循环荷载下成层饱水地基的一维固结

针对成层饱水地基模型，根据Ｔｅｒｚａｇｈｉ固结方程，运用Ｌａｐｌａｃｅ变换及矩阵传递法求解了循环荷载下成层饱水地基一维变形问题，得到了变换域内的通解。通过Ｌａｐｌａｃｅ逆变换计算了成层饱水地基在循环荷载下的一维变形及有效应力。经典的Ｔｅｒｚａｇｈｉ一维固结理论解是本文的一个特例，对于随时间任意变化荷载下成层的固结，只需利用Ｆｏｕｉｅｒ级数将荷载展开，就可用本文的方法求解。此外，本文对常见的循环荷载进行了变换，结合双层的地基算例，对各种循环荷载下地基中有效应力及变形进行了计算分析。结果表明：循环荷载下成层饱水地基固结，其有效应力和变形呈振荡增长，其变化步调与荷载并不一致，且振荡幅度不随时间减小。     

饱和土中爆炸应力波传播特性研究

在饱和土地层中建设了大量的工程项目,由于安全和防卫的需要,这些重要的工程必须考虑爆炸应力波荷载的作用,研究饱和土中爆炸应力波传播特性有着重要的意义.基于应力波传播理论,初步分析了爆炸荷载作用下饱和土介质的变形特性、压缩特性和强度特性;采用有效应力动力分析方法,推导了爆炸应力波在饱和土介质中传播的有效应力运动方程.研究结果可以为饱和土介质中建筑设施的抗爆安全评估提供理论依据.     

非饱和土简化固结理论及其应用

非饱和土固结理论中的边界条件对土体的固结有着重要的影响,它反映了土体在固结过程中边界的透气透水状态。针对实际工程中边界条件的复杂多样性,该文引入一个统一形式边界条件,构建了一个在瞬时均布荷载作用下,由顶面统一边界、底面完全不渗透边界组成的非饱和土一维固结计算模型。基于Fredlund非饱和土一维固结理论,采用Laplace变换等方法得到了Laplace域内超孔隙压力的解,再通过Laplace逆变换得到了时间域内相应解答。运用一个典型算例,设置合理的边界参数,将统一边界条件下的半解析解退化到几种常规边界条件下的解与文献中已有的结果进行比较,验证了所得解的正确性,并对非饱和土一维固结特性进行了简要分析。研究结果表明：统一边界条件下的半解析解相当于一个通解,具有广泛的适用性;通过改变相关边界参数的取值,可以模拟土层边界条件由完全不渗透到完全渗透的变化过程;固结过程中,边界条件对超孔隙气压力和超孔隙水压力的消散影响很大。因此,该文的研究具有一定的学术价值,所得的半解析解对不同边界条件下的实际工程具有参考价值。

     

膨胀土动力性质的研究

本文通过对静、动三轴试验的研究，探讨了重塑土在长期重复荷载下的动的应力－应变关系、动强度特性以及影响它们的主要因素，得到了累积塑性应变和循环次数的函数式以及临界动应力与围压、含水量等的关系，并同英国Ｈｅａｔｈ ＤＬ的结果进行了对比，所得结果可供工程应用参考。     

高速列车荷载作用下高架桥和地基振动分析

提出了一种准解析方法来分析高速列车运行荷载作用下高架桥的动力响应。着重考虑了桥梁和地基的动力相互作用。通过动力子结构方法把研究对象分成两部分，一个是列车荷载作用下三维高架桥的有限元振动模型，另一个是基于傅里叶级数展开的轴对称群桩基础与周围分层地基动力相互作用模型，两者通过桩基承台节点处的连续条件进行结合。用薄层单元构建了应力波的透射边界条件来模拟远场地基对近场有限元区域的影响作用。用阻抗函数来表示群桩基础对上部桥梁结构的支撑作用。通过数值计算考察了软弱地基上新干线高架桥在高速列车荷载作用下的振动特性，分析了列车轮轴荷重，运行速度和群桩基础等因素对高架桥振动的影响；本分析模型和方法在计算上具有很高的效率。同时根据计算结果与现场实测的对比说明了本方法的可靠性。     

圆形洞室在径向非均匀荷载下的瞬态响应

基于弹性介质动力学理论,研究了圆形洞室在瞬态径向非均匀荷载下的动力响应。利用波函数展开法与Laplace变换法,并考虑圆形洞室内表面应力边界非均匀条件,得到单位脉冲荷载下圆形洞室二维空间中应力和位移场在时域内的数值解。并通过算例,分析了径向非均匀瞬态荷载下的波动特性以及剪切模量等因素对应力位移场在径向和环向上分布特征的影响。研究结果表明,随着时间推移环向应力与位移的振动响应均表现出异步性,峰值出现的位置随时间在0-π之间变化,发生极值旋转;无量纲时间t~*2时,径向应力发生明显衰减,而径向位移与环向响应在无量纲时间t~*8时,才出现明显衰减,径向应力的振动周期最小;剪切模量对洞室表面应力位移幅值有显著影响;在非均匀荷载作用下,非均匀处响应幅值明显大于其他位置,径向应力、位移响应大于环向,衰减速度也更快。     

大面积混凝土在变形荷载作用下的应力控制

大面积混凝土构筑物容易在施工水化热，外界热源（大气温差，生产热源等）和砼自身收缩等变形荷载的作用下引起开裂，本文采用理论力学方法，建立三维庆力模型，根据构筑物边界条件，推导大面积混凝土在变形荷载作用下的应力近似解，并结合混凝土工程，分析各种相关参数对构筑物变形荷载应力的影响，为土建工程的裂缝控制提供计算方法。     

上覆非饱和层的饱和地基稳态响应分析

基于多孔弹性饱和介质及多孔弹性非饱和介质的动力控制方程,研究了上覆非饱和层的饱和半空间成层地基在竖向谐振荷载作用下的稳态响应问题。通过引入位移函数,并利用Cauchy-Reimann条件,分别求得了Fourier变换域内饱和土与非饱和土的位移、应力和孔压的一般解;结合不同的边界条件和连续条件,经过Fourier逆变换,得到竖向简谐荷载作用下成层土的稳态响应积分表达式;当将上覆非饱和层饱和半空间分别退化为均质饱和弹性半空间及上覆弹性层饱和半空间时,结果与已有结果均吻合得较好。通过数值算例分析,着重研究了上覆非饱和土层的饱和度、厚度以及地表透气透水条件对动力响应的影响。     

真空预压的有效应力原理浅论

通过分析有效应力原理解释固结过程的前提条件,并结合真空预压机理的再分析,阐述了真空预压过程中固结产生的有效应力原理是加固土体作为"地基",在抽真空所产生的"负压荷载"以及其较大渗流力所产生的"摩擦荷载"等外荷变化的共同作用下使其孔隙压力减小,有效应力增大而使土体固结的。此种解释将能为完善真空预压设计、施工和监测产生较大的影响。     

混凝土预制装配式扩展基础抗拔试验

根据预制装配式基础在上拔荷载作用下的室内足尺试验,监测了试验加载过程中基础构件的位移和应力变化,研究了预制装配式基础在上拔荷载作用下的协同工作性能。试验结果表明：在上拔荷载作用下：1) 预制装配式基础连接法兰盘、底板拼装连接缝附近测点的上拔位移变化规律与基础顶部基本一致,基础各构件之间整体承载性能好。基础荷载-位移曲线分弹性、弹塑性屈服和破坏3个阶段;2) 法兰盘连接锚栓、槽钢连接锚栓和连接槽钢等各构件的测点应力均随荷载增加而增加,且处于弹性阶段;3) 预制装配式基础拼装底板以拼装缝为轴,呈两边向下弯折趋势,基础底板外边缘角点上拔位移量小于基础顶部,且相同部位连接构件在同一级荷载作用下的应力状态和应力大小呈不同的变化规律;4) 基础拼装间隙、拼装过程中螺帽拧紧程度以及基础预制加工误差是预制装配式基础共同工作性能的影响因素,但其整体工作性能好,可按土重法计算基础抗拔极限承载力。     

A note on the deformation of consolidating spherical shell

This paper presents the solutions of the problem of deformation of a consolidating spherical shell of poro-elastic material. Jana and Sanyal have treated the same problem and obtained approximate solutions using Laplace Transform technique. The loading conditions taken by them seem to be unrealistic. By considering boundary conditions which are physically realisable, solutions have been derived in this paper. To obtain the solutions truncated Hankel transform technique has been used and no approximation has been made.     

Dynamic elastic response of an infinite discrete multi-layered cylindrical shell subjected to uniformly distributed pressure pulse

A discrete multi-layered cylindrical shell (DMC) consists of a thin inner cylindrical shell and helically cross-winding flat steel ribbons. The dynamic elastic response of such cylindrical shell under uniformly distributed pressure pulse is studied in this paper. Under the axisymmetric plane strain assumption, the solution of the problem is divided into two parts: a quasi-static part satisfying inhomogeneous stress boundary conditions and a dynamic part complying with homogeneous stress boundary conditions. The quasi-static part is determined by homogeneous linearity method and boundary conditions, and the dynamic part was worked out by means of finite Hankel transform and Laplace transform. The dynamic response of a DMC is compared with the response of monobloc cylindrical shell. Parametric analyses with the consideration of major influential factors, such as thickness ratio of the inner shell to that of the complete shell, material parameters and winding-angle, are discussed.     

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.     

On a problem of the vibration of functionally graded conical shells with mixed boundary conditions

This paper presents a theoretical approach to solve vibration problems of functionally graded (FG) truncated conical shells under mixed boundary conditions. The material properties of FG shell are assumed to vary continuously through the thickness of the conical shell. The fundamental relations, motion and strain compatibility equations of FG truncated conical shells are derived by means of the Airy stress function method. Two cases of mixed boundary conditions are investigated. The basic equations are solved by using Galerkin method and fundamental cyclic frequencies of FG truncated conical shells are obtained. The results are compared and validated with the results available in the literature. The detailed parametric studies are carried out to investigate the influences of radius-to-thickness ratio, lengths-to-radius ratio, material composition and mixed boundary conditions on the fundamental cyclic frequencies of truncated conical shells.     

Application of the weight function method to two-dimensional elastodynamic fracture mechanics

In this paper, the weight function method is used for two-dimensional mixed-mode crack analyses of clastostatic and elastodynamic problems. By the use of the Laplace transformation method and an indirect boundary element method, the dynamic stress intensity factors for a finite sheet containing a central or an edge crack are evaluated. A Green's function method is introduced which depends on the weight function for an impulsive applied load. The Green's function can be used to determine stress intensity factors for arbitrary time dependence of the boundary conditions. The stress intensity factors obtained by the weight function method are compared where possible, with existing solutions.     

Stability analysis of arbitrarily shaped moderately thick viscoelastic plates using Laplace–Carson transformation and a simple hp cloud method

In this paper, the stability analysis of moderately thick time-dependent viscoelastic plates with various shapes is studied using the Laplace–Carson transformation and simple hp cloud meshless method. The shear effect of the plate is described by the first order shear deformation theory. The mechanical properties of the materials are supposed to be linear viscoelastic based on the constant bulk modulus. The displacement field is assumed to be the product of two functions, one being a function of geometrical parameters and the other a known exponential function of time. The simple hp cloud method is used for discretization which is based on Kronecker-delta properties. Thus, the essential boundary conditions can be imposed directly. A numerical investigation is made by employing the inverse of Laplace–Carson transformation. The time history of buckling coefficients of viscoelastic plates of various shapes with different boundary conditions is considered. Moreover, a number of numerical results are presented to study the effect of thickness, aspect ratio, different boundary conditions, and various shapes on the time history of buckling coefficients of the viscoelastic plate.     

Three-dimensional dynamic fracture analysis with the dual reciprocity method in Laplace domain

In this paper, the dual reciprocity boundary element method in the Laplace domain has been developed for the analysis of three-dimensional elastodynamic fracture mechanics mixed-mode problems. The boundary element method is used to calculate the unknowns of transformed boundary displacement and traction and the domain integrals in the elastodynamic equation are transformed into boundary integrals by the use of the dual reciprocity method. The transformed dynamic stress intensity factors are determined by the crack opening displacement (COD) directly in the Laplace domain. By using Durbin's inversion technique, the dynamic stress intensity factors in the time domain are obtained. Several numerical examples are presented to demonstrate the good agreement with existing solutions.     

Analytical expressions for stress and displacement fields in viscoelastic axisymmetric plane problem involving time-dependent boundary regions

An analytical solution is developed in this paper for viscoelastic axisymmetric plane problems under stress or displacement boundary condition involving time-dependent boundary regions using the Laplace transform. The explicit expressions are given for the radial and circumferential stresses under stress boundary condition and the radial displacement under displacement boundary condition. The results indicate that the two in-plane stress components and the displacement under corresponding boundary conditions have no relation with material constants. The general form of solutions for the remaining displacement or stress field is expressed by the inverse Laplace transform concerning two relaxation moduli. As an application to deep excavation of a circular tunnel or finite void growth, explicit solutions for the analysis of a deforming circular hole in both infinite and finite planes are given taking into account the rheological characteristics of the rock mass characterized by a Boltzmann or Maxwell viscoelastic model. Numerical examples are given to illustrate the displacement and stress response. The method proposed in this paper can be used for analysis of earth excavation and finite void growth.     

Numerical operational methods for time-dependent linear problems

A general and systematic discussion on the use of the operational method of Laplace transform for numerically solving complex time-dependent linear problems is presented. Application of Laplace transform with respect to time on the governing differential equations as well as the boundary and initial conditions of the problem reduces it to one independent of time, which is solved in the transform domain by any convenient numerical technique, such as the finite element method, the finite difference method or the boundary integral equation method. Finally, the time domain solution is obtained by a numerical inversion of the transformed solution. Eight existing methods of numerical inversion of the Laplace transform are systematically discussed with respect to their use, range of applicability, accuracy and computational efficiency on the basis of some framework vibration problems. Other applications of the Laplace transform method in conjunction with the finite element method or the boundary integral equation method in the areas of earthquake dynamic response of frameworks, thermaliy induced beam vibrations, forced vibrations of cylindrical shells, dynamic stress concentrations around holes in plates and viscoelastic stress analysis are also briefly described to demonstrate the generality and advantages of the method against other known methods.