Analytic Solution for Dynamic Loading on Half‐Space Medium

Liou, Gin-Show; Lee, George C.; Ketter, Robert L.

doi:10.1061/(asce)0733-9399(1991)117:7(1485)

Cited by 8 publications

(7 citation statements)

References 3 publications

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“…Liou has developed a technique to decompose the boundary conditions to fit the general solutions of wave equations in cylindrical coordinates for the cases of layered media. The technique has been successfully applied to find the impedance functions for foundations on layered half-space medium [10] and axial symmetric foundation embedded in layered medium [11]. Liou and Chung [12] extended the methods which are prescribed harmonic tractions time history to found the shapes function of the stress and displacement fields in interior domain.…”

Section: Introductionmentioning

confidence: 99%

Solving of the Transcendental Equations in Layered Media

Lei¹,

Chung²

2015

Proceedings of the 4th International Conference on Information Technology and Management Innovation

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In this paper, we use an efficient method to solve the wave numbers of transient wave propagation in layered media. To solve those problems, the analytic solution for the interior domain is combined both a homogeneous solution and a particular solution, the exterior domain is described by a homogeneous solution only. To obtain the homogeneous solution, one has challenge to solve the complex root of the transcendental equations will be discussed. For the soil-structure interaction problem, the wave number of transient wave propagation in layered media will be used for the impedance matrix of embedded axial symmetric foundation.

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Section: Introductionmentioning

confidence: 99%

Solving of the Transcendental Equations in Layered Media

Lei¹,

Chung²

2015

Proceedings of the 4th International Conference on Information Technology and Management Innovation

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“…For example, Lysmer (1965) used the analytic solution for constant normal ring traction on half-space medium to generate a vertical compliance function (inverse of impedance function) for a rigid circular plate; and Luco and Westmann (1971) calculated all the compliance functions for a rigid circular plate on a half-space medium by reducing Fredholm integral equations to algebraic equations using the finite difference method. Liou et al (1991;1992) developed a technique to decompose the prescribed tractions on half-space and layered half-space media, which can match with general solutions of wave equations in cylindrical coordinates, to generate all the impedance functions for a rigid circular plate rigidly welded on soil medium.…”

Section: Introductionmentioning

confidence: 99%

“…For the substructure of foundation, the classical plate theory with ignorance of inertial force is employed to solve the problem of the foundation plate subjected to the assumed unknown contact stress. For the soil medium with prescribed unknown contact stresses, the technique, developed by Liou (1989Liou ( , 1991Liou ( , 1992, is employed to decompose the prescribed unknown contact stresses in order to match with the general solution of wave equations in cylindrical coordinates. Then, the condition of displacement continuity for the foundation plate and soil medium is imposed through variational principle to obtain the unknown intensities of piecewise linear contact stresses and the impedance functions for the foundation plate.…”

Section: Introductionmentioning

confidence: 99%

Effect of Flexibility on Impedance Functions for Circular Foundation

Liou

Huang

1994

J. Eng. Mech.

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This paper investigates the effect of foundation rigidity on impedance functions for a circular foundation on a viscoelastic soil medium. In addition to vertical and rocking impedances, the paper also investigates the influence on coupling impedance for horizontal and rocking motions of foundation and horizontal impedance. To generate impedance functions for flexible foundation, a substructure technique is used. For the substructure of the flexible foundation, classical plate theory with neglecting inertial force is employed to obtain the deformation of the foundation due to the interaction stress. For the substructure of the soil medium, the technique, which can deal with wave equations in cylindrical coordinates with arbitrarily prescribed boundary conditions, is employed to obtain the displacement field in the soil medium due to the interaction stresses. Then, with the help of the variational principle, the displacement continuity condition of both substructures is imposed to generate the impedances for the flexible foundation. To demonstrate the effectiveness of the presented procedure, comparison with some previous numerical results is made. Selected numerical results of the presented procedure are presented. Also, comparison between results with and without the assumption of relaxed stress condition is given in order to show the significance of the assumption.

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“…2-3 show the comparisons. In these figures, damping ratio ξ = 0.05 is selected, the thickness L of layer is gradually increased from a 0 L = 0.5 to a 0 L = 0.1 , and the numerical results are compared to that of Liou's previous work [11,15]. In general, one can observed that the results of impedance functions for the case of one layer stratum is approaching that for the case of half-space medium, as a 0 L is getting smaller.…”

Section: Numerical Investigationsmentioning

confidence: 99%

“…The technique has been successfully applied to find the impedance functions for foundations on layered half-space medium [11,12] and axial symmetric foundation embedded in layered medium [13]. For the cases of foundation embedded in half-space medium, one can approximate the cases by increasing the thickness of a layered medium, if material damping exists in the half-space medium.…”

Section: Introductionmentioning

confidence: 99%

Calculation of impedances for axial symmetric foundation embedded in half-space medium using solutions for one layer stratum

Chung

Liou

2013

Lat. Am. j. solids struct.

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The paper is devoted to develop a new scheme to calculate impedance matrices for axial-symmetric foundations embedded in halfspace medium. The half-space medium can be approximated by increasing thickness of one layer stratum on rigid bedrock due to the effect of material damping. However, as thickness increases, the numerical problem will arise. This problem is caused by the numerical contamination by some negligible reflection waves from rigid bedrock. In reality, the effect of these reflection waves on impedance is getting small as the thickness of the one layer stratum increases. Therefore, the scheme will employ the solutions for one layer stratum with suppressing these reflection waves to generate the impedance for the case of half-space. The numerical results by the presented scheme are compared with the results by other scheme in order to show that the new numerical scheme is effective and the solutions in layered medium can be extended to obtain the results for the cases of layered half-space medium. Some numerical results of torsional, vertical, horizontal, coupling and rocking impedances with different embedded depths will be presented and comments on the numerical scheme will be given.

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Analytic Solution for Dynamic Loading on Half‐Space Medium

Cited by 8 publications

References 3 publications

Solving of the Transcendental Equations in Layered Media

Solving of the Transcendental Equations in Layered Media

Effect of Flexibility on Impedance Functions for Circular Foundation

Calculation of impedances for axial symmetric foundation embedded in half-space medium using solutions for one layer stratum

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