Dual integral equations applied to the steady-state vibration elastic contact problem for the half-space

1977 ◽  
Vol 7 (4) ◽  
pp. 437-447
Author(s):  
I. Zlatina
Keyword(s):  
Steady State ◽  
Contact Problem ◽  
Integral Equations ◽  
Half Space ◽  
Elastic Contact ◽  
Dual Integral Equations

scholarly journals Dynamic Behavior of an Embedded Foundation under Horizontal Vibration in a Poroelastic Half-Space

2019 ◽  
Vol 9 (4) ◽  
pp. 740 ◽  
Author(s):  
Yang Chen ◽  
Wen Zhao ◽  
Pengjiao Jia ◽  
Jianyong Han ◽  
Yongping Guan
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Mixed Boundary ◽  
Fredholm Integral Equations ◽  
Wave Forces ◽  
Dual Integral Equations ◽  
Horizontal Vibration ◽  
Embedded Foundation ◽  
Embedded Foundations ◽  
Caisson Foundations

More and more huge embedded foundations are used in large-span bridges, such as caisson foundations and anchorage open caisson foundations. Most of the embedded foundations are undergoing horizontal vibration forces, that is, wind and wave forces or other types of dynamic forces. The embedded foundations are regarded as rigid due to its high stiffness and small deformation during the forcing process. The performance of a rigid, massive, cylindrical foundation embedded in a poroelastic half-space is investigated by an analytical method developed in this paper. The mixed boundary problem is solved by reducing the dual integral equations to a pair of Fredholm integral equations of the second kind. The numerical results are compared with existing solutions in order to assess the accuracy of the presented method. To further demonstrate the applicability of this method, parametric studies are performed to evaluate the dynamic response of the embedded foundation under horizontal vibration. The horizontal dynamic impedance and response factor of the embedded foundation are examined based on different embedment ratio, foundation mass ratio, relative stiffness, and poroelastic material properties versus nondimensional frequency. The results of this study can be adapted to investigate the horizontal vibration responses of a foundation embedded in poroelastic half-space.

scholarly journals Contact problem for bonded nonhomogeneous materials under shear loading

2003 ◽  
Vol 2003 (29) ◽  
pp. 1821-1832
Author(s):  
B. M. Singh ◽  
J. Rokne ◽  
R. S. Dhaliwal ◽  
J. Vrbik
Keyword(s):  
Contact Problem ◽  
Integral Equations ◽  
Plane Surface ◽  
Shear Loading ◽  
Fredholm Integral Equations ◽  
Nonhomogeneous Medium ◽  
Dual Integral Equations ◽  
Fourier Cosine ◽  
Common Plane ◽  
Perfect Bonding

The present paper examines the contact problem related to shear punch through a rigid strip bonded to a nonhomogeneous medium. The nonhomogeneous medium is bonded to another nonhomogeneous medium. The strip is perpendicular to they-axis and parallel to thex-axis. It is assumed that there is perfect bonding at the common plane surface of two nonhomogeneous media. Using Fourier cosine transforms, the solution of the problem is reduced to dual integral equations involving trigonometric cosine functions. Later on, the solution of the dual integral equations is transformed into the solution of a system of two simultaneous Fredholm integral equations of the second kind. Solving numerically the Fredholm integral equations of the second kind, the numerical results of resultant contact shear are obtained and graphically displayed to demonstrate the effect of nonhomogeneity of the elastic material.

scholarly journals Steady state temperatures in a quarter plane

1996 ◽  
Vol 19 (2) ◽  
pp. 371-380 ◽  
Author(s):  
B. D. Aggarwala ◽  
C. Nasim
Keyword(s):  
Steady State ◽  
Boundary Value Problem ◽  
Integral Equations ◽  
Boundary Value ◽  
Dual Integral Equations ◽  
Discontinuous Boundary ◽  
Quarter Plane

The discontinuous boundary value problem of steady state temperatures in a quarter plane gives rise to a pair of dual integral equations which are not of Titchmarch type. These dual integral equations are considered in this paper.

scholarly journals Elastic Contact Problem of Elastic Half-Space Indented by an Arbitrary Shaped Punch

2003 ◽  
Vol 69 (687) ◽  
pp. 1545-1551
Author(s):  
Toshikazu SHIBUYA ◽  
Terutaka KAI ◽  
Kikuo KISHIMOTO ◽  
Hirotsugu INOUE ◽  
Kentaro TAKAHASHI
Keyword(s):  
Contact Problem ◽  
Half Space ◽  
Elastic Half Space ◽  
Elastic Contact

Contact Problem Involving Frictional Heating for Rough Half-Space

2004 ◽  
Vol 71 (2) ◽  
pp. 287-290 ◽  
Author(s):  
Volodymyr Pauk
Keyword(s):  
Contact Problem ◽  
Integral Equations ◽  
Half Space ◽  
Contact Pressure ◽  
Heat Generation ◽  
Gaussian Distribution ◽  
Frictional Heating ◽  
Nonlinear Integral Equations ◽  
Plane Contact ◽  
Contact Size

Plane contact problem of a punch sliding over a half-space is considered. The surface of the half-space is assumed to be rough and the roughness heights have the Gaussian distribution. The heat generation due to the friction is taken into account. The problem is reduced to nonlinear integral equations which are solved approximately. The effects of the frictional heating and the roughness on the contact size and on the contact pressure are presented.

Elastic contact problem of elastic half-space indented by an arbitrary shaped stamp

2002 ◽  
Vol 2002 (0) ◽  
pp. 373-374
Author(s):  
Toshikazu SHIBUYA ◽  
Terutaka KAI ◽  
Kikuo KISHIMOTO ◽  
Hirotsugu INOUE ◽  
Kentaro TAKAHASHI
Keyword(s):  
Contact Problem ◽  
Half Space ◽  
Elastic Half Space ◽  
Elastic Contact
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