Dynamic torsional response of pre-strained end bearing pile embedded in pre-strained isotropic saturated soil medium

The influence of initial strain state on the dynamic response of an end bearing pile embedded in isotropic saturated soil is investigated through the linearized theory of small elastic perturbation superposed on largely stressed bodies. The governing equations for soil, based on Blot＇s poroelasticity theory, are derived in the cylindrical coordinates, and the pile is modeled by using the one-dimensional elastic theory. The analytical solutions of pile impedance, frequency response of both twist angle and time history of velocity response are obtained by using of separation of variables technique. Finally, a parametric study of the influence of initial strains on the torsional impedance, twist angle, and velocity response at the top of the pile is carried out.     

Stability of rigid solids embedded in an elastic medium

The stability of a two-dimensional continuum consisting of rigid solids embedded in an elastic homogeneous medium with a fixed boundary is investigated. With each solid is associated the scalar where are balanced dead loads acting at points M of the solid, and where S is the area of the surface of the solid. If is the shear modulus of the elastic medium, it is shown that (i) the inequality +4>0, when it applies to each solid, is a sufficient condition for stability of the continuum; (ii) the inequality +40 is a necessary condition for stability of a single circular solid embedded in an infinite elastic medium.     

Dynamic effects of moving load on a poroelastic soil medium by an approximate method

The problem of the dynamic response of a fully saturated poroelastic soil stratum on bedrock subjected to a moving load is studied by using the theory of Mei and Foda under conditions of plane strain. The applied load is considered to be the sum of a large number of harmonics with varying frequency in the form of a Fourier expansion. The method of solution considers the total field to be approximated by the superposition of an elastodynamic problem with modified elastic constants and mass density for the whole domain and a diffusion problem for the pore fluid pressure confined to a boundary layer near the free surface of the medium. Both problems are solved analytically in the frequency domain. The effects of the shear modulus, permeability and porosity of the soil medium and the velocity of the moving load on the dynamic response of the soil layer are numerically evaluated and compared with those obtained by the exact solution of the problem. It is concluded that for fine poroelastic materials, the accuracy of the present method against the exact one is excellent.     

Dynamic instability of axially loaded shafts in the Mathieu map

It is shown that the Mathieu eigenvalues can be straightforwardly utilized to study the instability regions of an axially loaded simply supported shaft, the shaft being modeled as a continuous rotating beam. When a harmonic axial load is taken into account, the equation of motion of the system, here written according to the Lagrangian formulation of continuous systems, proves to be the Mathieu equation. It follows that the conditions for the stable or unstable motion of the shaft can be graphically investigated once the operation line corresponding to an actual rotating shaft is drawn in the Mathieu map.     

Dynamic and quasi-static bending of saturated poroelastic Timoshenko cantilever beam

Based on the three-dimensional Gurtin-type variational principle of the incompressible saturated porous media, a one-dimensional mathematical model for dynamics of the saturated poroelastic Timoshenko cantilever beam is established with two assumptions, i.e., the deformation satisfies the classical single phase Timoshenko beam and the movement of the pore fluid is only in the axial direction of the saturated poroelastic beam. Under some special cases, this mathematical model can be degenerated into the Euler-Bernoulli model, the Rayleigh model, and the shear model of the saturated poroelastic beam, respectively. The dynamic and quasi-static behaviors of a saturated poroelastic Timoshenko cantilever beam with an impermeable fixed end and a permeable free end subjected to a step load at its free end are analyzed by the Laplace transform. The variations of the deflections at the beam free end against time are shown in figures. The influences of the interaction coefficient between the pore fluid and the solid skeleton as well as the slenderness ratio of the beam on the dynamic/quasi-static performances of the beam are examined. It is shown that the quasi-static deflections of the saturated poroelastic beam possess a creep behavior similar to that of viscoelastic beams. In dynamic responses, with the increase of the slenderness ratio, the vibration periods and amplitudes of the deflections at the free end increase, and the time needed for deflections approaching to their stationary values also increases. Moreover, with the increase of the interaction coefficient, the vibrations of the beam deflections decay more strongly, and, eventually, the deflections of the saturated poroelastic beam converge to the static deflections of the classic single phase Timoshenko beam.     

Dynamic torsional buckling of a double-walled carbon nanotube embedded in an elastic medium

An elastic double-shell model based on continuum mechanics is presented to study the dynamic torsional buckling of an embedded double-walled carbon nanotube. Based on the presented model, a condition is derived to predict the buckling load of the embedded double-walled nanotube, and the effect of the van der Waals forces to the buckling load is discussed when an inner nanotube is inserted into an embedded outer one. In particular, the paper shows that the buckling load of the embedded double-walled nanotube is always between that of the isolated inner nanotube and that of the embedded outer nanotube for both dynamic and static torsional buckling, due to the effect of the van der Waals forces. This result is different from that obtained by the existing analysis neglecting the difference of the radii for the embedded double-walled nanotube, which indicates that disregarding the difference of the radii of multi-walled nanotubes cannot properly describe the effect of the van der Waals forces between interlayer spacing. In particular, for static torsional buckling of a double-walled nanotube, it is shown that the critical buckling load cannot only be enhanced, but also be reduced when inserting an inner nanotube into an isolated single-walled one. Additionally, it is shown that the elastic medium always increases the critical buckling load of double-walled nanotubes. The critical buckling load of embedded double-walled nanotubes for dynamic torsional buckling is proved to be no less than that for static torsional buckling.     

A rigid line in a confocal elliptic inhomogeneity embedded in an infinite medium under antiplane shear

An effective method is developed and used to investigate the antiplane problem of a rigid line in a confocal elliptic inhomogeneity embedded in an infinite medium. The analytical solution is obtained. The proposed method is based upon the use of conformal mapping and the theorem of analytic continuation. Special solutions which are verified by comparison with existing ones are provided. Finally, the characteristics of stress singularity at the tip of the rigid line inhomogeneity are analyzed and the extension forces for the crack and the rigid line inhomogeneity are derived. The project supported by the National Natural Science Foundation of China, the State Education Commission Foundation and the Failure Mechanics Lab of SEdC.     

Response of a solid infinite cylinder embedded in a poroelastic medium and subjected to a lateral load

This paper presents an analytical solution for the response of a poroelastic medium around a laterally loaded rigid cylinder using Biot’s consolidation theory. A plane-strain section of the cylinder-porous medium system is considered and the problem is formulated in polar coordinates. Expressions for the pore fluid pressure, stresses and displacements in the Laplace domain are derived analytically. The inverse of the Laplace transform is evaluated numerically using an efficient scheme. Curves showing decay of the pore fluid pressure with time, the corresponding change in mean effective stress and the variation of displacement, are plotted in non-dimensional form.     

Energy method solution for the postbuckling response of an axially loaded bilaterally constrained beam

Bistable and multistable structures have shown great usefulness in many applications such as MEMS actuation and energy harvesting. Bistability of structures can be achieved through buckling. Confining a buckled beam between two lateral constraints allows it to buckle into higher modes as the axial load increases. This paper presents a theoretical study of the postbuckling response of a bilaterally constrained elastica subjected to gradually increased axial load. Equilibrium states are determined using an energy method. Under small deformation assumptions, the total potential energy is minimized under the defined constraints. The presented model allows for an accurate representation of the flatting behavior and the increase in the length of contact areas with the lateral constraints before the sudden snapping between equilibrium states. Mode transitions are manifested by jumps in the response curves. Previously developed models based on geometry and symmetries overestimate the required forces for higher equilibrium modes and do not match experimental observations. Results are validated with experimental force–displacement measurements under both force- and displacement-control. The kinetic energy released during buckling mode transitions is determined by a dynamic analysis.     

黏弹性饱和多孔介质中圆柱孔洞的频域响应

研究了无限黏弹性饱和多孔介质中圆柱孔洞(有衬砌)表面受轴对称简谐荷载和流体压力 作用下的频域响应问题. 引入Carcione提出的本构模型来描述介质的流变和松弛性质. 考 虑衬砌和介质的相对渗透性，孔洞处于半封闭状态，边界半透水. 引入两个势函数，在频域 中得到了应力、位移和超孔隙水压力响应解答. 并进行了算例分析，讨论了反映介质黏弹 性性质的最小质量因子，反映孔洞边界半透水性质的渗透性参数及衬砌和介质的相对刚度对 问题的影响. 分析结果表明：以上参数对圆柱孔洞的频域响应有很大影响.     

Steady laminar flow past a heated horizontal plate embedded in a saturated porous medium

In this paper we study the boundary layer equations for steady laminar flow past a heated horizontal plate embedded in a saturated porous medium by adopting the formulation of Chandrasekhara [3], Kolar and Sastri [7]. The velocity distribution and temperature distribution are determined by using the implicit Crank-Nicolson-Predictor-Corrector method of finite difference scheme [7] and [1]. With the help of a compute the distributions are estimated at both (i+1/2)th and (i+1)th levels and they are presented in tabular form. The curves for these distributions are plotted. We calculate the shear stress and skin friction at the wall and observe that the skin-friction directly depends upon the dimensions of the plate and inversely depends upon the Reynolds numberRe. The heat flux and the Nusselt number are evaluated. Further we observe that the Nusselt number depends upon the length of the porous plate.

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Stetige laminare Strömung über eine in einem gesättigten porösen Medium eingebettete horizontale Platte

Zusammenfassung Diese Untersuchung befaßt sich mit den Grenzschichtgleichungen für eine stetige laminare Strömung über eine beheizte Platte, die in ein gesättigtes poröses Medium eingebettet ist, mittels des Formalismus von Chandrasekhara [3], Kolar und Sastri [7]. Die Geschwindigkeits- und Temperaturverteilung wurden unter Benutzung der impliziten Crank-Nicolson-Korrekturmethode des Finiten-Elemente-Schemas bestimmt. Die (i+1/2). und die (i+1). Ebene der Verteilungen wurden mit Computer-Hilfe berechnet und in Tabellenform dargestellt. Die Graphen der Temperatur- und Geschwindigkeitsverteilung wurden ausgeplottet. Die Schubspannungen und die Oberflächenreibung an der Wand wurden berechnet und es konnte festgestellt werden, daß die Oberflächenreibung direkt von der Größe der Platte abhängt und umgekehrt proportional der Reynolds-ZahlRe ist. Der Wärmestrom und die Nusselt-Zahl wurden bestimmt. Weiterhin konnte festgestellt werden, daß die Nusselt-Zahl von der Länge der porösen Platte abhängt.

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Nomenclature C _p specific heat of the convective fluid - D skin friction - k permeability of the porous medium - k _f thermal conductivity of the fluid - k _m the coefficient of thermal conductivity of the porous medium - k _s the conductivity of the solid matrix - N(x) Nusselt number - q(x) specific heat flux - Re local Reynolds number - T temperature - T ₀ temperature of the free stream - T _w temperature of the plate - u velocity in thex-direction - u ₀ velocity of the free stream - V velocity iny-direction - x coordinate axis along the plate - y coordinate axis normal to the plate Greek symbols thermal diffusivity - thickness of the velocity boundary layers in thex direction - thickness of the velocity boundary layer in they-direction - the porosity of the medium - dimensionless variable - kinematic viscosity of the fluid - density of the fluid - shear stress     

Dynamic torsional buckling of multi-walled carbon nanotubes embedded in an elastic medium

In this paper the dynamic torsional buckling of multi-walled carbon nanotubes （MWNTs） embedded in an elastic medium is studied by using a continuum mechanics model. By introducing initial imperfections for MWNTs and applying the preferred mode analytical method, a buckling condition is derived for the buckling load and associated buckling mode. In particular, explicit expressions are obtained for embedded double-walled carbon nanotubes （DWNTs）. Numerical results show that, for both the DWNTs and embedded DWNTs, the buckling form shifts from the lower buckling mode to the higher buckling mode with increasing the buckling load, but the buckling mode is invari- able for a certain domain of the buckling load. It is also indicated that, the surrounding elastic medium generally has effect on the lower buckling mode of DWNTs only when compared with the corresponding one for individual DWNTs.     

Stress-strain state of a half-space with shear displacement and rotation of a rigid sphere partly embedded in it

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 27, No. 1, pp. 24–31, January, 1991.     

Dynamic response of an elastic medium containing crack

A fundamental solution for an infinite elastic medium containing a penny-shaped crack subjected to dynamic torsional surface tractions is attempted. A double Laplace–Hankel integral transform with respect to time and space is applied both to motion equation and boundary conditions yielding dual integral equations. The solution of the derived dual integral equations is based on an analytic procedure using theorems of Bessel functions and ordinary differential equations. The dynamic displacements’ field is obtained by inversion of the corresponding Laplace–Hankel transformed variable. Results of a representative example for a crack subjected to pulse surface tractions are obtained and discussed.