共查询到17条相似文献，搜索用时 203 毫秒
1.
采用解析层元法对存在地下点热源的岩土工程问题进行解答。首先从热弹性力学三维问题的基本控制方程出发,利用拉普拉斯-傅里叶积分变换推导出其在变换域内单层介质及下卧半空间的解析层元;然后结合有限单元法原理组装得到总刚度矩阵,结合边界条件,得到其在变换域内的解答,最后应用拉普拉斯-傅里叶积分逆变换技术,得到物理域内的解。编制了相应的计算程序,算例分析表明：该结果与已有文献吻合较好,该方法求解层状半空间的热-力耦合响应问题具有较好的适用性和较高的精度;层状岩土介质体系中,热扩散系数对温度及地表隆起的变化过程影响显著,但对其初始值和最终稳定值影响不明显;分层特性对岩土介质温度分布及地表位移变化过程均有显著影响。 相似文献
2.
基于Biot固结理论,运用解析层元方法求解竖向简谐荷载作用下二维层状饱和地基的动力响应问题。从直角坐标平面应变问题控制方程出发,通过Fourier-Laplace变换将偏微分方程组转化为常微分方程组,求解得到单层饱和地基的解析层元。结合层间连续条件和边界条件,组装得到多层饱和地基的总刚度矩阵方程,进而求得变换域内的解。借助Fourier-Laplace逆变换的数值积分方法,获得平面应变动力问题在物理域内的解,编制了相应的计算程序,其计算结果与已有文献结果吻合较好。通过算例分析了荷载圆频率、荷载作用深度及地基成层性对地基竖向位移的影响。计算结果表明：随荷载圆频率的增大,地基竖向位移先增加后减小;地基竖向位移在荷载作用点处呈现波峰,且受表层土性的影响较大。 相似文献
3.
层状可压缩岩基三维固结问题的状态空间解 总被引：1，自引：0，他引：1
采用状态空间法求解层状可压缩岩基的三维固结问题。首先从直角坐标系下考虑可压缩性的三维Biot固结问题的控制方程出发,通过Laplace-Fourier变换得到状态空间方程,解此方程并通过Cayley-Hamilton定理,得到单层可压缩岩基三维固结问题的传递矩阵;然后利用传递矩阵法,结合层间连续性条件和边界条件,得到了层状可压缩岩基三维固结问题在积分变换域内的解答;最后应用Laplace-Fourier逆变换技术,得到层状可压缩岩基三维固结问题在物理域内的理论解答。编制了相应的计算程序,进行了数值计算与分析,证明了压缩性对岩基固结问题的影响 相似文献
4.
从平面弹性力学的基本方程出发,利用Fourier积分变换等数学手段,推导出了单层平面问题的刚度矩阵,然后按有限元法组成总体刚度矩阵。通过求解由总体刚度矩阵所构成的代数方程和Fourier积分逆变换,得到在任意静荷载作用下多层弹性平面问题的精确解。由于刚度矩阵不含有正指数项,计算时不会出现溢出现象,从而克服了传递矩阵法的缺点。推导过程中摒弃了应力函数的选择,使得问题的求解更加合理化,同时也为进一步研究此类问题如温度场、动力学等奠定了理论基础。计算实例证明了推导结果的准确性。 相似文献
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为了给应用落锤式弯沉仪（falling weight deflectometer,简称FWD）准确识别路基性能劣化提供理论基础,建立了考虑路基非饱和特性的弹性层状路面在FWD荷载作用下的振动响应计算模型。通过Laplace-Hankel变换对模型的动力控制方程进行了推导求解,建立了路面和非饱和路基的动力刚度矩阵。并由层间连续性条件合成了公路结构的整体动力刚度矩阵,结合边界条件得出了FWD荷载作用下整个公路结构在变换域内的振动响应解。利用Laplace-Hankel逆变换对振动响应进行了空间-时间域内的数值求解,分析了FWD荷载频率和路基饱和度对振动响应的影响以及路基性能劣化与路表振动信号的关联性。研究结果表明：路表竖向动位移主要受FWD荷载低频成分的影响且随饱和度的增大而增大;相比较路表振动速度和路基表面竖向动应力,路表竖向动位移受路基性能劣化的影响更敏感,且在距荷载中心1.2 m位置处的路表竖向动位移变化率达到最大。研究结果可为路基性能劣化的反馈指标与位置选择提供科学依据。 相似文献
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层状地基中单桩负摩擦问题积分方程解法 总被引：9，自引：1，他引：8
利用Biot固结理论和积分方程方法研究了表面有堆载的层状地基中单桩负摩擦问题。根据层状饱和土的圆形载荷基本解得出了单桩在圆形均布载荷作用下在时间域内的第二类Fredholm积分方程组。运用Laplace变换对上述积分方程组进行简化。再结合传递和刚度矩阵传递到各个层中去,对变换域内的积分方程采用Schapery 逆变换方法得到时域内单桩的近似积分方程。求解积分方程组并进行相应的数值逆变换,就可得出层状地基中的单桩在表面圆形均布载荷作用下的位移、轴力、孔压和桩侧摩阻力随时间的变化情况。计算结果表明,桩侧剪力和孔压分层明显。 相似文献
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传递矩阵法分析层状地基中桩的扭转变形 总被引：2，自引：0，他引：2
研究了扭矩作用下单桩的扭转变形.采用积分变换和传递矩阵方法,求解了成层土在内部环形荷载作用下的基本解;利用此基本解并考虑桩土位移协调条件,提出了层状地基中单桩扭转变形分析的解析方法;并按此理论方法对匀质地基模型进行了数值计算,其结果与已有经典解答相当吻合. 相似文献
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《岩土力学》2015,(Z2)
为了研究硬壳层对低路堤软土地基动力响应的影响,将软土地基上的道路系统模拟成路面-路基-硬壳层-软土地基4层结构。假设路面、路基、硬壳层都为单相弹性土体,而软土地基采用饱和多孔介质模拟,通过积分变换法对模型进行推导求解,分别建立了路面、路基、硬壳层和软土地基的动力刚度矩阵,并考虑路表车辆荷载条件、层间连续条件和饱和软基表面透水条件,最终集成了道路结构的整体动力刚度矩阵,获得了车辆荷载作用下低路堤软土地基的动力响应解答。在该基础上,利用快速傅里叶逆变换方法对动力响应进行数值求解,详细分析了硬壳层厚度、模量和泊松比对动应力扩散作用的影响。研究结果表明,软土地基表面的动力响应对硬壳层厚度和模量的变化十分敏感,硬壳层的存在大大地减弱了软基顶面的竖向动应力,并且增大了竖向动应力的分布范围,可见硬壳层对交通荷载引起的动力响应有明显的扩散作用。 相似文献
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利用扩展精细积分法求解横观各向同性地基的平面应变问题。扩展精细积分法具有高精度和较高计算效率的特点,是求解微分方程的有效方法,相比于解析法可以节省大量理论推导工作量。从直角坐标下弹性力学控制方程出发,推导出Fourier变换域内地基的常微分矩阵方程;之后对地基微层元进行消元合并,进一步得到荷载作用在地基内部时层状地基的扩展精细积解。与已有文献的对比验证了方法的精确性,并分析了横观各向同性参数、层状性质和荷载作用点对计算结果的影响。结果表明：土体竖向位移随着横观各向同性参数n的增大而减小,而随着横观各向同性参数m的增大而增大;荷载作用点 的变化只对作用点以上的土体有影响,而上层土体的模量对竖向位移计算结果的影响更为显著,土体成层性对沉降的影响要比对竖向应力的影响更为显著。 相似文献
10.
天然地基通常含有不规则的分层界面。对此,提出了一种计算具有不规则界面的层状地基三维动力响应的薄层法,推导了简谐点源作用下不规则分层半空间三维动力问题的基本解。基于双重Fourier变换,获得弹性介质在频域-波数域内的薄层单元系统控制方程;利用模态叠加原理,推导了半无限长和有限长薄层单元的刚度矩阵,引入完美匹配层模拟波向底层半无限空间的传播,从而构建可考虑土层界面沿横向不规则分布的三维层状地基计算模型,获得了简谐点源作用下不规则分层地基三维动力问题的基本解;通过与既有方法的对比分析,验证了新方法的正确性。最后,利用该方法计算了具有倾斜分层界面的双层地基在简谐荷载作用下的动力响应,结果表明：界面倾斜导致的动力响应差异大,且随着倾斜度以及荷载频率的增加而变大。在进行天然地基的动力分析时,需考虑地基的不规则分层特性导致的振动响应差异。 相似文献
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After the application of a Laplace–Hankel transform, the governing equations of Biot’s consolidation are solved analytically by using the eigenvalue approach. Then the analytical layer-element of a single soil layer can be obtained in the transformed domain by synthesizing the generalized displacements and stresses, which are both expressed by six arbitrary constants. The elements of the analytical layer-element only contain negative exponential functions, which leads to a considerable improvement in computation efficiency and stability. The global stiffness matrix equation of multilayered soils is further obtained by assembling the interrelated layer-elements, and the actual solution is achieved by numerical inversion of the Laplace–Hankel transform after the solution in the transformed domain is obtained. Numerical examples are given to demonstrate the accuracy of this method and to study the influence of the layered soil properties and time history on the consolidation behavior. 相似文献
13.
This note presents an analytical solution to one-dimensional consolidation in unsaturated soils with a finite thickness under confinement in the lateral direction and vertical loading varying exponentially with time. The boundary conditions are that the top surface is permeable to water and air and the bottom is impermeable to water and air. The transfer relationship between the state vectors at the top surface and any depth is gained by applying the Laplace transform and Cayley-Hamilton mathematical methods to the governing equations of water and air, Darcy’s law and Fick’s law. The excess pore-air and pore-water pressures and settlement in the Laplace-transformed domain are obtained by using the Laplace transform with the initial and boundary conditions. By performing the inverse Laplace transforms, the analytical solutions of the excess pore-air and pore-water pressures at any depth and settlement are obtained in the time domain. 相似文献
14.
An analytical solution is developed in this paper to investigate the vertical time-harmonic response of a pipe pile embedded in a viscoelastic saturated soil layer. The wave propagation in the saturated soil is simulated by Biot’s 3D poroelastic theory and that in the pipe pile is simulated by 1D elastodynamic theory. Potential functions are applied to decouple the governing equations of the soil. The analytical solutions of the outer and inner soil in frequency domain are obtained by the method of separation of variables. The vertical response of the pipe pile is then obtained based on the continuity assumption of the displacement and stress between the pipe pile and both the outer and inner soil. The solution is compared with existing solutions to verify the validity. Numerical examples are presented to analyze the vibration characteristics of the pile. 相似文献
15.
Analytical layer element solutions for deformations of transversely isotropic multilayered elastic media under nonaxisymmetric loading 总被引：1，自引：0，他引：1
This paper presents the analytical layer element solutions for deformations of transversely isotropic elastic media subjected to nonaxisymmetric loading at an arbitrary depth. The state vectors for the nonaxisymmetric problem are deduced through the substitution of the Hu Hai‐chang solutions into the basic equations for the transversely isotropic elastic media. From the state vectors, the analytical layer element of a single layer is obtained in the Hankel transformed domain. The analytical layer element is an exact and symmetric stiffness matrix whose elements are without positive exponential functions, which can not only simplify the calculation but also improve the stability of computation. On the basis of the continuity conditions between adjacent layers, the global stiffness matrix is obtained by assembling the interrelated layer elements. The solutions for the multilayered elastic media in the transformed domain are obtained by solving the algebraic equation of the global stiffness matrix, which satisfies the boundary conditions. The actual solutions in the physical domain are further obtained by inverting the Hankel transform. Finally, some cases are analyzed to verify the solutions and evaluate the influences of the transversely isotropic character and stratified character of the media on the load–displacement responses. The numerical results show that the variations of the elastic properties between layers have a great effect on the displacements of the multilayered media. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
16.
The scaled boundary finite‐element method is derived for elastostatic problems involving an axisymmetric domain subjected to a general load, using a Fourier series to model the variation of displacement in the circumferential direction of the cylindrical co‐ordinate system. The method is particularly well suited to modelling unbounded problems, and the formulation allows a power‐law variation of Young's modulus with depth. The efficiency and accuracy of the method is demonstrated through a study showing the convergence of the computed solutions to analytical solutions for the vertical, horizontal, moment and torsion loading of a rigid circular footing on the surface of a homogeneous elastic half‐space. Computed solutions for the vertical and moment loading of a smooth rigid circular footing on a non‐homogeneous half‐space are compared to analytical ones, demonstrating the method's ability to accurately model a variation of Young's modulus with depth. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献