THE ILLUSTRATION CALCULATIONS OF SECOND ORDER EFFECTS IN ELASTIC HALF-SPACE ACTED UPON BY A NON-UNIFORM SHEAR LOAD

This paper is a continuation of [1]. An example is discussed in derail to illustrate the second order effects. Numerical calculations for the second order elastic material for the z-direction displacement and the stress t(rz) are carried out. It is found that the second order effect is to reduce z-direction displacement and to decrease t(rz)inside the circle but to increase its value outside the circle.

THE GENERAL SOLUTION OF SECOND ORDER EFFECTS IN ELASTIC HALF-SPACE ACTED UPON BY A NON-UNIFORM SHEAR LOAD

This paper is a continuation of [1]. A closed form solution to the second order elasticity problem, when an isotropic compressible elastic half-space undergoes a deformation owing to a non-uniformly distributed shear load, is presented. The method of integral transform is employed to determine the solutions.

Dynamic Stress and Pore Pressure Around Circular Cavity in Saturated Porous Elastic Half-space Under Harmonic Plane Dilatational Waves

Dynamic stress concentration and pore pressure concentration around an infinitely long cylindrical cavity of circular cross-section subjected to harmonic plane dilatational waves in fluid-saturated porous elastic half-space were obtained by a complex function method based on potential function and multi-polar coordinate. The steady state Biot’s dynamic field equations of porous elastic solid with a viscous liquid were uncoupled into Helmholtz equations via given potential functions. A circular cavity with large radius is used to replace the straight boundary of the saturated porous elastic half-space. The stresses and pore pressures were obtained by using complex functions in multi-polar coordinates with certain boundary conditions of the solid matrix and the fluid matrix. The approximate solutions were compared to existing numerical solutions. Then the variations of the coefficients of dynamic stress concentration and the pore pressures concentration on boundaries of the cavity were discussed with different parameter conditions. The results of the given numerical example indicate that the method used is useful and efficient to the scattering and dynamic stress concentration of plane dilatational waves in saturated porous elastic half-space.

USING FREDHOLM INTEGRAL EQUATION OF THE SECOND KINDTO SOLVE THE VERTICAL VIBRATION OF ELASTICPLATE ON AN ELASTIC HALF SPACE

The dual integral equations of vertical forced vibration of elastic plate on an elastic half space subject to harmonic uniform distribution loading are established according to the mixed boundary-value condition. By applying Abel transformation the dual integral equations are reduced to Fredholm integral equation of the second kind which is solved numerically.

UNIQUENESS FOR THE SOLUTIONS OF ELASTIC THIN PLATES AND SHALLOW SHELLS AS WELL AS THEIR CONTACT PROBLEM WITH HALF SPACE

The uniqueness for the solutions mentioned in the subject is proved by using the uniqueness of the solution for the internal boundary problem of Laplace and bi-Laplace equations of the first kind as well as of the second.

THERMOELASTIC PROBLEMS IN THE HALF SPACE—AN APPLICATION OF THE GENERAL SOLUTION IN ELASTICITY

In this paper, some thermoelastic problems in the half space are studied by using the general solutions of the elastic equations. The method presented here is extremely effective for the axisymmetric problems of the half space as well as the half plane problems.

SECOND ORDER EFFECTS IN AN ELASTIC HALF－SPACE ACTED UPON BY A NON－UNIFORM NORMAL LOAD

A closed form solution to the second order elasticity problem ,when an isotropiccompressible elastic half-space undergoes a deformation owing to a non-uniformlydistributed normal load,is presented,The method of integral transform is employedand the case when loading is distributed,in accordance with Hertz'x law ,is discussed.The limiting solution for incompressible isotropic elastic material is also derived.Numerical calculations for the second order elastic material for the displacement and the normal stress in the z-direction are carried out .It is found that,in comparison to the linear elastic case,the displacement increases and the normal stress decreases in the second order elastic material.

Scattering of SH-wave by multiple circular cavities in half space

In this paper,an analytic method is developed to address steady SH-wave scattering and perform dynamic analysis of multiple circular cavities in half space.The scattered wave function used for scattering of SH-waves by multiple circular cavities,which automatically satisfies the stress-free condition at the horizontal surface,is constructed by applying the symmetry of the SH-wave scattering and the method of multi-polar coordinates system.Applying this scattered wave function and method of moving coordinates,the original problem can be transformed to the problem of SH-wave scattering by multiple circular cavities in the full space.Finally,the solution of the problem can be reduced to a series of algebraic equations and solved numerically by truncating the infinite algebraic equations to the finite ones.Numerical examples are provided for case with two cavities to show the effect of wave number,and the distances between the centers of the cavities and from the centers to the ground surface on the dynamic stress concentration around the cavity impacted by incident steady SH-wave.

考虑土体弹性半空间的水-桩-土相互作用系统在SV波作用下的解析解

近海结构单桩基础所在海洋环境复杂,地震作用下近海桩基础结构工程可能遭受严重的破坏。针对桩基础结构在地震作用下的动力响应问题,建立了一种地震作用下考虑土体弹性半空间的水-桩-土相互作用系统简化解析解;首先,桩体假设为黏弹性材料,可在水-桩-土相互作用系统中分为多个桩段,土体和水体分别假设为线黏弹性介质和声学介质;然后,基于亥姆霍兹分解、分离变量法和水-桩-土连续性条件,得到了整个桩体的位移表达式;之后,把解析解退化为两种情况,分别与无水有土情况下的子结构方法以及有土有水情况下的刚性解析解方法进行了对比,从而验证弹性解析解的合理性;最后,通过使用本弹性解析解进行了一些参数分析,以此研究水体、土体和桩体3种参数对桩体位移动力响应的影响,研究结果对海上桩基设计有一定的参考价值。

两个具有初应力半空间界面波的传播特性

讨论了两个具有初应力的磁电弹半空间界面波的传播特性。在两个不同材料的具有初应力的磁电弹半空间中,由本构方程和控制方程以及界面的连续条件,推导得到两个半空间界面波(Stoneley波)的波速方程。根据对波速方程的数值分析,得到两个具有初应力的磁电弹半空间界面处的界面波的传播特性。研究结果为磁电弹材料在工程中的应用提供理论依据。

相邻明置刚性条形基础的水平-摇摆耦合阻抗研究

基于弹性半空间理论研究两相邻明置条形基础的水平-摇摆耦合动力阻抗。推导了频域内水平、垂直简谐条形均布激振下弹性地基位移的格林函数,将基础与地基的接触面分割成若干个子单元,利用格林函数建立各子单元的耦合柔度方程。根据基础的刚体位移决定各子单元的位移,由叠加原理得到土与相邻明置条形基础的水平-摇摆动力耦合阻抗函数。通过收敛性研究并与其他数值计算及混合边值法的精细解进行比较,证明此方法具有计算简便和精度高的特点,可用于全频段阻抗函数的计算。最后分析了相邻条形基础距宽比对水平-摇摆耦合动力相互作用的影响,计算表明:当两明置条形基础距宽比S/L<5.0时,应考虑其水平-摇摆的动力相互作用效应。

弹性半空间上中厚圆板弯曲的Fourier-Bessel级数解

本文对各向同性弹性半空间地基上中厚度圆板一般弯曲问题进行了系统的分析。板的挠度、荷载、地基反力及板下地基表面的沉降均被展开为二重Fourier-Bessel级数,这些级数中的待定系数由板的边界条件、板的控制方程及板-地基的相容条件加以确定,从而将弹性半空间地基与中厚度圆板的相互作用问题转化为数值积分和代数方程组的求解问题。数值计算表明,该级数解具有较快的收敛速度。

半无限弹性空间中移动荷载动力响应的频域-波数域比例边界有限元法分析

基于Fourier积分变换和虚功原理,形成了频域-波数域比例边界有限元法,分析了移动荷载作用下半空间域弹性空间动力响应。首先对半无限域弹性体的动力控制方程进行时间到频域,荷载移动方向的空间域到波数的Fourier积分变换,然后选择比例中心,利用虚功原理,在地铁隧道孔洞横截面环向上采用有限元法意义离散,建立了频域-波数域比例边界有限元方程,进而形成了一阶微分矩阵方程形式的半无限空间动力刚度。文中理论推导表明:利用文中方法分析半无限域中沿地铁隧道结构纵轴向的移动荷载动力响应问题,不仅可避免无穷边界计算处理误差,而且可极大减小计算分析量。计算结果表明:半无限弹性地基的振动响应随移动荷载速度增大而增大,尤其是当荷载速度增大到土体剪切波速后,振动波传播到土体表面引起土体振动显著增大,土体振动性增大,将会对土体及表面结构的安全性形成一定影响,另一方面土体的振动在沿地铁隧道纵轴向的衰减比竖向慢。

典型沥青路面结构路基工作区深度分析

该文基于实测“胎-路”界面条件,分别采用弹性半空间体理论、层状弹性体系理论计算不同工况下典型沥青路面结构的路基工作区深度,计算结果表明路基工作区深度随轴重显著变化,并基于计算结果提出路基工作区深度的推荐值:轴重小于100 kN时,路基工作区深度取0.8 m;轴重小于130 kN时,路基工作区深度取1 m;对于轴重小于150 kN的道路,路基工作区深度建议值为1.2 m。对于路基工作区范围内的土基,必须采取有效的工程处理措施以确保路基路面结构具备足够的承载力。

Static response of a layered magneto-electro-elastic half-space structure under circular surface loading

A cylindrical system of vector functions, the stiffness matrix method and the corresponding recursive algorithm are proposed to investigate the static response of transversely isotropic,layered magneto-electro-elastic（MEE） structures over a homogeneous half-space substrate subjected to circular surface loading. In terms of the system of vector functions, we expand the extended displacements and stresses, and deduce two sets of ordinary differential equations, which are related to the expansion coeficients. The solution to one of the two sets of these ordinary differential equations can be evaluated by using the stiffness matrix method and the corresponding recursive algorithm. These expansion coeficients are then integrated by adaptive Gaussian quadrature to obtain the displacements and stresses in the physical domain. Two types of surface loads, mechanical pressure and electric loading,are considered in the numerical examples. The calculated results show that the proposed technique is stable and effective in analyzing the layered half-space MEE structures under surface loading.

弹性半空间-理想流体层中Stoneley波的动力特性

为了解弹性半空-理想流体层中Stoneley波的动力特性,并为进一步开发利用海洋资源提供调查方法,根据弹性固体与理想流体动力学方程,推导了弹性半空间-理想流体层中Stoneley波的特征方程.基于该特征方程,分析了固液两介质的物理特性对流体动压力的影响,以及固体和流体介质的位移分布情况.结果表明,该体系中Stoneley波在固体中的位移分布类似于半空间Rayleigh波,而在流体中的位移分布有明显的规律性;弹性半空-理想流体层中Stoneley波具有频散性,且其波速小于弹性半空间中Rayleigh波的波速.

海上风机大直径单桩水平-摇摆耦合振动特性

基于弹性半空间理论,在Abaqus有限元软件中建立海上风机三维大直径薄壁空心桩-土动力相互作用模型,通过荷载控制法研究桩的水平-摇摆耦合振动,分析无量纲频率、单桩长径比、厚径比、桩土弹性模量比值、桩基周围冲刷对单桩动力阻抗的影响,并将所得结果无量纲化,增加其适用性。研究结果表明,无量纲频率对桩基动力特性的影响与其他因素紧密相联;长径比、弹性模量比、厚径比、桩基周围冲刷坑深度对桩基动力特性均存在较大影响;刚度随着长径比的增大而增大,但存在一定的临界桩长,在无量纲频率较低时,阻尼的趋势与刚度类似;当基础周围的冲刷深度达到2倍直径时,基础的刚度将会下降到原来的1/3左右,且阻尼的下降也非常显著。

土-结构相互作用对基础隔震体系的影响

本文应用子结构法 ,分析了土 结构相互作用对线性基础隔震体系基频和结构反应的影响。分析模型中 ,上部结构取为具有埋置刚性基础的均质剪切梁式模型 ,地基取为均质、各向同性的粘弹性半空间。上部结构和刚性基础之间设置隔震层。通过对隔震体系反应的传递函数及基于FFT的地震时程反应的分析 ,讨论了地基土柔性、基础埋深和隔震层刚度对于基础隔震体系基频和结构反应的影响。

Analytical solutions for dynamic pressures of coupling fluid-solid-porous medium due to P wave incidence

Wave reflection and refraction in layered media is a topic closely related to seismology,acoustics,geophysics and earthquake engineering.Analytical solutions for wave reflection and refraction coefficients in multi-layered media subjected to P wave incidence from the elastic half-space are derived in terms of displacement potentials.The system is composed of ideal fluid,porous medium,and underlying elastic solid.By numerical examples,the effects of porous medium and the incident wave angle on the dynamic pressures of ideal fluid are analyzed.The results show that the existence of the porous medium,especially in the partially saturated case,may significantly affect the dynamic pressures of the overlying fluid.

A new method to calculate near-field radiation excited by heterogeneous fault rupture

This paper derives from the representation theory the formula for calculating the radiation excited by heterogeneous fault rupture based on box-like discretization scheme. Preliminary validation indicates that our algorithm has very high computation precision and efficiency; therefore, it is a very practical tool to investigate strong ground motion problems. Additionally, the equations given in this study can also be used to invert the fault rupture process.