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1.
Arabinda Mukhopadhyay 《Pure and Applied Geophysics》1965,60(1):29-41
Summary In this paper, the problem of a normal load moving over the surface of a layer of ice, lying on a rigid foundation, has been considered. FollowingHearmon, the ice is taken to be transversely isotropic. Two cases have been considered-in the first case, the rigid foundation is taken to be smooth, and in the second case, it is taken to be in welded contact with the layer of ice. Expressions have been obtained in both cases for the stresses at any point of the layer. From detailed numerical calculations, it has been found that the value of the normal stress at a point directly below the moving load falls of approximately as that of 1/z with increase in the depthz below the surface. On calculating the normal stress at the boundary between the layer of ice and the foundation, it is found that the normal stress falls off rapidly as we move away along the boundary from the point directly below the load. 相似文献
2.
A transversely isotropic material in the sense of Green is considered. Using a series of potential functions proposed in [Eskandari-Ghadi M. A complete solution of the wave equations for transversely isotropic media. J Elasticity 2005; 81:1–19], the solutions of the transient wave equations within a half-space under surface load are obtained in the Laplace–Hankel domain for axisymmetric problems. The solutions are investigated in detail in the special case of a surface point force pulse varying with time as Heaviside function. Using Cagniard–De Hoop method, the inverse Laplace transform and inverse Hankel transform of the solutions are then obtained in the form of integrals with finite limits. For validity of the analytical results, the final formulations for surface waves are degenerated for an isotropic material and compared with the existing formulation obtained by Pekeris [The seismic surface pulse. Proc Natl Acad Sci USA 1955;41:469–80], to show that they are exactly the same. The numerical evaluations of the integrals for some transversely isotropic materials as well as an isotropic one are obtained. The present approach is then numerically verified by comparing a particular case of displacements for the surface of an isotropic half-space subjected to a point load of Heaviside function with the solutions obtained by Pekeris [The seismic surface pulse. Proc Natl Acad Sci USA 1955;41:469–80]. In addition, the wave equations for the mentioned medium are obtained on the vertical line directly under the applied surface load. The final formulations are degenerated for an isotropic material and compared with the existing formulation given in Graff [Wave motion in elastic solids. New York: Dover Publications Inc; 1975 [New Ed edition, November 1991]], to show that they are also exactly the same. Then equations are presented in graphical forms using an appropriate numerical evaluation. 相似文献
3.
A model for investigations of ground motions due to continuously moving loads with constant and time-varying amplitudes is presented. The vertical displacements excited by moving load areas are obtained at a fixed observation point at the surface of the three-dimensional halfspace in time domain. The load is moving along a straight line with constant speed. To solve this nonaxisymmetric, initial boundary value problem a semi-analytical, discretized model is developed. It is based on Green's functions for a suddenly applied, stationary surface point load with Heaviside time dependency. These functions, also called influence functions of the halfspace, are valid for any homogeneous, isotropic and linear-elastic medium. The principle of superposition is used. Results are shown for the transient and the steady-state ground motions, and they are compared with analytical solutions. The load speed is varied in the subcritical range up to the propagation velocity of Rayleigh-waves. 相似文献
4.
Arabinda Mukhopadhyay 《Pure and Applied Geophysics》1966,65(1):12-28
Summary The object of this paper is to study the stresses produced in a porous liquid-saturated solid of the type considered byBiot [1]2) by a normal load moving along the surface of such a solid. Two cases have been considered. In the first case, the porous solid is taken to be semi-infinite, while in the second case we consider a layer of the liquid-saturated porous solid resting on a smooth rigid foundation. Expressions have been obtained for the stresses at any point in the medium due to a normal load moving along the free surface of the porous solid. Detailed numerical calculations have been carried out for liquid-saturated sandstone, using the data given byFatt [9] for such a medium. These calculations show that the normal stress zz in the solid falls off approximately as 1/z with increase in the depthz below the free surface, and that the stresses in the solid and in the liquid fall off rapidly as we move away from the point directly below the moving load. 相似文献
5.
A numerical method is shown to analyse the dynamic elastic-plastic responses of those structures with known elastic solutions. The displacement at one point at time t caused by a unit load applied at another point at zero time, called dynamic influence coefficient, is calculated from the known elastic solutions. Incremental plastic strain is accounted for by a set of additional incremental loads, so the stiffness matrix and the eigenvectors do not vary with time. From the incremental load including that caused by the incremental plastic strain, the displacement vs. time of the structure is obtained. This method is applied to simply supported beams with bilinear stress-strain relations with different strain-hardening rates and to a simply supported elastic-ideally plastic rectangular plate. This procedure can be extended to structures with no available known analytical elastic solutions. For these structures, the elastic solutions can be obtained by the finite element method. 相似文献
6.
In this paper, time-harmonic axisymmetric vibration of an incompressible viscoelastic half-space having shear modulus linearly increasing with depth is studied. The half-space is subjected to a vertical time-harmonic load on its surface. Numerical results concerning surface displacements due to a point force are given for the case of non-zero shear modulus at the surface. Hankel's transforms of the solutions have an infinite number of poles lying on the real axis of the complex plane in the non-dissipative case. A suitable contour of integration is used to avoid all the singularities. Calculations are performed for the dynamic as well as for the static case. In addition, vertical vibrations of a rigid disk on the considered half-space are investigated, and the influence of the non-homogeneity on the dynamic stiffness of the loaded area is demonstrated. 相似文献
7.
Arabinda Mukhopadhyay 《Pure and Applied Geophysics》1967,67(1):43-53
Summary The disturbances produced in a semi-infinite visco-elastic medium and in a layer of visco-elastic material resting on a rigid foundation by transient torsional body forces have been considered. Formal solutions have been obtained for a general type of body force, and this solution has been used to obtain the displacements for a transient torsional point source in the case of a semiinfinite medium, and for a cylindrical source of finite dimensions and a line source in the case of the layer of visco-elastic material mentioned above. Solutions have also been obtained for a transient shearing stress applied at the free surface of the layer mentioned above. 相似文献
8.
Yu Zhou Qiang Zhang Vijay P. Singh Mingzhong Xiao 《Stochastic Environmental Research and Risk Assessment (SERRA)》2015,29(3):665-677
Correlation associations have been detected using Pearson’s r which aims to analyze linear correlation between two variables. It should be noted here that associations between hydro-meteorological variables are usually nonlinear. In this sense, the classical correlation analysis method cannot truly reflect the inherent associations between variables characterized by nonlinear associations. In this case, a new algorithm has been proposed by using the ideas of local correlation, detrended cross-correlation analysis and multifractals, and this novel algorithm is called as the general detrended correlation analysis. The newly-proposed algorithm was evaluated for the validity with numerically-generated time series and the real world hydrological series. The results indicate that the newly-proposed algorithm can well reflect the nonlinear and non stationary associations between two hydrological series when compared to the classical relation detection method such as the Pearson correlation analysis method, and it is particularly the case under the condition that hydrological abrupt changes of the hydrological processes occur where the classical association analysis is not appropriate. 相似文献
9.
The problem of spatial dynamic response of a suspension bridge to the passage of trains of concentrated forces with random values is considered. The arrival of forces at the bridge is assumed to constitute a Poisson process of events. Such an excitation process is an appropriate model of vehicular traffic loads acting on the bridge. The bridge is idealized by a single-span thin-walled beam underslung to two cables. The response of the bridge in the space-time domain is described by a coupled system of non-linear, integro-differential equations. The dynamic influence functions of vertical and horizontal deflections at each cross-section point are obtained for the linear case. Cumulants and probability density functions of response are determined. Numerical methods have been used to develop a computer-oriented algorithm aimed at the numerical solution of the problem. As examples, numerical results for a particular bridge with some practical load cases are presented and illustrated by graphs. 相似文献
10.
The propagation of stress waves in a large-diameter pipe pile for low strain dynamic testing cannot be explained properly by traditional 1D wave theories. A new computational model is established to obtain a wave equation that can describe the dynamic response of a large-diameter thin-walled pipe pile to a transient point load during a low strain integrity test. An analytical solution in the time domain is deduced using the separation of variables and variation of constant methods. The validity of this new solution is verifi ed by an existing analytical solution under free boundary conditions. The results of this time domain solution are also compared with the results of a frequency domain solution and fi eld test data. The comparisons indicate that the new solution agrees well with the results of previous solutions. Parametric studies using the new solution with reference to a case study are also carried out. The results show that the mode number affects the accuracy of the dynamic response. A mode number greater than 10 is required to enable the calculated dynamic responses to be independent of the mode number. The dynamic response is also greatly affected by soil properties. The larger the side resistance, the smaller the displacement response and the smaller the refl ected velocity wave crest. The displacement increases as the stress waves propagate along the pile when the pile shaft is free. The incident waves of displacement and velocity responses of the pile are not the same among different points in the circumferential direction on the pile top. However, the arrival time and peak value of the pile tip refl ected waves are almost the same among different points on the pile top. 相似文献
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12.
本文给出了单位点质量负荷作用在球状成层地球模型上的解。对较新的G-D1066A地球模型求出了n直到10000阶的负荷勒夫数,并利用这组负荷勒夫数计算了格林函数的值。简述了如何利用格林函数计算地球对表面任何负荷的响应。讨论了负荷潮研究在地球物理和海洋学方面的一些应用。 相似文献
13.
Scattering and Diffraction of elastic in-plane P- and SV- waves by a surface topography such as an elastic canyon at the surface of a half-space is a classical problem which has been studied by earthquake engineers and strong-motion seismologists for over forty years. The case of out-of-plane SH waves on the same elastic canyon that is semi-circular in shape on the half-space surface is the first such problem that was solved by analytic closed form solutions over forty years ago by Trifunac. The corresponding case of in-plane P- and SV-waves on the same circular canyon is a much more complicated problem because, the in-plane P- and SV- scattered waves have different wave speeds and together they must have zero normal and shear stresses at the half-space surface. It is not until recently in 2014 that analytic solution for such problem is found by the author in the work of Lee and Liu. This paper uses the technique of Lee and Liu of defining these stress-free scattered waves to solve the problem of the scattered and diffraction of these in-plane waves on an almost-circular surface canyon that is arbitrary in shape. 相似文献
14.
Three-dimensional simulation of track on poroelastic half-space vibrations due to a moving point load 总被引：1，自引：0，他引：1
An analytical approach is used to investigate dynamic responses of a track system and the poroelastic half-space soil medium subjected to a moving point load under three-dimensional condition. The whole system is divided into two separately formulated substructures, the track sub-system and the ground. The ballast supporting rails and sleepers is placed on the surface of the ground. The rail is modeled by introducing the Green function for an infinitely long Euler beam subjected to the action of the moving point load and the reaction of sleepers represented by a continuous mass. Using the double Fourier transform, the governing equations of motion are then solved analytically in the frequency–wave-number domain. The time domain responses are evaluated by the inverse Fourier transform computation for a certain load velocities. Computed results show that dynamic responses of the soil medium are considerably affected by the fluid phase as well as the load velocity. 相似文献
15.
P. Hubert 《Stochastic Environmental Research and Risk Assessment (SERRA)》2000,14(4):297-304
A possible cause of nonstationarity in time series is the existence of some abrupt modification of their statistical parameters, and especially of a sudden change of the mean. Series with such a change exhibit a strong temporal persistence, with high values of the Hurst coefficient, but with poor possibilities to fit any autoregressive model. Some classical tests (Pettitt, 1979; Buishand, 1982) enable to find a possible change point of the mean and then to split the original nonstationary series into two stationary sub-series. The Bayesian procedure defined by Lee and Heghinian (1977) supposes the “a-priori” existence of a change of the mean somewhere in the series and yields at each time step an “a-posteriori” probability of mean change. But these classical tests and procedures consider only one change point in the original series. To go further and to explore the theoretical multiple singularity models defined by Klemeš (1974) and Potter (1976), a segmentation procedure of time series has been designed. This procedure yields an optimal partition (from a least squares point of view) of the original series into as many subseries as possible, all differences between two contiguous means remaining simultaneously significant. This last requirement is ensured using the Scheffe test of contrasts. The main problem has been to master the combinatory explosion while exploring the tree of all possible segmentations of a series. Some applications of the procedure to hydrometeorological time series are reviewed and some possible improvements are presented. 相似文献
16.
A new exact solution of the problem for propagating stationary potential wave of an arbitrary amplitude in a deep ideal homogeneous fluid was constructed. Calculated wavy surface is represented by transcendental Lambert’s complex functions. For a physical interpretation of the results real linear combinations of the solutions were formed. The range of the wave steepness values, in which the real sum of constructed comprehensive solutions describes waves with smooth crests, is defined. In the limiting case of waves with small but finite amplitude as well as infinitesimal amplitude, the real combinations of the solutions are transferred in classical nonlinear and linear asymptotic Stokes expressions. Another real combination of constructed complex solutions describing waves with cusped crests do not fall within the range of conditions for the existence of stationary waves. 相似文献
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18.
K. R. Nag 《Pure and Applied Geophysics》1972,98(1):72-86
Summary In this paper the displacement components due to a compressional point source in a layered half-space consisting of a liquid layer of finite thickness overlying a semi-infinite solid homogeneous medium have been deduced. Two different cases have been considered. In the first case the source is taken in the liquid layer and in the second case the source is taken in the solid layer. The displacement components in cylindrical coordinates have been obtained in closed form in detail at the interface for all values of distance from the source for the second case. 相似文献
19.
Ioannis K. Nikolos Maria Stergiadi Maria P. Papadopoulou George P. Karatzas 《水文研究》2008,22(17):3337-3348
Classical optimization methodologies based on mathematical theories have been developed for the solution of various constrained environmental design problems. Numerical models have been widely used to represent an environmental system accurately. The use of methodologies such as artificial neural networks (ANNs), which approximate the complicated behaviour and response of physical systems, allows the optimization of a large number of case scenarios with different set of constraints within a short period of time, whereas the corresponding simulation time using a numerical model would be prohibitive. In this paper, a combination of an ANN with a differential evolution algorithm is proposed to replace the classical finite‐element numerical model in water resources management problems. The objective of the optimization problem is to determine the optimal operational strategy for the productive pumping wells located in the northern part of Rhodes Island in Greece, to cover the water demand and maintain the water table at certain levels. The conclusions of this study show that the use of ANN as an approximation model could (a) significantly reduce the computational burden associated with the accurate simulation of complex physical systems and (b) provide solutions very close to the optimal ones for various constrained environmental design problems. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
20.
We study singular elastic solutions at an angular corner left by a crack that has kinked. We have in mind a geophysical context
where the faults on either side of the kink are under compression and are ready to slip, or have already slipped, under the
control of Coulomb friction. We find separable static singular solutions that are matched across the sides of the corner by
applying appropriate boundary conditions. In our more general solution we assume that one of the sides of the corner is about
to slide, i.e. it is just contained by friction, and the other may be less pressured. Our solutions display power law behaviour
with real exponents that depend continuously on the angle of the corner, the coefficient of static friction and the difference
of shear load on both sides of the corner. When friction is the same on both sides of the kink, the solutions split into a
symmetric and an antisymmetric solution. The antisymmetric solution corresponds to the simple shear case; while the symmetric
solution appears when the kink is loaded by uniaxial stress along the bisector of the kink. The antisymmetric solution is
ruled out under this model with contact since the faults cannot sustain tension. When one side of the corner is less pressured
one can also distinguish modes with contact overall from others that must open up on one side. These solutions provide an
insight into the stress distributions near fault kinks, they can also be used as tools for improving the numerical calculation
of kinks under static or dynamic loads. 相似文献