Elastic displacement fields of multi-layered transversely isotropic materials under rectangular loads

Zhang, Pengchong; Liu, Jun; Lin, Gao; Wang, Wenyuan

doi:10.1080/19648189.2016.1229233

Cited by 9 publications

(8 citation statements)

References 37 publications

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“…Chen applied the PIM to derive the Green's function for a transversely isotropic multilayered half‐space. Zhang et al studied the elastic displacement fields of multilayered transversely isotropic materials under rectangular loads by using the PIM. Recently, by combining the integral transformation techniques, Ai and his cooperators extended the PIM to deal with the poroelastic and thermoelastic as well as porous thermoelastic problems for multilayered media, and this approach showed a good applicability for complicated multilayered models.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, by combining the integral transformation techniques, Ai and his cooperators extended the PIM to deal with the poroelastic and thermoelastic as well as porous thermoelastic problems for multilayered media, and this approach showed a good applicability for complicated multilayered models. The PIM is a highly accurate method to solve sets of first‐order ordinary differential equations and can ensure to achieve any desired accuracy of the solutions. Therefore, this paper aims to employ the extended PIM into dynamic response problems of transversely isotropic multilayered media subjected to a moving load.…”

Section: Introductionmentioning

confidence: 99%

“…With the help of the conversion from the fixed coordinate system to the moving coordinate system, the fundamental governing equations for the steady‐state response of an elastic body in the moving coordinate system can be obtained. The partial differential equations in the moving system can be reduced to the ordinary differential ones in the transformed domain by using Fourier transform, and then the ordinary differential equations are solved by using the PIM . The actual solutions in the physical domain recovered by means of the corresponding numerical inversion.…”

Section: Introductionmentioning

confidence: 99%

“…Due to the complexity of the computational models, it is an arduous work to employ the analytical methods to investigate the dynamic response problems in transversely isotropic multilayered media, while the numerical methods are relatively easier. The precise integration method (PIM) is stable and efficient in dealing with complex models, which has been widely applied in the wave propagation analysis and the field of elasticity, poroelasticity, thermoelasticity, and porous thermoelasticity of multilayered media. Zhong et al and Gao et al investigated the wave propagation in stratified media in combination with the extended Wittrick‐Williams algorithm and the PIM.…”

Section: Introductionmentioning

confidence: 99%

“…The partial differential equations in the moving system can be reduced to the ordinary differential ones in the transformed domain by using Fourier transform, and then the ordinary differential equations are solved by using the PIM. [47][48][49][50][51][52][53][54][55][56][57] The actual solutions in the physical domain recovered by means of the corresponding numerical inversion. Finally, several examples are carried out to confirm the feasibility of the presented method and to analyze the influence of the material properties and the load characteristics.…”

mentioning

confidence: 99%

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3D dynamic response of a transversely isotropic multilayered medium subjected to a moving load

Ren

2017

Num Anal Meth Geomechanics

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Summary The dynamic problem of a transversely isotropic multilayered medium is reducible to quasi‐static problem by introducing a moving system that travels synchronously with the load. Based on the governing equations in the moving system, the ordinary differential equations in the Fourier transformed domain are deduced. An extended precise integration method is adopted to solve the ordinary differential equations, and the solution in the physical domain is recovered by the inverse Fourier transform. Numerical examples are performed to verify the accuracy of the presented method and to analyze the influence of material properties and the load characteristic.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

3D dynamic response of a transversely isotropic multilayered medium subjected to a moving load

Ren

2017

Num Anal Meth Geomechanics

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Micro‐inertia origin of instabilities in granular materials

Wautier

Bonelli²,

Nicot

2018

Num Anal Meth Geomechanics

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Summary Within the framework of the second‐order work theory, the onset of instabilities is explored numerically in loose granular materials through three‐dimensional DEM simulations. Stress controlled directional analysis are performed in Rendulic's plane, and a particular attention is paid to transient evolutions at the microscale. Thanks to a micromechanical analysis, the onset and development of transient mechanical instabilities is explored. It is shown that these instabilities result from the unjamming and bending of a few force chains associated with a local burst of kinetic energy. This burst of kinetic energy propagates to the whole sample and provokes a generalized unjamming of force chains. As force chains buckle, a phase transition from a quasi‐static to an inertial regime is observed. At the macroscopic scale, this results in a transient softening and a loss of controllability. After the collapse of existing force chains, the development of plastic strain is eventually stopped as new stable force chains are built.

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The dynamic responses of an infinite plate resting on a poroelastic layered half‐space soil medium with imperfect interface to a moving load

et al. 2021

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The present study deals with the dynamic responses of an infinite plate resting on a poroelastic layered half-space soil medium with imperfect interfaces to a moving load. Kirchhoff thin plate theory is employed to analyze the plate, while Biot's fully dynamic poroelastic theory is used to characterize the poroelastic half-space. Applying the Fourier transform and vector functions, the completely coupled system of equations of motion for the layered system are reduced to a system of decoupled ordinary differential equations which could be solved semianalytically. The propagation relationships for the layered structure with imperfect interfaces are derived by the novel and efficient dual variable and position (DVP) method. In so doing, the calculated expansion coefficients in the transformed domain are utilized to calculate the unknowns in the physical domain by integration at each field point. Numerical analyses validate the obtained results by comparing with the existing work, and soil vertical displacements, accelerations and pore water pressures induced by moving load are calculated. Moreover, the effects of the different factors are investigated. Computed result shows apparent influences of load velocity, intrinsic permeability and imperfect bonded condition of the soil medium on the dynamic responses of the whole system.

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Elastic displacement fields of multi-layered transversely isotropic materials under rectangular loads

Cited by 9 publications

References 37 publications

3D dynamic response of a transversely isotropic multilayered medium subjected to a moving load

3D dynamic response of a transversely isotropic multilayered medium subjected to a moving load

Micro‐inertia origin of instabilities in granular materials

The dynamic responses of an infinite plate resting on a poroelastic layered half‐space soil medium with imperfect interface to a moving load

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