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1.
A new method for solving Biot's consolidation of a finite soil layer in the cylindrical coordinate system 总被引:3,自引:0,他引:3
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
2.
This paper presents an alternative analytical technique to study a plane strain consolidation of a poroelastic soil by taking into account the anisotropy of permeability. From the governing equations of a saturated poroelastic soil, the relationship of basic variables for a point of a soil layer is established between the ground surface (z=0) and the depth z in the Laplace-Fourier transform domain. Combined with the boundary conditions, an exact solution is derived for plane strain Biot's consolidation of a finite soil layer with anisotropic permeability in the transform domain. Numerical inversions of the Laplace transform and the Fourier transform are adopted to obtain the actual solution in the physical domain. Numerical results of plane strain Biot's consolidation for a single soil layer show that the anisotropic of permeability has a great influence on the consolidation behavior of the soils. 相似文献
3.
A new analytical solution to axisymmetric Biot's consolidation of a finite soil layer 总被引:1,自引:0,他引:1
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
4.
This paper presents a theoretical solution for the basic equation of axisymmetric problems in elastodynamics. The solution
is composed of a quasi-static solution which satisfies inhomogeneous boundary conditions and a dynamic solution which satisfies
homogeneous boundary conditions. After the quasi-static solution has been obtained an inhomogeneous equation for dynamic solution
is found from the basic equation. By making use of eigenvalue problem of a corresponding homogeneous equation, a finite Hankel
transform is defined. A dynamic solution satisfying homogeneous boundary conditions is obtained by means of the finite Hankel
transform and Laplace transform. Thus, an exact solution is obtained. Through an example of hollow cylinders under dynamic
load, it is seen that the method, and the process of computing are simple, effective and accurate. 相似文献
5.
Ebrahim Asadi Ahmad R. Farrahi Shahriar J. Fariborz 《Theoretical and Applied Fracture Mechanics》2011,56(2):112-121
The solutions of axisymmetric Volterra type climb and glide edge dislocations are obtained in a layer by means of the Hankel transforms. Utilizing the same procedure, Green’s function solution is obtained for a layer under self-equilibration normal ring traction. The distributed dislocation technique is used to construct integral equations for a system of co-axial annular cracks where the layer is under axisymmetric normal loads. These equations are solved numerically to obtain dislocation density on the cracks surfaces. The results are employed to determine stress intensity factors for annular and penny-shaped cracks and the interaction between two co-axial penny-shaped cracks is studied. Moreover, the stress intensity factors of the interacting cracks are determined such that they can be further used in conjunction with strain energy density (SED) failure criterion to obtain the possible direction of crack initiation that may not be apparent under mixed mode conditions. 相似文献
6.
Based on the three dimensional elastic theory, the state equation of the axisymmetric free vibration of transversely isotropic
circular plates is established. Taking the advantage of finite Hankel transform, two exact solutions are derived for two boundary
conditions, i. e. the rigid-slipping boundary and elastic simply supported boundary. Finally, numerical results are presented
and compared with those of FEM.
The project is supported by the National Natural Science Foundation of China and the Zhejiang Provincial Natural Science Foundation. 相似文献
7.
考虑固结的基坑开挖回弹问题有限层求解 总被引:1,自引:0,他引:1
在综述前人有关基坑变形研究成果的基础上,指出开挖回弹量直接影响到基坑的稳定性和建筑物的后期沉降,但相关研究很少考虑土体在开挖过程中的固结影响.现引入固结有限层法,通过增加开挖部分的耦合矩阵和开挖部分的渗透矩阵,建立三维横观各向同性土体考虑固结的开挖回弹问题的有限层求解格式,并编制了相应的计算程序,以分析开挖过程中坑底土体的动态固结过程和负孔压的消散规律,研究固结对坑底土体回弹的影响程度.结果表明坑底土体的孔压随时间逐步消散,从负孔压慢慢消散到零,且符合Mandel-Cryer效应,坑底的回弹量随时间不断增加,且中心点回弹量较大,边缘点回弹量相对较小,总体成中心对称的倒锅底形. 相似文献
8.
9.
A second-order closure turbulence model is used to simulate the plume behaviour of a passive contaminant dispersed in a convective boundary layer. A time-splitting finite element scheme is used to solve the set of partial differential equations. It is shown that the second-order closure model compares favourably with recent findings from laboratories, wind-tunnel experiments and large-eddy simulations. We also compare the second-order closure model with the commonly used K-diffusion model for the same meteorological conditions. Case studies also show the effects of model parameters and turbulence variables on the plume behaviour. 相似文献
10.
Rama Subba Reddy Gorla Frank Jankowski David Textor 《International Journal of Heat and Fluid Flow》1988,9(4):421-426
An analysis is presented to investigate the time-mean characteristics of the laminar boundary layer near an axisymmetric stagnation point when the velocity of the oncoming flow relative to the body oscillates. Different solutions are obtained for the small and high values of the reduced frequency parameter. The range of Reynolds number considered was from 0.01 to 100. Numerical solutions for the velocity functions are presented, and the wall values of the velocity gradients are tabulated. 相似文献
11.
Axisymmetric problem of a nonhomogeneous elastic layer 总被引:3,自引:0,他引:3
Summary The paper deals with a theoretical treatment of elastic behavior for a medium with nonhomogeneous materials property, which
is defined by the relation , i.e., shear modulus of elasticity G varies with the dimensionless axial coordinate by the power product form, arbitrarily. Fundamental differential equation for such nonhomogeneous medium has been already
proposed in [5]. It is given by a second-order partial differential equation. However, it was found that the fundamental equation
is not sufficient in general to solve several kinds of boundary-value problems. On the other hand, it is shown in the present
paper making use of the fundamental equations system for a nonhomogeneous medium, which has been proposed in our previous
paper [7], it is possible to solve axisymmetric problems for a thick plate (layer) subjected to an arbitrarily distributed
load or a concentrated load on its surfaces. Numerical calculations are carried out for several cases, taking into account
the variation of the nonhomogeneous parameter m. The numerical results for displacements stress and components are shown in graphical form.
Accepted for publication 25 March 1997 相似文献
12.
A method is developed for the transient responses of axisymmetric plain strain problems of cylindrical shells subjected to
dynamic loads. Firstly, a special function was introduced to transform the inhomogeneous boundary conditions into the homogeneous
ones. Secondly, using the method of separation of variables, the quantity that the displacement subtracts the special function
was expanded as the multiplication series of Bassel functions and time functions. Then by virtue of the orthogonal properties
of Bessel functions, the equation with respect to the time variable was derived, of which the solution is easily obtained.
The displacement solution was finally obtained by adding the two parts mentioned above. The present method can avoid the integral
transform and is fit for arbitrary loads. Numerical results are presented for internally shocked isotropic and cylindrically
isotropic cylindrical shells and externally shocked cylinders, as well as for an externally shocked, cylindrically isotropic
cylindrical shell that is fixed at the internal surface.
Contributed by Ding Hao-jiang
Foundation item: the National Natural Science Foundation of China (10172075)
Biography: Ding Hao-jiang (1934-) 相似文献
13.
A THEORETICAL SOLUTION OF CYLINDRICAL SHELLS FOR AXISYMMETRIC PLAIN STRAIN ELASTODYNAMIC PROBLEMS 总被引:1,自引:0,他引:1
IntroductionTheanalysisfordynamicproblemofelasticbodieshasbeenstudiedformanyyears.Basedonthemomentlessthinshelltheory ,HuthandCole[1]studiedthestresswaveinasphericalshellproducedbypressureloadsin 1 955.Mcivor[2 ]discussedtheflexuralstressandmembranestressina… 相似文献
14.
In this work, the similarity equation describing the thermal boundary layers of laminar narrow axisymmetric jets is derived based on boundary layer assumptions. The equation is solved exactly. Some properties of the thermal jet are discussed. By introducing new-defined non-dimensional coordinates, the similarity solution results in a “universal” format. The results can also be applied in the boundary layer problem of species diffusion. 相似文献
15.
Feng Wenjie Nie Hui Han Xu 《Acta Mechanica Solida Sinica》2007,20(3):275-282
This paper analyzes the dynamic magnetoelectroelastic behavior induced by a penny- shaped crack in a magnetoelectroelastic layer.The crack surfaces are subjected to only radial shear impact loading.The Laplace and Hankel transform techniques are employed to reduce the prob- lem to solving a Fredholm integral equation.The dynamic stress intensity factor is obtained and numerically calculated for different layer heights.And the corresponding static solution is given by simple analysis.It is seen that the dynamic stress intensity factor for cracks in a magnetoelec- troelastic layer has the same expression as that in a purely elastic material.And the influences of layer height on both the dynamic and static stress intensity factors are insignificant as h/a>2. 相似文献
16.
Russell Hooper Matthijs Toose Christopher W. Macosko Jeffrey J. Derby 《国际流体数值方法杂志》2001,37(7):837-864
A modified boundary element method (BEM) and the DEVSS‐G finite element method (FEM) are applied to model the deformation of a polymeric drop suspended in another fluid subjected to start‐up uniaxial extensional flow. The effects of viscoelasticity, via the Oldroyd‐B differential model, are considered for the drop phase using both FEM and BEM and for both the drop and matrix phases using FEM. Where possible, results are compared with the linear deformation theory. Consistent predictions are obtained among the BEM, FEM, and linear theory for purely Newtonian systems and between FEM and linear theory for fully viscoelastic systems. FEM and BEM predictions for viscoelastic drops in a Newtonian matrix agree very well at short times but differ at longer times, with worst agreement occurring as critical flow strength is approached. This suggests that the dominant computational advantages held by the BEM over the FEM for this and similar problems may diminish or even disappear when the issue of accuracy is appropriately considered. Fully viscoelastic problems, which are only feasible using the FEM formulation, shed new insight on the role of viscoelasticity of the matrix fluid in drop deformation. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
17.
解析法求解成层渗透各向异性地基Biot固结轴对称问题 总被引:2,自引:0,他引:2
采用解析法研究成层渗透各向异性地基,该法从渗透各向异性Biot固结轴对称问题的基本方程(静力平衡方程,物理方程及渗透连续方程)出发,利用Laplace~Hankel变换及有关矩阵理论等,得到Biot固结基本量不同深度之间的传递矩阵。利用传递矩阵,边界条件以及Laplace~Hankal逆变换技术可求解多层渗透各向异性地基体系,采用更为有效的F.Durbin的方法实现Laplace逆变换。编制了计算 相似文献
18.
Zhiyong Ai Chao Wu 《力学学报》2009,41(5):801
对多层地基的平面应变固结问题进行了研究,并同时考虑了土体的渗透各向异性和孔隙
流体的可压缩性. 从平面应变Biot固结的控制方程出发,对时间t, 坐标z和x进行
Laplace和Fourier变换,建立了地基表面(z=0)和任意深度z处的基本量
在Laplace-Fourier变换域内的传递矩阵关系. 利用传递矩阵
法,结合土层连续条件和边界条件,并应用Laplace-Fourier逆变换技术,推导出渗透各向
异性可压缩多层地基平面应变固结的理论解. 基于该解,编制了计算程序,并进行了
数值计算. 讨论了土体的渗透各向异性、孔隙流体的可压缩性以及地基的分层特性对地基固
结的影响,分析结果表明:土体的渗透各向异性、孔隙流体的可压缩性,以及地基的分层特
性对地基的固结行为有着重要的影响. 相似文献
19.
This paper presents an analytical solution of the one-dimensional consolidation in unsaturated soil with a finite thickness under vertical loading and confinements in the lateral directions. The boundary contains the top surface permeable to water and air and the bottom impermeable to water and air. The analytical solution is for Fredlund's one-dimensional consolidation equation in unsaturated soils. The transfer relationship between the state vectors at top surface and any depth is obtained by using the Laplace transform and Cayley-Hamilton mathematical methods to the governing equations of water and air, Darcy's law and Fick's law. Excess pore-air pressure, excess pore-water pressure and settlement in the Laplace-transformed domain are obtained by using the Laplace transform with the initial conditions and boundary conditions. By performing inverse Laplace transforms, the analytical solutions are obtained in the time domain. A typical example illustrates the consolidation characteristics of unsaturated soil from an- alytical results. Finally, comparisons between the analytical solutions and results of the finite difference method indicate that the analytical solution is correct. 相似文献
20.
Numerical analysis of one-dimensional nonlinear large-strain consolidation by the finite element method 总被引:1,自引:0,他引:1
Joseph R. Feldkamp 《Transport in Porous Media》1989,4(3):239-257
The nonlinear partial differential equation model of Gibson et al. which governs one-dimensional large-strain consolidation is solved numerically using a semi-discrete formulation involving a Galerkin weighted residual approach. The use of quadratic Lagrange basis functions usually complicates the task of solving the system of time-dependent ordinary differential equations that are obtained with the semi-discrete Galerkin procedure. However, an efficient algorithm has been discovered yielding the advantages of quadratic interpolation without undue computational burden.Although considerable effort has already been made to solve the PDE of large-strain consolidation by numerical methods, a satisfactory set of benchmarks is still needed to assess accuracy. To fill this need, three procedures are reported which allow numerical solutions of the large-strain model to be reliably evaluated. One involves the use of perturbation methodology to provide a solution when only self-weight effects are present. A second utilizes an analytical solution developed by Philip when self-weight effects are absent and the third involves the exact calculation of the discharge flux through the upper boundary of a deposit consolidating through self-weight effects alone. All three are restricted to early-time consolidation and are illustrated in the context of the finite element method. 相似文献