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基于Biot波动理论和广义热弹性理论,对简谐线源荷载（力荷载和热荷载）作用下的热-流-固耦合地基的动力响应问题进行了研究。将地基看成是均质各向同性、完全饱和的多孔半空间介质,利用无量纲化和Fourier变换方法对热-流-固耦合控制方程进行简化,得到了变换域内应力分量、位移分量、温度分布及超孔隙水压力的一般解,并利用Fourier逆变换得到了相应的积分形式解答。通过数值计算对按热-流-固耦合理论、饱和多孔弹性理论和热弹性理论得到的结果进行了比较,同时分析了热-流-固耦合条件下热荷载激振频率对竖向应力、竖向位移、温度分布以及超孔隙水压力的影响。 相似文献
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The thermomechanical responses of a porous elastic medium subjected to time harmonic loads (normal force and thermal source) are investigated analytically in the context of generalised thermoelastic theory with one relaxation time. The material of the foundation, obeying Biot’s dynamic poroelastic theory, is idealised as a uniform, fully saturated poroelastic half-space stratum. The coupled governing equations are established based on Biot’s dynamic poroelastic theory and on generalised thermoelastic theory. Assuming the disturbances to be harmonically time dependent, the general solutions of stress, displacement, temperature distribution and excess pore water pressure are deduced using the Fourier transform, and the transformed solutions are numerically inverted. The differences among the coupled thermo-hydro-mechanical dynamic model (THMD), the hydro-mechanical dynamic model (HMD) and the thermo-elastic dynamic model (TMD) are discussed. In addition, the effects of the thermal loading frequency on the displacement, stress, temperature distribution and excess pore water pressure components are analysed in the numerical results. 相似文献
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为研究空沟对高速列车引起地基振动的隔振效果,在已有研究基础上改进出一种新的解析研究模型。模型中首次运用了饱和半空间模型来研究地基上隔振沟对高速列车的隔振效果;隔振沟则通过在饱和半空间土体上设置3个合适宽度、截面为矩形的弹性层来模拟;中间矩形弹性层为路堤,路堤上方放置了枕木与轨道。枕木与轨道分别通过纵向异性Kirchhoff薄板与Euler梁来模拟,饱和土地基采用Biot多孔饱和介质理论来描述。控制方程通过傅立叶变换与傅立叶级数展开,在变换域中进行求解。研究表明,随着列车运行速度的提高,空沟的隔振效果明显提高;饱和土体固-液相的耦合作用对隔振沟的隔振效果的影响明显,尤其当列车运行速度超过土体表面Rayleigh波速时,随着土体渗透系数的增加,空沟隔振效果显著降低。此外,列车运行速度超过土体表面波速时,饱和土地基上空沟的隔振效果明显优于相应单相弹性地基上空沟的隔振效果。 相似文献
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在考虑横观各向同性含液饱和多孔介质固体骨架和流体可压缩性以及固体骨架的黏弹性特征下,基于横观各向同性含液饱和多孔介质u-w形式的三维动力控制方程,以固相位移u、液相相对位移w为基本未知量,综合运用Laplace变换、双重Fourier变换等方法,在直角坐标系下通过引入中间变量,将六元2阶动力控制方程组化为两组各含4个未知变量的常微分方程组,给出了直角坐标系下横观各向同性含液饱和多孔介质三维黏弹性动力反应的积分形式一般解;作为理论推导的验证,通过引入初始条件和边界条件,对横观各向同性含液饱和多孔介质半空间黏弹性瞬态反应问题进行了求解。解答的退化验证表明,所推导的理论解是正确的。 相似文献
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Leonidas T. Stavridis 《Geotechnical and Geological Engineering》2011,29(4):431-442
This paper develops a systematic procedure concerning the determination of the interaction of an arbitrary multistory frame
with the elastic layered foundation soil by making use only of the soil surface deformational characteristics. The paper focuses
on the response of the foundation beam through which the frame rests on the ground, showing the need for prestressing the
beam in order to ensure better functionality. The investigation addresses the dual goal of excluding the undesirable cracked
state of the beam and reducing its structural height together with the overall amount of reinforcement needed. A set of soil
layered profiles is considered and it is investigated to what extent the required prestressing force depends not only on the
soil deformational properties at hand, but also on the method of analysis used. The results are compared for both the elastic
half-space and the Winkler’s method, taking into account either the whole structure stiffness, or the stiffness of the foundation
beam only, as it is usually considered in practice. 相似文献
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运用对偶积分方程来求解层状横观各向同性地基与墙下条形基础的共同作用问题。从直角坐标平面应变问题控制方程出发,通过傅里叶（Fourier）变换和层间连续性条件,可以得到层状横观各向同性地基的传递矩阵解。基于该传递矩阵解,并利用条形基础与地基接触的混合边值条件,推导出一组关于基础挠度和地基反力的对偶积分方程。考虑墙下条形基础受到竖向集中荷载的情况,利用弹性薄板理论先求解出条形基础挠度;随后应用雅可比（Jacobi）正交多项式和级数展开的方法,将对偶积分方程转化为线性代数方程组进行求解。编制了相应的计算程序,其计算结果与有限元软件ABAQUS的结果基本吻合,从而验证了所提理论的正确性。算例分析表明,板土相对刚度与地基成层性对地基反力、地表沉降和沿z轴竖向正应力有很大的影响。 相似文献
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竖向圆形荷载作用下弹性半空间问题的位移和应力解是桩基分析的基础。利用Hankel积分变换,首先导出了弹性地基半空间位移与应力的积分形式的通解。通过适当地引入边界条件和界面位移和应力的连续条件,求得了内部作用竖向圆形荷载时弹性地基半空间位移与应力的积分形式解。在此基础上,给出了不同深度处荷载作用投影范围内竖向位移和竖向正应力的平均值。数值结果验证了解析解的正确性。 相似文献
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为使多层地基土中深基坑支护设计考虑支护结构-土的非线性共同作用,提出由集中力弹簧模型建立支护桩与土相互作用的p-y曲线,进而根据一般弹性地基梁的挠曲微分方程,并考虑桩与锚杆的变形协调,推导出考虑非线性共同作用的预应力锚杆支护桩的挠曲微分方程,应用有限差分法计算预应力锚杆支护桩的位移和内力。实例计算表明,计算结果能更好地满足工程实际的要求。 相似文献
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A hierarchical finite element is presented for the geometrically nonlinear free and forced vibration of a non-uniform Timoshenko beam resting on a two-parameter foundation. Legendre orthogonal polynomials are used as enriching shape functions to avoid the shear-locking problem. With the enriching degrees of freedom, the accuracy of the computed results and the computational efficiency are greatly improved. The arc-length iterative method is used to solve the nonlinear eigenvalue equation. The computed results of linear and nonlinear vibration analyses show that the convergence of the proposed element is very fast with respect to the number of Legendre orthogonal polynomials used. Since the elastic foundation and the axial load applied at both ends of the beam affect the ratios of linear frequencies associated with the internal resonance, they influence the nonlinear vibration characteristics of the beam. The axial tensile stress of the beam in nonlinear vibration is investigated in this paper, and attention should be paid to the geometrically nonlinear vibration resulting in considerably large axial tensile stress in the beam. 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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考虑路面和地基之间的相互作用,建立了路面-双层地基的三维模型,将车辆荷载模拟成矩形移动荷载,利用Fourier变换方法对车辆荷载作用下路面-双层地基系统的三维振动问题进行了研究。假设地基为上部弹性土体和下部为饱和土体组成的双层混合结构,整个系统置于刚性基岩上。通过引入势函数,利用Lame分解理论和积分变换方法分别对弹性土层和饱和土层进行求解。在Fourier变换域内,联立路面和下卧双层地基系统的的运动方程,获得了车辆荷载作用下路面-双层地基系统三维振动的位移和孔压响应的积分形式解,并利用IFFT算法和自适应数值积分算法得到了数值计算结果。研究结果可为路基动力响应分析提供参考。 相似文献
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假定土骨架服从标准线性固体黏弹性本构关系,研究了深埋圆形隧洞的饱和黏弹性土-弹性衬砌耦合系统在轴对称爆炸作用下的瞬态动力响应。首先,基于饱和土的Biot模型和衬砌的弹性理论,通过引入势函数和Laplace变换,利用弹性衬砌和饱和黏弹性土界面处的连续性条件以及边界条件,得到饱和黏弹性土体和弹性衬砌位移、应力和孔隙水压力等在Laplace变换域中的解析解。其次,利用Laplace数值Crump逆变换得到耦合系统在时间域的动力响应,数值分析了不同土体模型下土体-衬砌耦合系统的径向位移和环向应力以及土体孔隙水压力等。结果表明：对不同土体模型的土体-衬砌耦合系统,其在爆炸载荷作用下的动力响应性态基本一致,但动力响应的振动周期和幅值等具有明显的差异。同时,对于饱和黏弹性土-弹性衬砌系统,土体黏性参数对土体径向位移和孔隙水压力有明显的影响,但对土体环向应力影响较小。 相似文献
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Analytical solutions for Euler‐Bernoulli Beam on Pasternak foundation subjected to arbitrary dynamic loads 
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下载免费PDF全文 In this paper, the dynamic response of an infinite beam resting on a Pasternak foundation and subjected to arbitrary dynamic loads is developed in the form of analytical solution. The beam responses investigated are deflection, velocity, acceleration, bending moment, and shear force. The mechanical resistance of the Pasternak foundation is modeled using two parameters, that is, one accounts for soil resistance due to compressive strains in the soil and the other accounts for the resistance due to shear strains. Because the Winkler model only represents the compressive resistance of soil, comparatively, the Pasternak model is more realistic to consider shear interactions between the soil springs. The governing equation of the beam is simplified into an algebraic equation by employing integration transforms, so that the analytical solution for the dynamic response of the beam can be obtained conveniently in the frequency domain. Both inverse Laplace and inverse Fourier transforms combined with convolution theorem are applied to convert the solution into the time domain. The solutions for several special cases, such as harmonic line loads, moving line loads, and travelling loads are also discussed and numerical examples are conducted to investigate the influence of the shear modulus of foundation on the beam responses. The proposed solutions can be an effective tool for practitioners. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
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This paper presents an investigation of the steady-state response of pavement systems subjected to a moving traffic load. The traffic loads are simulated by four rectangular load pressures, and the rigid and flexible pavement systems are regarded as an infinite plate resting on a poroelastic half-space soil medium. The contact surface between the plate and the poroelastic half-space is assumed to be smooth and fully permeable. Kirchhoff small-deflection thin-plate theory is employed to analyze the plate, while Biot’s fully dynamic poroelastic theory is used to characterize the poroelastic half-space. The frequency wave-number domain solution of the pavement system is obtained by the compatibility condition between the plate and the poroelastic half-space. By applying the inverse fast Fourier transform, the time domain solution is obtained. Also, the influences of the load speed, the permeability of the soil, and the flexural rigidity of the plate on the response of the pavement system are investigated. The numerical results show that the influences of these parameters on the dynamic response of the pavement system are significant. 相似文献
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运动荷载附近有限层厚软土地基的振动研究 总被引：4，自引：4，他引：0
基于Biot多孔弹性介质的波动理论,研究了运动荷载附近软土地基的振动问题。假设一条形均布荷载作用在地基表面,则该模型可视为平面应变问题进行分析。通过引入4个势函数和Helmholtz原理,并利用Fourier变换及逆变换技术,获得了运动荷载作用下软土地基的应力、位移和孔隙水压力的解答。利用离散Fourier逆变换得到数值计算结果,分析了荷载速度,频率以及软土的渗透系数及多孔弹性参数对运动荷载作用下地表竖向位移及土体中任一点孔隙水压力分布的影响。 相似文献
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上覆单相弹性层饱和地基上刚性条形基础竖向振动的混合边值问题 总被引：1，自引：0，他引：1
根据Biot动力控制方程,运用Fourier积分变换技术,并按照混合边值条件和连续条件建立了上覆单相弹性层饱和地基上刚性条形基础竖向振动的对偶积分方程,并将其退化到完全饱和地基的情形。通过引进正交多项式将对偶积分方程化为线性代数方程组,从而得到了上覆单相弹性层的饱和地基上刚性条形基础的竖向振动规律。通过算例分析得到,单相弹性层的厚度对动力柔度系数有着较大的影响,在单相弹性层厚度较小时（小于条形基础半宽的0.1）,动力柔度系数曲线与完全饱和的基本重合;完全饱和地基上刚性基础的竖向振动是上覆弹性层厚度Hn=0的特例。 相似文献