicular load which is generated by the passage of a quarter car on a road with harmonic surface irregularity. The governing equations of motion are derived based on Hamilton’s principle and Timoshenko beam theory and then are solved in the frequency–wavenumber domain with a moving coordinate system. The analytical solutions are expressed in a general form of Cauchy’s residue theorem. The results are validated by the case of an Euler–Bernoulli beam on a Winkler foundation, which is a special case of the current system and has an explicit form of solution. Finally, a numerical example is employed to investigate the influence of properties of the beam (the radius of gyration and the shear rigidity) and the foundation (the shear viscosity, rocking, and normal stiffness) on the deflected shape, maximum displacement, critical frequency, and critical velocity of the system.

Natural Frequencies of a Railroad Track

1987 ◽  
Vol 54 (2) ◽  
pp. 299-304 ◽  
Author(s):  
S. P. Patil
Keyword(s):  
Natural Frequency ◽  
Elastic Layer ◽  
Natural Frequencies ◽  
Unit Length ◽  
Added Mass ◽  
Winkler Foundation ◽  
Railroad Track

The natural frequency of an infinite railroad track was first determined by Timoshenko as ωR = √k/m, where k is the constant for the massless Winkler foundation and m is the mass per unit length of the rail. The natural frequencies of the track are determined here by modeling the track as a beam resting on a 3-D inertial elastic layer. It is shown that the mass of the supporting foundation has a significant effect on the natural frequencies of a railroad track. Finally, the concept of “added mass” is introduced in order to determine the natural frequency in a desired mode of vibration, by modeling the track as a beam on the massless Winkler foundation and adding the mass of the foundation to the beam.

The Frictionless Contact Problem for an Elastic Layer Under Gravity

1975 ◽  
Vol 42 (1) ◽  
pp. 136-140 ◽  
Author(s):  
M. B. Civelek ◽  
F. Erdogan
Keyword(s):  
Elastic Layer ◽  
Mixed Boundary ◽  
Contact Problems ◽  
Simple Problem ◽  
Frictionless Contact ◽  
Continuous Contact ◽  
Crack Problems ◽  
Contact Stress Distribution ◽  
Length Of Separation ◽  
Clamping Pressure

The paper presents a technique for solving the plane frictionless contact problems in the presence of gravity and/or uniform clamping pressure. The technique is described by applying it to a simple problem of lifting of an elastic layer lying on a horizontal, rigid, frictionless subspace by means of a concentrated vertical load. First, the problem of continuous contact is considered and the critical value of the load corresponding to the initiation of interface separation is determined. Then the mixed boundary-value problem of discontinuous contact is formulated in terms of a singular integral equation by closely following a technique developed for crack problems. The numerical results include the contact stress distribution and the length of separation region. One of the main conclusions of the study is that neither the separation length nor the contact stresses are dependent on the elastic constants of the layer.

Plane Contact Problems

2010 ◽  
pp. 271-279
Author(s):  
Robert Asaro ◽  
Vlado Lubarda
Keyword(s):  
Contact Problems ◽  
Plane Contact

Settlement of a strip footing on a confined clay layer

1983 ◽  
Vol 20 (3) ◽  
pp. 535-542
Author(s):  
Brian B. Taylor ◽  
Elmer L. Matyas
Keyword(s):  
Stress Distribution ◽  
Plane Strain ◽  
Poisson’S Ratio ◽  
Ground Surface ◽  
Finite Depth ◽  
Strip Footing ◽  
Poisson's Ratio ◽  
Clay Layer ◽  
Line Load ◽  
Settlement Analysis

A procedure is described that permits an estimation of either consolidation or immediate settlements of a uniformly loaded, flexible strip footing founded below the ground surface. The soil above the base of the footing is sand, and the soil below the base consists of clay, which extends to a finite depth. The procedure is based on a solution of Kelvin's equations for a line load acting within an infinite solid. Charts are presented which permit an estimate of settlement for various compression moduli, Poisson's ratio, and clay thickness.The proposed method predicts consolidation settlements that are generally slightly greater than those predicted from Boussinesq theory. Consolidation settlements increase as Poisson's ratio increases. Immediate settlements are slightly greater than those reported previously. Keywords: consolidation, elasticity, footings, plane strain, settlement analysis, stress distribution.

Sign in / Sign up

Export Citation Format

Share Document