下卧基岩饱和地基在移动荷载作用下的动力响应

基于Biot多孔弹性介质波动理论,在平面应变条件下研究了下卧基岩饱和地基在移动线荷载作用下的动力响应。通过引入势函数并利用Helmholtz原理,再经过Fourier变换和逆变换,获得了移动线荷载作用下饱和地基的位移、应力、孔隙水压力解答。最后通过快速逆傅里叶变化（IFFT）得到数值计算结果,详细分析了土颗粒的压缩性、孔隙水的压缩性、饱和土的剪切模量、孔隙率、渗透性、移动荷载速度和饱和土层厚度等参数对动力响应的影响     

冲击荷载下一端简支一端固支高桥墩的动力屈曲

考虑剪切变形和大位移的影响,建立一端简支一端固支高桥墩在冲击荷载作用下的非线性动力学基本方程式;通过位移形函数假设,采用伽辽金积分方法得到了时间变率的动力学控制方程;利用四阶Runge-Kutta法进行数值求解,得到冲击荷载作用下高桥墩的临界荷载、位移响应曲线以及各种荷载和几何参数对临界荷载的影响规律。通过数值算例比较了三角形冲击荷载和矩形冲击荷载作用下的荷载-位移幅值响应曲线;给出了矩形冲击荷载作用下,不同峰值的位移响应曲线、临界荷载随高桥墩柔度的变化曲线、不同冲击持续时间对临界荷载的影响     

任意形式荷载作用下饱和土中桩的扭转振动特性研究

基于Biot提出的饱水多孔介质的波动方程,研究了均质各向同性饱和土中弹性支承桩的耦合扭转振动问题。通过采用拉普拉斯变换及分离变量法求得土体扭转振动位移形式解。利用桩土系统衔接条件和边界条件,进而得到了桩顶转角响应的拉普拉斯变换域解。进一步采用拉普拉斯逆变换技术,得到了任意形式激振荷载作用下桩顶转角时域响应的数值解。最后,研究了骤加荷载和三角形荷载作用下主要参数对桩顶转角时域响应的影响。     

含任意直线型裂纹的直角域中圆柱夹杂对SH波的散射

摘 要: 采用Green函数及复变函数方法研究了SH波作用下直角域内任意直线型裂纹对圆柱弹性夹杂的影响。首先,取含有圆柱弹性夹杂的直角域内任意一点承受时间谐和的出平面线源荷载作用时的位移函数基本解作为适合本文的Green函数;其次,利用裂纹切割技术构造裂纹,并写出圆柱夹杂与裂纹同时存在时的位移场和应力场;最后,给出圆柱弹性夹杂动应力集中系数的算例和结果,并讨论了裂纹的存在对动应力集中系数的影响。     

出平面线源荷载对半空间中半圆形凸起的圆柱形弹性夹杂的散射

采用复变函数法和Green函数法,求解出平面线源荷载对半空间中半圆形凸起的圆柱形弹性夹杂的散射。首先,给出在含有半圆形凸起的圆柱形弹性夹杂的弹性半空间中,水平表面上任意一点承受时间谐和的出平面线源荷载作用时的位移函数,取该位移函数作为Green函数;然后,采用分区的思想,分别构造出夹杂内的驻波和夹杂外的散射波,满足"公共边界"处位移和应力的连续性条件,建立起求解该问题的无穷代数方程组;最后,给出了动应力集中系数和水平地面位移幅值的数值结果,并进行了讨论。     

半空间中椭圆夹杂与裂纹对SH波的散射

采用Green函数、复变函数和多极坐标方法求解弹性半空间中椭圆形弹性夹杂与任意方位的裂纹对SH波的散射问题。利用“保角映射”技术求解椭圆夹杂对SH波的散射位移场,并构造适合本问题的Green函数,即含椭圆形弹性夹杂的弹性半空间内任意一点承受时间谐和的反平面荷载作用时的位移基本解,结合裂纹“切割”法构造裂纹,进而得到椭圆夹杂和裂纹同时存在条件下的位移场与应力场。最后,通过具体算例,讨论了不同参数对地表位移、弹性夹杂周边动应力集中系数和裂纹尖端动应力强度因子的影响规律。     

南海内孤立波作用下顶张力立管极值响应研究

内孤立波能够引起强剪切流和巨大的冲击荷载,对海洋平台和海洋立管等海上结构物会构成危险,而关于内孤立波对海洋立管作用的研究很少。本文根据描述内孤立波的KdV-mKdV方程,结合改进的Morison公式,采用有限单元法在时域内对内孤立波作用下顶张力立管的极值响应进行了数值模拟,并就内波振幅、立管内流、顶张力、弹性模量和壁厚的变化对极值响应的影响进行了探讨。结果表明,内孤立波会引起立管较大的极值响应,在立管的分析计算中应该加以考虑。     

网壳结构冲击响应分析方法及抗冲击特性研究

在明确网壳结构冲击响应关键问题的基础上,提出了实用有效的网壳结构冲击响应分析方法,包括网壳结构冲击响应的特征指标（荷载作用与特征响应）、冲击响应的分析流程与计算模型三部分。并应用此方法对典型网壳（Kiewitt-8型单层球面网壳）的冲击响应特性进行研究,分析了荷载作用特点、主要节点的速度与位移变化规律、主要杆件的应力变化规律及网壳结构的能量变化特征;结果表明网壳的荷载作用是短时超强的半正弦脉冲;响应特点是在冲击瞬间冲击区局部响应骤增,并逐渐向支座方向传播,从冲击区到支座,结构局部响应依次达到极值,此外,冲击区破坏将导致速度与能量时程曲线突变。上述成果为网壳结构抗冲击研究奠定了基础,也为其他大型结构抗冲击研究提供借鉴。     

埋置移动荷载作用下饱和成层地基-梁耦合系统动力响应分析

针对地铁列车运行中引起的地表振动问题,研究了埋置移动荷载作用下饱和成层地基-梁耦合系统的动力响应。将地基土体采用Biot饱和多孔介质理论来模拟,将地下轨道结构简化为埋置无限长Euler-Bernoulli梁,埋置移动荷载作用在梁上。并采用传递透射矩阵法(TRM法)考虑地基的成层性。利用Fourier变换及逆变换,结合梁与土体间的力与位移连续条件,得到了地基在时间空间域内的动力响应解答。当饱和成层地基退化为均质黏弹性地基时,所得解与已有解能很好地吻合。最后,通过数值算例分析了梁的刚度﹑埋置深度及荷载移动速度、频率等因素对地表振动的影响。     

任意排列的弹性实心桩屏障对平面SH波的多重散射

为了弥补以往假设单重散射的计算方法中不考虑桩列作为整体屏障从而忽略桩间互相干涉关系的不足,提出了一种新的理论计算方法以求解任意直径、任意排列的弹性桩对入射平面SH波的多重散射。通过桩土界面的位移、应力连续条件可以求得待定的多重散射系数。多重散射中,每根桩的第一重散射即为通常的单重散射;第二重散射可表示为该桩被其余桩的第一重散射波之和所激发的散射波;以此类推至无穷多重散射。将无限重散射叠加即任意直径、任意排列弹性桩对平面SH波的多重散射的精确解。随后数值算例分析讨论了不同散射重数、剪切模量、桩间距以及桩数等对单排弹性桩屏障隔离效果的影响,绘制了屏障后的无量纲位移曲线,并引入透射系数来评价非连续弹性桩屏障的隔振效果,对实际工程中的振动污染治理和屏障隔振设计提出了有意义的结论和建议。     

无限长条板中弹性与粘弹性界面裂纹尖端场

研究无限长条板中粘弹性-弹性界面Griffith裂纹在 Ⅰ 型突加载荷作用下,裂纹尖端动态应力强度因子的时间响应。利用积分变换方法、Fourier和Laplace变换,分别推导出了弹性和粘弹性问题的控制方程组;引入位错密度函数,并结合边界条件,导出了反映裂纹尖端奇异性的Cauchy型奇异积分方程组,运用Chebyshev正交多项式化奇异积分方程组为代数方程组,用配点法进行求解;最后用Laplace积分变换数值反演方法,将拉氏域内的解反演到时间域内,求得动态应力强度因子的时间响应,并对材料参数的影响进行了分析。结果表明,剪切松弛参量对 Ⅰ 型动应力强度因子的影响小于对 Ⅱ 型的影响,而膨胀松弛参量对 Ⅰ 型动应力强度因子的影响大于对 Ⅱ 型的影响。      

Diffraction of a stress wave by a cylindrical cavity in an infinite elastic strip

The scattering of an incident plane shock wave by a cylindrical circular cavity in an infinite elastic strip is considered. In the Laplace transformed domain, boundary conditions at the plane surfaces and those at the circular hole are satisfied with the help of the Fourier transformation and the Schmidt method. A numerical Laplace inversion technique is taken to obtain the stresses in the physical space.     

Transient analysis of stress waves around two rectangular cracks under impact load

The three-dimensional response of two rectangular cracks in an infinite elastic medium to impact load is investigated in this paper. Fourier and Laplace transforms are applied and the problem is reduced to that of solving dual integral equations in the Laplace transform domain. To solve these equations, the crack surface displacement is expanded in a double series of functions which are zero outside of the cracks. The unknown coefficients accompanied in that series are solved with the aid of the Schmidt method. The dynamic stress intensity factors are computed numerically.     

Dynamic stress intensity factors studied by boundary integro-differential equations

The boundary integro-differential equation method is illustrated by two numerical examples concerning the study of the dynamic stress intensity factor around a penny-shaped crack in an infinite elastic body. Harmonic and impact load on the crack surface has been considered. Applying the Laplace transform with respect to time to the governing equations of motion the problem is solved in the transformed domain by the boundary integro-differential equations. The Laplace transformed general transient problem can be used to solve the steady-state problem as a special case where no numerical inversion is involved.     

Transient wave propagation and early short time transient responses of laminated composite cylindrical shells

The generalized ray method (GRM) and the method of reverberation ray matrix (MRRM) have been successfully used to study the transient elastic wave transmission in the beams, planar trusses, space frames and infinite layered media. In this paper, the GRM and MRRM are extended to investigate the early short time transient responses of laminated composite cylindrical shells with finite size under impact load. Using the Laplace transformation, the ray groups transmitting in the laminated cylindrical shells under the shock load are yielded by means of the boundary conditions. The reverberation-ray matrix representing the multi-reflected and scattered waves in the laminated cylindrical shells with finite structural size is deduced. Using FFT algorithm, the transient response corresponding to each ray group can be derived. Through the numerical simulations, it is seen that the early short time transient accelerations of the laminated composite cylindrical shells under impact loads are very large, but the early short time transient shear strain and displacement are very small. Furthermore, the effects of the stacking sequence, thickness of the composite cylindrical shells and different shock loads on the early short time transient responses of the laminated composite cylindrical shells with finite size are also analyzed.     

Effect of Couple-Stresses on the Transient Dynamic Stress Intensity Factors for a Crack in an Infinite Elastic Medium Under an Impact Stress Wave

This study applies linearized couple-stress theory to evaluate the dynamic stresses around a crack in an infinite elastic medium that is subjected to an incoming shock stress wave impinging normal to the crack. The boundary conditions with respect to the crack are reduced to dual integral equations using a Fourier transform in the Laplace domain. To solve these equations, the differences in the displacement and rotation at the crack are expanded by a series of functions that are zero-valued outside the crack in the Laplace domain.     

Transient analysis of multiple parallel cracks under anti-plane dynamic loading

The problem of a homogeneous linear elastic body containing multiple non-collinear cracks under anti-plane dynamic loading is considered in this work. The cracks are simulated by distributions of dislocations and an integral equation relating tractions on the crack planes and the dislocation densities is derived. The integral equation in the Laplace transform domain is solved by the Gaussian–Chebyshev integration quadrature. The dynamic stress intensity factor associated with each crack tip is calculated by a numerical inverse Laplace scheme. Numerical results are given for one crack and two or three parallel cracks under normal incidence of a plane horizontally shear stress wave.     

爆炸荷载作用下深埋圆形隧洞饱和土-衬砌系统的动力响应

考虑隧洞衬砌内壁对爆炸波的反射作用及其负压效应,将衬砌视为弹性介质,研究了深埋圆形隧洞饱和土-弹性衬砌耦合系统在隧洞轴线发生爆炸时的轴对称瞬态动力响应。首先,基于Biot理论和弹性理论,考虑边界条件以及弹性衬砌和饱和土接触面处的连续性条件,利用Laplace变换得到饱和土和弹性衬砌位移、应力和孔隙水压力等在Laplace变换域中的解析表达式。在此基础上,利用Laplace数值逆变换得到其时间域的动力响应,数值分析重点考察了不同隧洞模型和不同爆炸载荷模型对饱和土动力响应的影响,并进行了参数研究。结果表明:爆炸波反射产生的负压效应对饱和土体的动力响应有显著影响。同时,饱和土-壳体衬砌系统、饱和土-弹性衬砌系统和无衬砌饱和土隧洞的响应性态基本一致,但响应周期和幅度依次增大。     

Dynamic stress intensity factors around two rectangular cracks in a half space under impact load

Summary In this paper, the mixed boundary value problem for two rectangular cracks,which are embedded in a half-space, is analyzed under the action of an impact load. The cracks are situated perpendicular to the plane surface of the half space. The wave front of the incident stress impinges on the cracks at right angles to their surfaces. In the Laplace transform domain, the boundary conditions at the plane surface are satisfied using the Fourier transform technique, while those at the surfaces of the cracks are satisfied using the Schmidt method. The stress intensity factors defined in the Laplace transform domain are inverted in the physical space with the aid of a numerical method.     

Sudden twisting of an external circular crack in an infinite medium with a cylindrical inclusion

In this paper the torsional impact response of an external circular crack in an infinite medium bonded to a cylindrical inclusion has been investigated. The infinite medium and cylindrical inclusion are assumed to be of different homogeneous isotropie elastic materials. Laplace and Hankel transforms are used to reduce the problem to the solution of a pair of dual integral equations. These equations are solved by using an integral transform technique and the results are expressed in terms of a Fredhol integral equation of the second kind. By solving Fredholm integral equation of the second kind the numerical results for the dynamic stress-intensity factor are obtained which measure the load transmission on the crack.