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1.
Based on convolution-type constitutive equations for linear viscoelastic materials with damage and the hypotheses of Timoshenko beams, the equations governing quasi-static and dynamical behavior of Timoshenko beams with damage were first derived. The quasi-static behavior of the viscoelastic Timoshenko beam under step loading was analyzed and the analytical solution was obtained in the Laplace transformation domain. The deflection and damage curves at different time were obtained by using the numerical inverse transform and the influences of material parameters on the quasi-static behavior of the beam were investigated in detail.  相似文献   

2.
General exact solutions in terms of wavelet expansion are obtained for multi- term time-fractional diffusion-wave equations with Robin type boundary conditions. By proposing a new method of integral transform for solving boundary value problems, such fractional partial differential equations are converted into time-fractional ordinary differ- ential equations, which are further reduced to algebraic equations by using the Laplace transform. Then, with a wavelet-based exact formula of Laplace inversion, the resulting exact solutions in the Laplace transform domain are reversed to the time-space domain. Three examples of wave-diffusion problems are given to validate the proposed analytical method.  相似文献   

3.
The fractional calculus approach in the constitutive relationship model of viscoelastic fluid was introduced. The velocity and temperature fields of the vortex flow of a generalized second fluid with fractional derivative model were described by fractional partial differential equations. Exact analytical solutions of these differential equations were obtained by using the discrete Laplace transform of the sequential fractional derivatives and generalized Mittag-Leffier function. The influence of fractional coefficient on the decay of vortex velocity and diffusion of temperature was also analyzed.  相似文献   

4.
In this paper the method of transformation of the boundaries for structure theadmissible displacements with various boundary conditions is presented What is called themethod of transformation of the boundaries is that. first we transform the actual systeminto the basic system and additional boundary forces and displacements on the basis of thesuperposition principle, then apply variational principles to the basic system,finally find thepermissible displacement of the actual system by means of the method of transformation ofthe series.In this paper, we also give mixed energy prinapies under Variation of boundaryconditions. The mixed energy principles as the potential and complementary energyprinciples under variation of boundary conditions are all the chief theoretical fundamentalof the method of transformation of the boundaries.Applying the method of transformation of the boundaries. we form the permissibledisplacements of rectangular plates of plane stress and bending problems with various edgeconditio  相似文献   

5.
An analytical method was derived for the thermal consolidation of layered, saturated porous half-space to variable thermal loading with time. In the coupled governing equations of linear thermoelastic media, the influences of thermo-osmosis effect and thermal filtration effect were introduced. Solutions in Laplace transform space were first obtained and then numerically inverted. The responses of a double-layered porous space subjected to exponential decaying thermal loading were studied. The influences of the differences between the properties of the two layers (e.g., the coefficient of thermal consolidation, elastic modulus) on thermal consolidation were discussed. The studies show that the coupling effects of displacement and stress fields on temperature field can be completely neglected, however, the thermo-osmosis effect has an obvious influence on thermal responses.  相似文献   

6.
The method of double Fourier transform was employed in the analysis of the semi-infinite elastic foundation with vertical load.And an integral representations for the displacements of the semi-infinite elastic foundation was presented.The analytical solution of steady vibration of an elastic rectangle plate with four free edges on the semi-infinite elastic foundation was also given by combining the analytical solution of the elastic rectangle plate with the integral representation for displacements of the semi- infinite elastic foundation.Some computational results and the analysis on the influence of parameters were presented.  相似文献   

7.
An analytical method was presented for the torsional vibrations of a rigid disk resting on transversely isotropic saturated soil. By Hankel transform, the dynamic governing differential equations for transversely isotropic saturated poroelastic medium were solved. Considering the mixed boundary-value conditions, the dual integral equations of torsional vibrations of a rigid circular plate resting on transversely isotropic saturated soil were established. By appropriate transform, the dual integral equations were converted into a Fredholm integral equation of the second kind. Subsequently, the dynamic compliance coefficient, the torsional angular amplitude of the foundation and the contact shear stress were expressed explicitly. Selected examples were presented to analyse the influence of saturated soil's anisotropy on the foundation's vibrations.  相似文献   

8.
EXACT ANALYSIS OF WAVE PROPAGATION IN AN INFINITE RECTANGULAR BEAM   总被引:1,自引:0,他引:1  
The Fourier series method was extended for the exact analysis of wave propagation in an infinite rectangular beam. Initially, by solving the three-dimensional elastodynamic equations a general analytic solution was derived for wave motion within the beam. And then for the beam with stress-free boundaries, the propagation characteristics of elastic waves were presented. This accurate wave propagation model lays a solid foundation of simultaneous control of coupled waves in the beam.  相似文献   

9.
A new analytical method is presented to study the axisymmetric Biot's consolidation of a finite soil layer. Starting from the governing equations of axisymmetric Blot's consolidation, and based on the property of Laplace transform, the relation of basic variables for a point of a finite soil layer is established between the ground surface (z= 0) and the depth z in the Laplace and Hankel transform domains. Combined with the boundary conditions of the finite soil layer, the analytical solution of any point in the transform domain can be obtained. The actual solution in the physical domain can be obtained by inverse Laplace and Hankel transforms. A numerical analysis for the axisymmetric consolidation of a finite soil layer is carried out.  相似文献   

10.
A new method is developed to solve Biot's consolidation of a finite soil layer in the cylindrical coordinate system. Based on the governing equations of Biot's consolidation and the technique of Laplace transform, Fourier expansions and Hankel transform with respect to time t, coordinate θ and coordinate r, respectively, a relationship of displacements, stresses, excess pore water pressure and flux is established between the ground surface (z = 0) and an arbitrary depth z in the Laplace and Hankel transform domain. By referring to proper boundary conditions of the finite soil layer, the solutions for displacements, stresses, excess pore water pressure and flux of any point in the transform domain can be obtained. The actual solutions in the physical domain can be acquired by inverting the Laplace and the Hankel transforms.  相似文献   

11.
This paper presents general semi-analytical solutions to Fredlund and Hasan's one-dimensional(1D) consolidation equations for unsaturated soils subject to different initial conditions, homogeneous boundaries and time-dependent loadings. Two variables are introduced to transform the two-coupled governing equations of pore-water and poreair pressures into an equivalent set of partial differential equations(PDEs), which are solved with the Laplace transform method. The pore-water and pore-air pressures and settlement are obtained in the Laplace transform domain. The Crump's method is used to perform inverse Laplace transform to obtain the solutions in the time domain. The present solutions are more general in practical applications and show good agreement with the previous solutions in the literature.  相似文献   

12.
The meshless local Petrov-Galerkin (MLPG) method is used to analyze transient dynamic problems in 3D axisymmetric piezoelectric solids with continuously inhomogeneous material properties. Both mechanical and thermal loads are considered here. A 3D axisymmetric body is created by rotation of a cross section around an axis of symmetry. Axial symmetry of geometry and boundary conditions reduces the original 3D boundary value problem into a 2D problem. The cross section is covered by small circular sub-domains surrounding nodes randomly spread over the analyzed domain. A unit step function is chosen as test function, in order to derive local integral equations on the boundaries of the chosen sub-domains, called local boundary integral equations (LBIE). These integral formulations are either based on the Laplace transform technique or the time-difference approach. The local integral equations are non-singular and take a very simple form, despite of inhomogeneous and anisotropic material behaviour across the analyzed structure. Spatial variation of all physical fields (or of their Laplace transforms) at discrete time instants are approximated on the local boundary and in the interior of the sub-domain by means of the moving least-squares (MLS) method. The Stehfest algorithm is applied for the numerical Laplace inversion, in order to retrieve the time-dependent solutions.  相似文献   

13.
竖向荷载作用下半透水边界固结问题解   总被引:1,自引:0,他引:1  
本文基于Biot固结理论,采用积分变换的方法,获得了竖向点荷载、环形荷载作用下半透水边界固结问题基本解,并求得圆形分布荷载作用下的固结解,计算分析了圆形分布荷载作用下的竖向位移、总应力和孔压的时间效应。  相似文献   

14.
In this work, the generalized thermoelastic solutions with bounded boundaries for the transient shock problem are proposed by an asymptotic method. The governing equations are taken in the context of the generalized thermoelasticity with one relaxation time (L–S theory). The general solutions for any set of boundary conditions are obtained in the physical domain by the Laplace transform techniques. The corresponding asymptotic solutions for a thin plate with finite thickness, subjected to different sudden temperature rises in its two boundaries, are obtained by means of the limit theorem of Laplace transform. In the context of these asymptotic solutions, two specific problems with different boundary conditions have been conducted. The distributions of displacement, temperature and stresses, as well as the propagations, intersections and reflections of two elastic waves, named as thermoelastic wave and thermal wave separately, are obtained and plotted. These results are agreed with the results obtained in the existing literatures.  相似文献   

15.
基于Biot理论,采用渗流一力学耦合模型研究分析了内水压力作用下饱和土体中压力隧洞衬砌一土的相互作用问题。假定衬砌和土体均为饱和多孔介质,且衬砌和土体完全接触。运用积分变换理论,在hplace变换域中得到了衬砌和土体中的应力、位移和孔隙水压力解答,并利用bplace数值逆变换得到时域中的解。文末的算例分析结果表明:(1)采用渗流一力学耦合模型能较好地反映隧洞衬砌与土体相互作用中应力和变形的随时间变化过程;(2)衬砌和土体的相对刚度对隧洞的计算结果有很大影响。  相似文献   

16.
This study is intended to analyze dynamic behavior of beams on Pasternak-type viscoelastic foundation subjected to time-dependent loads. The Timoshenko beam theory is adopted in the derivation of the governing equation. Ordinary differential equations in scalar form obtained in the Laplace domain are solved numerically using the complementary functions method to calculate exactly the dynamic stiffness matrix of the problem. The solutions obtained are transformed to the real space using the Durbin's numerical inverse Laplace transform method. The dynamic response of beams on viscoelastic foundation is analyzed through various examples.  相似文献   

17.
Based on the well-known Durbin method, an efficient numerical method was developed for the inversion of the two-sided Laplace transform. The accuracy of the method was verified using examples. As an application of the method, transient elastic waves propagating in a two-layered piezoelectric medium subjected to anti-plane concentrated loading and in-plane electric displacement loading were investigated. One-sided and two-sided Laplace transforms were applied to determine the shear stresses and electric displacements in the double Laplace transform domain. Subsequently, the Durbin method for one-sided Laplace transform inversion and the extended Durbin method for two-sided Laplace transform inversion were used to implement the numerical inversions. Additionally, the numerical results of the transient stresses and electric displacements were evaluated and discussed. It showed that the arrival time of transient waves satisfies physical phenomena, and the transient solution oscillates near the static solution and rapidly approximates the static solution.  相似文献   

18.
In this study, the problem of an isotropic sector subjected to anti-plane shear loadings is investigated. The loadings were applied to the arc of the sector, and the radial edges of the sector were under traction-free or fixed conditions. Depending on these conditions, three problems, namely, free–free, fixed–free, and fixed–fixed edges were studied. A procedure using the finite Mellin transform combined with the Laplace transform was proposed for solving these problems. Explicit closed form solutions for the displacement and stress fields throughout the sector were obtained. The stress intensity factor (SIF) for each problem was analyzed using the obtained stress fields. It was determined that the SIF disappeared under the special condition of a fixed–fixed edge. Other special cases having anti-symmetric conditions were deduced from the derived solutions, and the results of these verified those cited in the literature as well as those obtained using finite element analysis (FEA).  相似文献   

19.
Laplace Transform and New Mathematical Theory of Viscoelasticity   总被引:1,自引:0,他引:1  
BRILLA  JOZEF 《Meccanica》1997,32(3):187-195
In this paper generalized variational principles in thesense of the Laplace transform for viscoelastic problems arederived. Then mathematical theory of viscoelasticity ingeneralized Hardy spaces and in weighted anisotropic Sobolevspaces and spectral theory of corresponding non-selfadjointoperators is elaborated. Finally the Laplace transform--FEMfor numerical analysis of time-dependent problems of themathematical physics is proposed and analysed.  相似文献   

20.
The semi-analytical solutions to Fredlund and Hasan's one-dimensional(1 D)consolidation for unsaturated soils with a semi-permeable drainage boundary are presented. Two variables are introduced to transform the two coupled governing equations of pore-water and pore-air pressures into an equivalent set of partial differential equations(PDFs), which are easily solved by the Laplace transform method. Then, the pore-water pressure, pore-air pressure, and soil settlement are obtained in the Laplace domain. The Crump method is adopted to perform the inverse Laplace transform in order to obtain the semi-analytical solutions in the time domain. It is shown that the proposed solutions are more applicable to various types of boundary conditions and agree well with the existing solutions from the literature. Several numerical examples are provided to investigate the consolidation behavior of an unsaturated single-layer soil with single, double, mixed, and semi-permeable drainage boundaries. The changes in the pore-air and pore-water pressures and the soil settlement with the time factor at different values of the semi-permeable drainage boundary parameters are illustrated. In addition, parametric studies are conducted on the pore-air and pore-water pressures at different ratios(the air permeability coefficient to the water permeability coefficient) and depths.  相似文献   

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