桩基非线性静动力学特性研究
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摘要
桩基由于其具有承载能力高、稳定性好、基础沉降及差异变形小、抗震性能好以及能适应各种复杂的地质条件等特点而在各种工程领域中得到广泛应用,同时也使得对桩基力学特性的研究成为工程师和研究人员非常关注的问题。但是由于承台、桩、土的相互作用,桩基的载荷传递与变形过程属于复杂的非线性力学系统,桩基在各种静载荷与动载荷作用下,其载荷传递机理和破坏模式与桩基本身的材料强度、抗弯刚度、桩侧土体的抗力、摩阻力、桩端土体的承载能力以及施加载荷的方式等因素都密切相关,这给桩基的理论分析、数值计算和设计与施工带来很多困难。因此,不论是从理论上还是实际工程需要上,建立桩-土系统非线性静动力学特性分析的数学模型,提供高效的数值计算方法都具有重要的意义。
本论文的研究内容主要包括三个方面:(a)从工程力学和连续介质力学相结合的观点出发,建立了具有初始位移的桩基大变形分析的数学模型,发展了相应的数值计算方法,研究了桩基大变形行为的力学特性;(b)从连续介质力学的框架出发,建立了桩—土耦合系统非线性分析的数学模型,发展了相应的数值计算方法,研究了桩—土耦合系统(包括单桩和群桩)的非线性静动力学特性;(c)从连续介质力学混合物理论出发,建立了两相不可压流体饱和多孔介质空间轴对称问题的控制方程,发展了相应的数值计算方法,研究了桩-饱和土耦合系统的动力学特性。主要研究成果如下:
(1)利用弧坐标建立了具有初始位移的桩基大变形分析的积分型数学模型及其退化模型,其中,地基抗力采用广义粘弹性Winkler模型来描述。这是一组强非线性变下限积分-微分方程组,并提出了求解这类变下限积分-微分方程组的方法。通过引入一组辅助函数,将变下限积分-微分方程组转化为一组非线性微分方程,然后分别在空间域内和时间域内采用微分求积方法和隐式差分格式来进行离散,得到了离散化的非线性代数方程组并进行迭代求解;最后研究了桩基的非线性静动力学特性,得到了桩基变形前后的构形、弯矩和剪力,考察了两类不同初始位移等参数对桩基大变形力学行为的影响。
(2)与积分型数学模型相对应,利用弧坐标建立了具有初始位移的桩基大变形分析的微分型数学模型。这类模型的特点是:(a)避开了求解积分—微分方程的困难;(b)更易于推广应用,包括研究各种间断性条件的影响。作为应用,研究了在弹性或弹塑性土体中具有初始位移的桩基大变形静力学特性,比较了土的弹性和弹塑性性质对桩基力学特性的影响。作为模型的退化,得到了具有初始位移的桩基小变形问题的解析解,并与大变形理论的解进行比较,给出了桩基小变形理论的适用范围。
(3)在微分型数学模型的基础上,进一步建立了具有初始位移和间断性条件的桩基大变形分析的数学模型。同时,在空间区域内,采用微分求积单元法(DQEM)来离散非线性数学模型,并提出了在使用DQEM求解桩基大变形分析中处理多个变量具有间断性条件的有效方法,得到了一组非线性DQEM的离散化方程,它是关于时间域内的一组具有奇异性的非线性微分-代数方程,并在时域内采用向后二阶差分求解了这类非线性微分-代数方程组。作为数值算例,分析了弹性土体中具有一个或多个弹性铰接头或弹性层状土中的桩基,受组合载荷作用时的构形、转角、弯矩和剪力,并考察了弹性铰接头的接头刚度和位置等参数对桩基非线性力学特性的影响,得到了一些有益的结论。
作为模型的进一步推广和应用,给出了其它工程结构领域中的多种算例,包括各种梁的大变形问题,简单框架的大变形问题,组合框架的大变形问题等,并与现有结果进行了比较,吻合良好。
(4)从连续介质力学理论出发,建立了两类桩-土非线性耦合系统的数学模型,其中一类非线性来自于层状土介质的非线性双曲型本构模型,另外一类非线性来自于几何非线性的影响。在考察土的非线性本构模型的基础上,运用无网格迦辽金方法(EFGM)研究了非线性桩-土耦合系统的静动力学特性,包括摩擦桩桩周摩阻力及非线性单桩承载特性等,并进行了参数研究。
同时,从单桩的非线性计算结果和试验出发,提出了群桩的非线性相互作用因子的概念和计算群桩非线性沉降的方法。作为应用分析了由两根单桩、三根单桩、四根单桩和九根单桩等所组成的桩群的非线性力学特性,并与有限元计算结果和已有的现场试验结果进行了比较,吻合良好。
还研究了单桩和群桩在β-型地震激励下的非线性振动特性,得到了群桩中各桩在β-型地震激励下的承载特性。
对于在几何非线性条件下的桩-土耦合系统问题,发展了具有连接条件和间断性条件的空间轴对称问题的微分求积单元法,并用以研究了桩-土非线性耦合系统的力学特性。特别提出了在运用微分求积单元法时处理单元连接条件、边界条件和对称轴处奇异性的有效方法,大大提高了非线性桩—土耦合系统的计算精度和计算效率。
(5)从连续介质力学混合物理论出发,在小变形条件下,建立了两相不可压流体饱和多孔介质空间轴对称问题的控制方程,其中,固相材料采用弹性和微分型粘弹性本构关系。推广微分求积方法于两相不可压流体饱和多孔介质并结合二阶向后差分格式,研究了固相为弹性、粘弹性材料的流体饱和土的动力学特性,并与现有解析结果相一致。推广微分求积方法为微分求积单元法研究了饱和流体多孔介质中桩-土耦合系统的动力学特性,提出了在运用微分求积单元法来求解这类问题时弹性结构和流体饱和土间的连接条件及处理方法,得到了良好的计算结果。
Pile foundation has been widely used in many engineering fields due to that it has many advantages including high carrying capacity, good stability, little settlement and deformation difference, good earthquake resistance and broad applicability to complicated geological conditions. At the same time, the research on mechanical characteristics of piles has also been of interest to engineers and researches. However, duo to that the interactions among the cap, the piles and soil, the load transfers and deformation processes of pile foundations are all complicated, so the pile-soil system belongs to one of nonlinear mechanical systems essentially. The load transmission mechanism and breakage patterns of a pile are related with the material strength and the bending rigidity of the pile itself, the resistance, friction and the bearing capacity of the soil as well as the manners of loadings imposed to the pile, this makes the academic analysis, numerical simulation and design of piles become very difficult. Therefore, whether in theory or in practice, it is significant to establish the rational mathematical models of pile-soil systems and to provide efficient numerical methods.
The main contents of this thesis include the following three parts: (a) Based on the view of the engineering mechanics and continuum mechanics, mathematical models for the analysis of the large deformation of piles with initial displacements are established by using the arc-coordinate, the corresponding numerical methods are developed, the nonlinear mechanical characteristics of piles are analyzed; (b) Based on the theoretical framework of continuum mechanics, mathematical models for the nonlinear analysis of pile-soil coupling systems are established, the corresponding numerical methods are developed, the nonlinear static and dynamic characteristics of pile-soil coupling systems including single pile and pile-groups are analyzed; (c) Based on the porous theory of continuum mechanics, governing equations of space-axisymmetrical problems for incompressible fluid-saturated visco-elastic porous media are presented in the case of small deformations, the corresponding numerical methods are developed, and then the dynamic characteristics of saturated soil and pile are analyzed. The main research results are as follows:
(1) An integral-type mathematical model and its degenerated models of the large deformation analysis of piles with initial displacements are established by using the arc-coordinate, in which a generalized viso-elastic Winkler model is used to describe the resistance of the soil. This is a set of strong nonlinear integral-differential equations, and a method is proposed to solve this kind of integral-differential equations by introducing new functions, and the integral-differential equations are transformed into a set of nonlinear differential equations. And then, the differential quadrature method (DQM) and the implicit difference scheme are applied to discretize the set of nonlinear differential equations in the spatial and temporal domain, respectively. A set of nonlinear discretization algebraic equations are obtained and solved by the iterative method. Finally, the nonlinear static and dynamic characteristics of piles are analyzed. The configuration, the bending moment and shear force of the deformed pile are yielded. The effects of initial displacements and the other parameters on the mechanical behaviors of the deformed pile are considered in detail.
(2) Corresponding to the integral-type mathematical mode above, the differential-type mathematical model of the large deformation analysis of piles with initial displacements is established. The characteristics of this model are: (a) avoid the difficulty to solve the integral-differential equations; (b) easily extend and apply to analyze nonlinear mechanical problems of structures with various discontinuity conditions. As application, the static characteristics of large deformation of piles with the initial displacements are analyzed under the elastic or plastic soil. The effect of the characteristics of elastic and plastic soils on the pile is compared. As a degradation of model, the analytical solutions of the problem under the case of small deformations are presented for two initial displacements given. The range of application of the small deformation theory of piles is given by comparing the solutions with the large deformation theory.
(3) Base on the differential-type model above, the nonlinear mathematical model of large deformation analysis of piles with the discontinuities and the initial displacements is further established. At the same time, the differential quadrature element method (DQEM) is used to discretze the nonlinear mathematical model in the spatial domain, and an effective method is presented to deal with problems of multivariable with discontinuity conditions in large deformation analysis. A set of nonlinear DQEM discretization algebraic equations are obtained, which are a set of nonlinear differential-algebra equations with singularity in the temporal domain. The second order backward differentiation scheme is applied to solve this kind of differential-algebra equations. Finally, numerical examples are given and the responses of deformed piles with one or more elastic joints or pile in layered soil under the combined loadings are yielded, including the configuration, the angle and the bending moment and so on. The effects of parameters, such as the rigidity and the position of joint, on the responses of deformed piles are analyzed. Some useful conclusions are given.
As the further promotions and applications of the model, some numerical examples in other structures are presented, including the large deformation analysis of beams, simple frames and combined frames and so on. The obtained results are compared with those in the existing results; they are good agreement with each other.
(4) Based on the theory of continuum mechanics, two nonlinear pile-soil coupling models are established, in which the non-linearity comes from two aspects: one is the nonlinear constitutive relation of the soil, another is the geometrical nonlinearity. Based on the nonlinear constitutive relation of the soil, the element free Galerkin method (EFGM) is used to analyze the nonlinear static and dynamic mechanical behaviors of pile-soil coupling systems, such as the friction resistance and the load bearing capacities, while the study of parameters is carried through.
At the same time, the nonlinear interaction factor and a method for solving the settlement of pile-groups are developed from the results of the nonlinear single pile and field tests obtained. As application, the mechanical characteristics of pile-groups, such as, 2 piles, 3 piles, 2×2 piles and 3×3 piles and so on, are analyzed. Comparison with the FEM results and field tests point out that they are very close.
On the other hand, the nonlinear vibration characteristics of pile-groups under the type-βearthquake impulse are studied and the load bearing characteristics of the individual pile in pile-groups are obtained.
Under the case of geometrical nonlinearity, the DQEM of space-axisymmetric body for the pile-soil coupling system with continuity conditions and discontinuity conditions is developed. And the nonlinear mechanical characteristics of pile-soil coupling system are further studied by using the DQEM developed in this paper. In especial, an effective method of applying DQEM to deal with the unit connection conditions, the boundary conditions and the singularity conditions is presented, this makes the calculation accuracy and efficiency of nonlinear pile-soil coupling systems are increased and improved.
(5) Based on the porous media theory (PMT), governing equations of space-axisymmetrical problem for incompressible fluid-saturated visco-elastic porous media are presented in the case of small deformations, in which the elastic or the differential-type constitutive relation is applied to describe the characteristics of solid skeleton. The differential quadrature method (DQM) and the second-order backward difference scheme are used to analyze the dynamic characteristics of the fluid-saturated elastic or visco-elastic porous soil. Comparison with the analytical results points out that they are agreement. And then, extend the DQM to DQEM and analyze the dynamic characteristics of pile-soil system in the fluid-saturated porous media. An effective method to deal with the connection conditions between the elastic structure and the fluid-saturated porous soil as well as the pile is developed in applying DQEM and good results are obtained.
本论文的研究内容主要包括三个方面:(a)从工程力学和连续介质力学相结合的观点出发,建立了具有初始位移的桩基大变形分析的数学模型,发展了相应的数值计算方法,研究了桩基大变形行为的力学特性;(b)从连续介质力学的框架出发,建立了桩—土耦合系统非线性分析的数学模型,发展了相应的数值计算方法,研究了桩—土耦合系统(包括单桩和群桩)的非线性静动力学特性;(c)从连续介质力学混合物理论出发,建立了两相不可压流体饱和多孔介质空间轴对称问题的控制方程,发展了相应的数值计算方法,研究了桩-饱和土耦合系统的动力学特性。主要研究成果如下:
(1)利用弧坐标建立了具有初始位移的桩基大变形分析的积分型数学模型及其退化模型,其中,地基抗力采用广义粘弹性Winkler模型来描述。这是一组强非线性变下限积分-微分方程组,并提出了求解这类变下限积分-微分方程组的方法。通过引入一组辅助函数,将变下限积分-微分方程组转化为一组非线性微分方程,然后分别在空间域内和时间域内采用微分求积方法和隐式差分格式来进行离散,得到了离散化的非线性代数方程组并进行迭代求解;最后研究了桩基的非线性静动力学特性,得到了桩基变形前后的构形、弯矩和剪力,考察了两类不同初始位移等参数对桩基大变形力学行为的影响。
(2)与积分型数学模型相对应,利用弧坐标建立了具有初始位移的桩基大变形分析的微分型数学模型。这类模型的特点是:(a)避开了求解积分—微分方程的困难;(b)更易于推广应用,包括研究各种间断性条件的影响。作为应用,研究了在弹性或弹塑性土体中具有初始位移的桩基大变形静力学特性,比较了土的弹性和弹塑性性质对桩基力学特性的影响。作为模型的退化,得到了具有初始位移的桩基小变形问题的解析解,并与大变形理论的解进行比较,给出了桩基小变形理论的适用范围。
(3)在微分型数学模型的基础上,进一步建立了具有初始位移和间断性条件的桩基大变形分析的数学模型。同时,在空间区域内,采用微分求积单元法(DQEM)来离散非线性数学模型,并提出了在使用DQEM求解桩基大变形分析中处理多个变量具有间断性条件的有效方法,得到了一组非线性DQEM的离散化方程,它是关于时间域内的一组具有奇异性的非线性微分-代数方程,并在时域内采用向后二阶差分求解了这类非线性微分-代数方程组。作为数值算例,分析了弹性土体中具有一个或多个弹性铰接头或弹性层状土中的桩基,受组合载荷作用时的构形、转角、弯矩和剪力,并考察了弹性铰接头的接头刚度和位置等参数对桩基非线性力学特性的影响,得到了一些有益的结论。
作为模型的进一步推广和应用,给出了其它工程结构领域中的多种算例,包括各种梁的大变形问题,简单框架的大变形问题,组合框架的大变形问题等,并与现有结果进行了比较,吻合良好。
(4)从连续介质力学理论出发,建立了两类桩-土非线性耦合系统的数学模型,其中一类非线性来自于层状土介质的非线性双曲型本构模型,另外一类非线性来自于几何非线性的影响。在考察土的非线性本构模型的基础上,运用无网格迦辽金方法(EFGM)研究了非线性桩-土耦合系统的静动力学特性,包括摩擦桩桩周摩阻力及非线性单桩承载特性等,并进行了参数研究。
同时,从单桩的非线性计算结果和试验出发,提出了群桩的非线性相互作用因子的概念和计算群桩非线性沉降的方法。作为应用分析了由两根单桩、三根单桩、四根单桩和九根单桩等所组成的桩群的非线性力学特性,并与有限元计算结果和已有的现场试验结果进行了比较,吻合良好。
还研究了单桩和群桩在β-型地震激励下的非线性振动特性,得到了群桩中各桩在β-型地震激励下的承载特性。
对于在几何非线性条件下的桩-土耦合系统问题,发展了具有连接条件和间断性条件的空间轴对称问题的微分求积单元法,并用以研究了桩-土非线性耦合系统的力学特性。特别提出了在运用微分求积单元法时处理单元连接条件、边界条件和对称轴处奇异性的有效方法,大大提高了非线性桩—土耦合系统的计算精度和计算效率。
(5)从连续介质力学混合物理论出发,在小变形条件下,建立了两相不可压流体饱和多孔介质空间轴对称问题的控制方程,其中,固相材料采用弹性和微分型粘弹性本构关系。推广微分求积方法于两相不可压流体饱和多孔介质并结合二阶向后差分格式,研究了固相为弹性、粘弹性材料的流体饱和土的动力学特性,并与现有解析结果相一致。推广微分求积方法为微分求积单元法研究了饱和流体多孔介质中桩-土耦合系统的动力学特性,提出了在运用微分求积单元法来求解这类问题时弹性结构和流体饱和土间的连接条件及处理方法,得到了良好的计算结果。
Pile foundation has been widely used in many engineering fields due to that it has many advantages including high carrying capacity, good stability, little settlement and deformation difference, good earthquake resistance and broad applicability to complicated geological conditions. At the same time, the research on mechanical characteristics of piles has also been of interest to engineers and researches. However, duo to that the interactions among the cap, the piles and soil, the load transfers and deformation processes of pile foundations are all complicated, so the pile-soil system belongs to one of nonlinear mechanical systems essentially. The load transmission mechanism and breakage patterns of a pile are related with the material strength and the bending rigidity of the pile itself, the resistance, friction and the bearing capacity of the soil as well as the manners of loadings imposed to the pile, this makes the academic analysis, numerical simulation and design of piles become very difficult. Therefore, whether in theory or in practice, it is significant to establish the rational mathematical models of pile-soil systems and to provide efficient numerical methods.
The main contents of this thesis include the following three parts: (a) Based on the view of the engineering mechanics and continuum mechanics, mathematical models for the analysis of the large deformation of piles with initial displacements are established by using the arc-coordinate, the corresponding numerical methods are developed, the nonlinear mechanical characteristics of piles are analyzed; (b) Based on the theoretical framework of continuum mechanics, mathematical models for the nonlinear analysis of pile-soil coupling systems are established, the corresponding numerical methods are developed, the nonlinear static and dynamic characteristics of pile-soil coupling systems including single pile and pile-groups are analyzed; (c) Based on the porous theory of continuum mechanics, governing equations of space-axisymmetrical problems for incompressible fluid-saturated visco-elastic porous media are presented in the case of small deformations, the corresponding numerical methods are developed, and then the dynamic characteristics of saturated soil and pile are analyzed. The main research results are as follows:
(1) An integral-type mathematical model and its degenerated models of the large deformation analysis of piles with initial displacements are established by using the arc-coordinate, in which a generalized viso-elastic Winkler model is used to describe the resistance of the soil. This is a set of strong nonlinear integral-differential equations, and a method is proposed to solve this kind of integral-differential equations by introducing new functions, and the integral-differential equations are transformed into a set of nonlinear differential equations. And then, the differential quadrature method (DQM) and the implicit difference scheme are applied to discretize the set of nonlinear differential equations in the spatial and temporal domain, respectively. A set of nonlinear discretization algebraic equations are obtained and solved by the iterative method. Finally, the nonlinear static and dynamic characteristics of piles are analyzed. The configuration, the bending moment and shear force of the deformed pile are yielded. The effects of initial displacements and the other parameters on the mechanical behaviors of the deformed pile are considered in detail.
(2) Corresponding to the integral-type mathematical mode above, the differential-type mathematical model of the large deformation analysis of piles with initial displacements is established. The characteristics of this model are: (a) avoid the difficulty to solve the integral-differential equations; (b) easily extend and apply to analyze nonlinear mechanical problems of structures with various discontinuity conditions. As application, the static characteristics of large deformation of piles with the initial displacements are analyzed under the elastic or plastic soil. The effect of the characteristics of elastic and plastic soils on the pile is compared. As a degradation of model, the analytical solutions of the problem under the case of small deformations are presented for two initial displacements given. The range of application of the small deformation theory of piles is given by comparing the solutions with the large deformation theory.
(3) Base on the differential-type model above, the nonlinear mathematical model of large deformation analysis of piles with the discontinuities and the initial displacements is further established. At the same time, the differential quadrature element method (DQEM) is used to discretze the nonlinear mathematical model in the spatial domain, and an effective method is presented to deal with problems of multivariable with discontinuity conditions in large deformation analysis. A set of nonlinear DQEM discretization algebraic equations are obtained, which are a set of nonlinear differential-algebra equations with singularity in the temporal domain. The second order backward differentiation scheme is applied to solve this kind of differential-algebra equations. Finally, numerical examples are given and the responses of deformed piles with one or more elastic joints or pile in layered soil under the combined loadings are yielded, including the configuration, the angle and the bending moment and so on. The effects of parameters, such as the rigidity and the position of joint, on the responses of deformed piles are analyzed. Some useful conclusions are given.
As the further promotions and applications of the model, some numerical examples in other structures are presented, including the large deformation analysis of beams, simple frames and combined frames and so on. The obtained results are compared with those in the existing results; they are good agreement with each other.
(4) Based on the theory of continuum mechanics, two nonlinear pile-soil coupling models are established, in which the non-linearity comes from two aspects: one is the nonlinear constitutive relation of the soil, another is the geometrical nonlinearity. Based on the nonlinear constitutive relation of the soil, the element free Galerkin method (EFGM) is used to analyze the nonlinear static and dynamic mechanical behaviors of pile-soil coupling systems, such as the friction resistance and the load bearing capacities, while the study of parameters is carried through.
At the same time, the nonlinear interaction factor and a method for solving the settlement of pile-groups are developed from the results of the nonlinear single pile and field tests obtained. As application, the mechanical characteristics of pile-groups, such as, 2 piles, 3 piles, 2×2 piles and 3×3 piles and so on, are analyzed. Comparison with the FEM results and field tests point out that they are very close.
On the other hand, the nonlinear vibration characteristics of pile-groups under the type-βearthquake impulse are studied and the load bearing characteristics of the individual pile in pile-groups are obtained.
Under the case of geometrical nonlinearity, the DQEM of space-axisymmetric body for the pile-soil coupling system with continuity conditions and discontinuity conditions is developed. And the nonlinear mechanical characteristics of pile-soil coupling system are further studied by using the DQEM developed in this paper. In especial, an effective method of applying DQEM to deal with the unit connection conditions, the boundary conditions and the singularity conditions is presented, this makes the calculation accuracy and efficiency of nonlinear pile-soil coupling systems are increased and improved.
(5) Based on the porous media theory (PMT), governing equations of space-axisymmetrical problem for incompressible fluid-saturated visco-elastic porous media are presented in the case of small deformations, in which the elastic or the differential-type constitutive relation is applied to describe the characteristics of solid skeleton. The differential quadrature method (DQM) and the second-order backward difference scheme are used to analyze the dynamic characteristics of the fluid-saturated elastic or visco-elastic porous soil. Comparison with the analytical results points out that they are agreement. And then, extend the DQM to DQEM and analyze the dynamic characteristics of pile-soil system in the fluid-saturated porous media. An effective method to deal with the connection conditions between the elastic structure and the fluid-saturated porous soil as well as the pile is developed in applying DQEM and good results are obtained.
引文
[1]高大钊,赵春风,徐斌,桩基础的设计方法与施工技术[M],机械工业出版社,1999.
[2]林天健,熊厚金,王利群,桩基础设计指南[M],中国建筑工业出版社,1999.
[3]Novak,M.,Dynamic stiffness and damping of pile[J],Canad.Geotech.J.1974,11:574-598.
[4]Novak,M.,Soil-pile interaction in horizontal vibration[J],Earthquake Engineering and Structure Dynamics,1977,5:263-281.
[5]Novak,M.,Piles under dynamic loads[C],Proceedings:Second International Conference on Recent Advances in Geotechnical Earthquake Engineering and Sore Dynamics,1991:2433-2456.
[6]Anestis,S.,Impedances of soil layer with disturbed boundary zone[J],Journal of Geotechnical Engineering,1985,112(3):363-369.
[7]Anestis,S.,Vertical and torsional of foundations in inhomogeneous media[J],Journal of Geotechnical Engineering,1987,114(9):1002-1021.
[8]Poulos,H.G.,Behavior of laterally loaded piles:I-single piles[J],Soil Mech.and Found.Div.,ASCE,1971,97(5):711-731.
[9]Wong S.C.,Poulos,H.G.,Approximate pile-to-pile interaction factor between two dissimilar piles[J],Computers and Geothechnics,2005,32:613-618.
[10]Poulos,H.G.,and Davis,E.H.,Pile foundation analysis and design[M].Gohn Wiley and Sons,New York,N.Y,1980.
[11]Chow,Y.K.,Axial and lateral response of pile groups embedded in nonhomogeneous soils[J].Int.G.Nuner.Anal.Methods Geomech.,1987,11(3):621-638.
[12]宫全美,基于Mindlin位移解的群桩沉降计算[J],地下空间,2001,21(3):167-177.
[13]Roesset,J.M.,Dynamic stiffness of pile groups[M],Analysis and Design of Pile Foundations.J.R.Meyer,ed.,ASCE,New York,N.Y.,263-286,1984.
[14]Xu,K.J.,Poulos,H.G.,General elastic analysis of piles and pile groups[J],Int J Numer Anal Method Geomech,2000,24:1109-1138.
[15]Koo,K.K.,Chau,K.T.,Yang X.,Lam,S.S.and Wong,Y.L.,Soil-pile-structure interactions under SH waves[J],Earthquake Engineering and Structural Dynamics[J],2003,32(3):395-415.
[16]Chau,K.T.,Yang X.,Nonlinear Interaction of Soil-Pile in Horizontal Vibration[J],J.Eng.Mech.2005,131(8):847-858.
[17]程昌钧,胡育佳,受轴力作用的桩基在水平振动时的抗力,上海大学学报(自然科学版)[J],2005,11(3):275-281.
[18]Hu Yu-jia,Cheng Chang-jun,Characteristics of piles under horizontal vibration,Applied Mathematics and Mechanics[J],2005,26(6):700-708.
[19]Hu Yu-jia,Zhu Yuan-yuan,Cheng Chang-jun,EFGM for Nonlinear Mechanical Behaviors of Single Pile and Pile Group[C],ICNM-5,2008,429-437.
[20]Hikmet,H.H.,Free vibration of semi-rigid connected and partially embedded piles with the effects of the bending moment,axial and shear force[J],Engineering Structures,2006,28:1911-1918.
[21]Apirathvorakij V.,Quasi-static bending of a cylindrical elastic bar partially embedded in a saturated elastic half-space[J],Int.J.Soil and Stru,1980,16(7):625-644.
[22]Zeng,X.,Rajapakse,R.K.N.D.,Dynamic axial load transfer from elastic bar to poroelastic medium[J],J.Eng.Mech.ASCE,1999,125(9):1048-1055.
[23]王建华,陆建飞,沈为平,层状地基中考虑固结和流变的垂直桩的理论分析[J],水利学报,2001,4:57-61.
[24]李强,王奎华,谢康和,饱和土桩纵向振动引起土层复阻抗分析研究[J],土工程学报,2004,26(5):679-683.
[25]Jin,B.,Zhou,D.Zhong,Z.,Lateral dynamic compliance of pile embedded in poroelastic half space[J],Soil.Dyn.Earthquake Eng.,2001,21:519-525.
[26]陆建飞,王建华,考虑固结和流变的层状地基中的水平单桩的理论分析[J],岩土力学与工程学报,2001,20(3):386-390.
[27]陆建飞,频率域半空间饱和土中水平受荷桩的动力分析[J],岩土力学与工程学报,2002,21(4):577-581.
[28]杨军,宋二祥,陈肇元,桩在饱和土中水平振动的辐射阻尼简化算法[J],岩土力学,2002,23(2):179-183.
[29]Wang,J.H.,Zhou,X.L.,Dynamic response of pile groups embedded in a poroelastic medium[J],Soil.Dyn.Earthquake Eng.,2003,23:235-242.
[30]Maeso,O.,Aznarez,J.J.,Garcia,F.,Dynamic impedances of piles and groups of piles in saturated soils[J],Computers and Structures,2005,83:769-782.
[31]Nogami,T.,Novak,M.Time domain axial response of dynamically loaded single piles [J].J.Geotech.Engg.Div.ASCE,1987,112(11):1241-1252.
[32]El Naggar,M.H.,Novak,M.Nonlinear analysis for dynamic lateral pile response[J].Soil Dynamics and Earthquake Engineering,1996,15(4):233-244.
[33]胡安峰,谢康和,水平载荷下单桩动力反应分析[J],浙江大学学报,2003,37(4):420-425.
[34]黄茂松,吴志明,任青,层状地基中群桩的水平振动特性[J],岩土工程学报,2007,29(1):32-38.
[35]胡春林,程昌钧,非线性粘弹性桩基纵向混沌运动[J],岩土力学,2005,26(10):1541-1544.
[36]胡春林,程昌钧,陈中学,桩基非线性轴向振动的多时间尺度分析[J].振动与冲击,2007,26(5):54-59.
[37]任九生,程昌钧,非线性粘弹性桩耦合运动中的混沌分析[J],振动与冲击,2006,25(5):21-23.
[38]任九生,程昌钧,纵向振动粘弹性桩的分叉和混沌运动[J],振动与冲击,2005,24(5):11-13.
[39]Cai S.,Wang S.,A simple estimation of the force exerted by internal solitons on cylindrical piles[J],Ocean Engineering,2006,33:974-980.
[40]Matlock H.,Correlation for design of lateral loaded piles in soft clay[C],Proc.2~(nd)Offshore Technology Conference,Vol.1,Houston,TX.OX.C 1204,1970:577-594.
[41]Reese,L.C.,Cox,W.R.,and Koop,F.D.Field testing and analysis of laterally loaded piles in stiff clay[C],Proc.7th Offshore Tech.Conf.,ASCE et al.,1975:671-690.
[42]O'Neill,M.W.,Hawkins,R.A.and Mahar,L.J.Load transfer mechanisms in piles and pile groups[J],J.Geotech.Engrg.Div.,ASCE,1982,108(12):1605-1623.
[43]O'Neill,M.W.,Ghazzaly,O.I.,and Ha,H.B.Analysis of three-dimensional pile groups with non-linear soil response and pile-soil-pile interaction[C],Proc.9th Offshore Tech.Conf.,ASCE et al.,1977:245-256.
[44]Bogard,D.and Matlock,H.Procedures for analysis of laterally loaded pile groups in soft clay[M],Geotechnical practice in offshore engineering,S.G.Wright,ed.,ASCE,New York,N.Y.,1983:499-535.
[45]Brown,D.A.,Morrison,C.and Reese,L.C.Lateral load behavior of pile group in sand[J],J.Geotech.Engig.,ASCE,1988,114(11):1261-1276.
[46]Kraft Jr.L.M.,Ray,R.P.and Kagawa,T.Theoretical t-z curves[J],J.Geotech.Engrg.Div.,ASCE,1981,107(11):1543-1562.
[47]Gazioglou,S.M.and O'Neill,M.W.Evaluation of p-y relationships in cohesive soils.Analysis and design of pile foundations[M],J.R.Meyer,ed.,ASCE,New York,N.Y.,1984:192-213.
[48]Nogami,T.and Chen,H.L.Simplified approach for axial pile group response analysis[J],J.Geotech.Engrg.,ASCE,1984,110(9):1239-1255.
[49]Nogami,T.and Paulson,S.K.Transfer matrix approach for nonlinear pile group response analysis[J],Int.J.Numer.Anal.Methods Geomech.,1985,9(4):299-316.
[50]Focht J A,and Koch K J.,Rational analysis of lateral performance of offshore pile groups[C],Proceeding of the 5th offshore technology conference 1973,Dallas,Texas,1997;701-708.
[51]田平,王惠初,粘土中横向周期性荷载桩的P-Y曲线统一法[J],河海大学学报,1993,(1):9-14.
[52]王惠初,武冬青,田平,粘土中横向静载桩P-Y曲线的一种新的统一法[J],河海大学学报,1991,(1):9-17.
[53]章连洋,陈竹昌,粘性土中P-Y曲线的计算新方法[J],港口工程,1991,(2):29-35.
[54]程泽坤,关于P—Y曲线法分析横向力作用下高桩结构物的讨论[J],港工技术,1997,(3):53-57.
[55]程泽坤,基于P-Y曲线法考虑桩土相互作用的高桩结构物分析[J],海洋工程,1998,(2):5-9.
[56]胡立万,郝军,陈鹭缨.用P-Y曲线法计算板桩结构[J],港工技术,2001,(1):24-26.
[57]杨国平,张志明.对大变位条件下横向受力桩P-Y曲线的研究[J],水运工程,2002,(7):40-45.
[58]Ellison,R.D.,D'Appoionia,E.and Thiers,G.R.Load-deformation mechanism for bored piles[J],J.Soil Mech.And Found.Div.,ASCE,1971,97(4):661-679.
[59]Christiano,P.,Rergstad,G.,and Ellison,R.,Behavior of driven piles partel:Numerical analysis,part Ⅱ:Deformation and failure mechanisms[C],Proc.2nd Iranian Conf.On Civ.Engrg.,Iran society of Civil Engineers,1976,3:1778-1834.
[60]Randolph,M.F.,The response of flexible piles to lateral loading[J],Geothecnique,Loadon,England,1981,31(2):247-259.
[61]Faruque,M.O.and Desai,C.S,3-D material and geometric nonlinear analysis of piles[C],Proc.Second Int.Conf.on Numerical Methods in Offshore Piling.Univ.of Texas.1982:553-575.
[62]Muqtadir,A.and Ddsai,C.S.,Three-dimensional analysis of a pile-group foundation[J],Int.J.Numer.Anal.Methods Geomech.,1986,10(1):41-58.
[63]Kuhlemeyer,R.L.,Vertical vibration of pile[J],ASCE J.Geotech.Engry.Div.,1979,105(GT2):273-288.
[64]Aristonous M.,Three-dimensional nonlinear study of pile[J],Journal of the Geotechnical Engineering,1991,117:429-447.
[65]傅旭东,称晓平,单桩承载力可靠度的非线性摄动随机有限元分析[J],岩土力学与工程学报,2003,22(1):103-109。
[66]Butterfield,R.and Banerjee,P.K.,The elastic analysis of compressible piles and pile groups[J].Geotechnique,1971,21:43-60.
[67]Semih K.,Time domain dynamic analysis of piles under impact loading[J],Soil Dynamics and Earthquake Engineering,2002,22:97-104.
[68]周常春,邓安福,水平载荷下群桩前后土抗力分布的数值计算[J],地下结构,2003,23(1):17-21.
[69]赵明华,吾鸣,轴、横向载荷下桥梁基桩的受力分析及试验研究[J],中国公路学报, 2002,15(1):50-54.
[70]Mizuno,H.,Pile damage during earthquakes in Japan(1923-1983)[J],Dynamic Response of Pile Foundations.ASCE,Geotech.Special Publ.11(Edited by T.Nogami),1987,53-78.
[71]Miura F.,Lessons from Damage to Pile Foundation Caused by Past Earthquake in Japan and the Necessity of Nonlinear Analyses of Pile foundation[C],Proceedings of the 4~(Th)International Conference on Nonlinear Mechanics,Shanghai:Shanghai University Press,2002,109-115.
[72]Miyasaka,T.,Study on the effectiveness of the high ductility aseismatic joint spliced pile subjected to liquefaction-induced large ground displacement[D],Doctor Thesis of Yamaguchi-University,1997(in Japanese).
[73]Izumi,H.,Dynamic behavior of high ductility aseismatic joint spliced pile foundations during strong earthquake motions[D],Doctor Thesis of Yamaguchi University,1999(in Japanese).
[74]三浦房纪,朱媛媛,在弹性基础上具有初始水平位移的桩基的临界载荷[M],日本土木学会论文集(日文),682/1-56,2001,143-153.(Miura F.and Zhu Y.,Critical Load of a Single Pile with Initial Horizontal Displacement iIl Elastic Ground,J.JSCE,No.682/I-56,2001,143-153)
[75]三浦房纪,朱媛媛,桩头的边界条件对受侧向基础位移桩临界载荷的影响[M],日本土木学会论文集(日文),682/1-56,2001,155-164.(Miura Eand Zhu Y,The Effect of Boundary Condition at Pile Head of a Pile on the Critical Load subjected to Lateral Ground Displacement,J.JSCE,No.682/I-56,2001,155-164)
[76]朱媛媛,三浦房纪,朱正佑,弹性地基上HDAJ接头桩的非线性稳定性分析[J],力学季刊,26(2),2005,216-223.
[77]朱媛媛,胡育佳,弹性基础上具有初始缺陷的桩基的大变形分析[J],力学季刊,2007,28(2):310-319.
[78]Yuan-yuan Zhu,Yu-jia Hu,Large Deformation Analysis of Piles with Elastic Joints[C],ICNM-5,2008:588-595.
[79]朱媛媛,胡育佳,求解具有弹性铰接头的桩基大变形动力学问题的微分—代数方法[C],上海市力学学会2007年年会论文集,2007:180-187.
[80]张雄,刘岩,无网格法[M],北京:清华大学出版社,2004.
[81]Belytschko T.,Krongauz Y.,Organ D et al.,Meshless methods:An overview and recent developments[J],Comput.Methods Appl.Mech.Engrg.,1996,139:3-47.
[82]Li S,Liu W K.Meshfree and partical methods and their applications[J],Appl.Mech.Rev.,2002,55(1):1-34.
[83]张雄,宋康祖,陆明万,无网格法的研究进展及其应用[J],计算力学学报,2003(20):731-742.
[84]Liszka T.,Orkisz J.,Finite difference method for arbitrary irregular meshes in nonlinear problems of applied mechanics[M],In:Ⅳ SmiRT,San Francisco,1997.
[85]Luo Y,Haussler-Combe U.,A generalized finite-difference method based on minimizing globle residual[J],Comput.Methods Appl.Mech.Engrg.,2002,191:1421-1438.
[86]Lucy L B.,A numerical approach to the testing of the fission hypothesis[J],The Astron.J.,1997,8(12):1013-1024.
[87]Gingold R.A.,Monaghan J.J.,Smoothed particle hydrodynamics:theory and applications to non-spherical stars[J],Mon.Not.Roy.Astrou.Soc.,1997,18:375-389.
[88]Johnson G.R.,Beissel S.R.,Normalized smoothing functions for SPH impact computations[J],Int.J.Num.Meth.Engrg.,1996,39:2725-2741.
[89]Lancaster P.,Salkauskas K.,Surfaces generated by moving least squares methods[J],Math,Comput.,1981,37(155):141-158.
[90]Nayroles B.,Touzot G.,Villon P.,Generalizing the finite element method:diffuse approximation and diffuse elements[J],Comput.Mech.,1992,10:307-318.
[91]Belytschko T.,Liu Y.Y.,Gu L.,Element free Galerkin methods[J],Int.J.Num.Mech.Engrg.,1994,37:229-256.
[92]Chung H.J.,Belytschko T.,An error estimate in the EFG method[J],Comput.Mech.,1998,21:91-100.
[93]Dolbow J.,Belytschko T.,Numerical integration of the Galerkin weak form in mesh-free methods[J],Comput.Mech.,1999,23:219-230.
[94]Belytschko T.,Krongauz Y.,Organ D et al.Smoothing and accelerated computations in the element free Galerkin method[J],J.Comput.Appl.Math,1996,74:111-126.
[95]Krongauz Y.,Belytschko T.,EFG approximation with discontinuous derivatives[J],Int.J. Num.Meth.Engrg.,1998,41 1215-1233.
[96]周维垣,寇晓东,无单元法及其工程应用[J],力学学报,1998,30(2):193-202.
[97]寇晓东,周维垣,应用无单元法近似计算拱坝开裂[J],水利学报,2000,28-35.
[98]庞作会,葛修润,郑宏等,一种新的数值方法——无网格伽辽金法(EFGM)[J],计算力学学报,1999,16(3):320-329.
[99]朱媛嫒,胡育佳,程昌钧,无网格方法在平面粘弹性力学问题中的应用[J],力学季刊,2006,27(3):404-412.
[100]Liu W K.,Jun S,Zhang Y F.,Reproducing Kernel Partical methods[J],Int.J.Numer.Meth.Fluids.,1995,20:1081-1106.
[101]Ohs R R.,Aluru N R.,Meshless analysis of piezoelectric devices[J],Comput.Mech.,2001,27:23-36.
[102]Duarte C A.,Oden J T.,An h-p adaptive method using clouds[J],Comput.Methods Appl.Mech.Engrg.,1996,139:237-262.
[103]Onate E.,Idelsohn S.,Zienkiewicz O C.et al.,A finite point method in computational mechanics:Applications to convective transport and fluid flow[J],Int.J.Num.Meth.Engrg.,1996,39:3839-3866.
[104]Atluri S N.,Zhu T.,A new meshless local Petrov-Galerkin(MLPG) approach in computational mechanics[J],Comput.Mech.,1998,22:117-127.
[105]Wendland H.,Meshless Galerkin method using radial basis functions.Math[J],Comput.,1999,68(228):1521-1531.
[106]尹华杰.无网格法及其在电磁场计算中的应用展望[J],电机与控制学报,2003,(7):107-111,132.
[107]Singh I.V.,A numerical solution of composite heat transfer problems using meshless method[J],International Journal of Heat and Mass Transfer,2004,47:2123-2138.
[108]Hua Lia,Wang QX,Lam KY,A variation of local point interpolation method(v LPIM)for analysis of microelectromechanical system(MEMS) device[J],Engineering Analysis with Boundary Elements.2004,28:1261-1270.
[109]Fleming M.,Rahman S.,An efficient element free galerkin methods for crack tip fields[J],Int.J.Num.Meth.Engng.,1997,40:1483-1504.
[110]Liu W.K.,Chen Y.,Aziz UR et al.,Generalized multiple scale reproducing kernel particle methods[J],Comput.Methods Appl.Mech.Engrg.,1996,139:91-157.
[111]周小平,周瑞忠,对无单元法插值函数的几点研究[J],福州大学学报(自然科学版).2000,28:52-56.
[112]Bellmam,R.E.,Kashef,B.G.,Casti,J.,Differential quadrature:A technique for the rapid solution of nonlinear partial differential equations[J],J.Comput.Phys.1972,10:40-52.
[113]Bert,C.W.,Jang,S.K.,Striz,A.J.,New methods for analyzing vibtation of structural components[C].Proc.AIAA Dynamics Specialist Conference,Monterey,CA,USA,Part2,1987:936-943.
[114]Bert,C.W.,Malik M.,Differential quadrature method in computational mechanics:a review[J],Applied Mechanics Reviews,1996,49:1-28.
[115]Civan,F.,Slepcevich,C.M.,Differential quadature for multidimensional problem[J],J.Math.Appl.,1984,101:423-443.
[116]Quan,J.R.,Chang,C.T.,New insights in solving distributed system equations by the quadrature methods-Ⅰ[J],Comput.Chem.Engrg.,1989,13:779-788.
[117]Quan,J.R.,Chang,C.T.,New insights in solving distributed system equations by the quadrature methods-Ⅱ[J],Comput.Chem.Engrg.,1989,13:1017-1024.
[118]Shu,C.,Richards,B.E.,parallel simulation of incompressible viscous flows by generalized differential quadrature[J],Computing Systems in Engineering,1992,(3):271-281.
[119]Striz,A.G.,Wang,X.,Bert,C.W.,Harmonic Differential Method and Applications to Structure Components[J],Acta Mechanica,1995,111:85-94.
[120]Chang,C.T.,Tasi,C.S.,Lin,T.T.,Modified differential quadrature and their application to structure components[J],Acta Mechanica,1995,111:85-94.
[121]Wang,X.,Bert,C.W.,A new approach in applying differential quadrature to static and free vibrational analyses of beams and plates[J],J.Sound & Vibration,1993,162:566-572.
[122]王鑫伟,调和微分求积法权系数矩阵的一种显式计算式[J],南京航空航天大学学报,1995;027(004):496-501.
[123]Hong z.z.,Triangular differential quadrature[J],Communications for Numerical Methods in Engineering,2000,16(4):401-408.
[124]聂国隽,仲政,用微分求积法求解梁的弹塑性问题[J],工程力学,2005,22(1):59-62.
[125]吕朝锋,陈伟球,边祖光,状态空间微分求积分法分析Winkler地基梁的自由振动,浙江大学学报(工学版)[J],2004,38(11):1451-1454.
[126]杨杰,彭建设,组合载荷作用下层合板非线性弯曲的半解析摄动DQ法[J],计算力学学报,2002,19(3):373-375.
[127]Li Jing-Jing,Cheng,Chang-Jun,Differential quadrature method for bending of orthotropic plates with finite deformation and transverse shear effect[J],Appl.Math and Mech.,2004,25(8):878-886.
[128]Li J.J.,Cheng C.J.,Differential quadrature method for nonlinear vibration of orthotropic plates with finite deformation and transverse shear effect[J],Journal of Sound and Vibration,2005,281:295-305.
[129]李晶晶,程昌钧,盛冬发,考虑高阶横向剪切正交各向异性板振动的微分求积分析方法[J],振动与冲击,2004;22(4):8-11.
[130]Sun Jian-An,Zhu Zheng-You,Application of differential quadrature method to solve entry flow of viscoelastic second-order fluid[J],Int.J.of Numer.Mech.Fluids,1999,30(8):1109-1117.
[131]Sun Jian-an,Zhu Zheng-you,Upwind local differential quadrature method for solving incompressible viscous flow[J],Compute.Methods in Appl.Mech.Engng,2000,188:495-504.
[132]Striz,A.G..,Chen,W.L.,Bert,C.W.,Free vibration of plates by the high accuracy differential quadrature element method[J],Journal of Sound and Vibration,1997,202:689-702.
[133]Han,J.B.,Liew,K.M.,Static analysis of Mindlin plates:the differential quadrature element method(DQEM),Comput.Methods Appl.Mech.Engrg,1999,177:51-75.
[134]王永亮,微分求积法和微分求积单元法——原理与应用[D],南京航空航天大学.2001.
[135]Liu,F.L.,Liew,K.M.,Static analysis of Reissner-Mindlin plates by the differential quadrature element method[J],J.Applied Mechanics,1998,65:705-710.
[136]Liu,F.L.,Liew,K.M.,Analysis of vibrating thick rectangular plates with mixed boundary constraints using differential quadrature element method[J].Journal of Sound and Vibration.1999,25(5):915-934.
[137]Liu F.L.and Liew K.M.,Vibration analysis of discontinuous Mindlin plates by differential quadrature element method[J],Vibration and Acoustics,1999,121:204-208.
[138]Yu-jia Hu,Yuan-yuan Zhu,Chang-jun Cheng,Differential-algebraic approach to large deformation analysis of frame structures subjected to dynamic loads[J],Applied Mathematics and Mechanics.2007,29(4):441-452.
[139]Yu-jia Hu,Yuan-yuan Zhu,Chang-jun Cheng,DQEM for Large Deformation Analysis of Structures with Discontinuity Conditions and Initial Displacements[J],Engineering Structures,2008,30:1473-1487.
[140]Wang X.W.,Wang Y.L.and Chen R.B.,Static and free vibrational analysis of rectangular plates by the differential quadrature element method[J],Commun.Numer.Meth.Engrg.,1998,14:1133-1141.
[141]Chen C N.,The two -dimensional frames model of the differential quadrature element method[J],Computers & Structures,1997,62(3):555-571.
[142]聂国隽,仲政,变截面门式刚架结构分析的微分求积单元法[J],力学季刊,2005,26(2):198-203.
[143]Bisshopp K.E.and Drucker D.C.,Large deflections of a cantilever beam[J],Quart.Appl.Math.,1945,3:272-275.
[144]Jenkins J.A.,Large deflection of diamond shaped frames[J],Int.Soils Struct.,1966,2:591-603.
[145]Bathe K.J,Large displacement analysis of three dimensional beam Structures[J],Internal J Number Methods Engrg,1979,4:961-986.
[146]Arregui I.,Destuynder P.,Salaun M.,An Eulerian approachfor large displacements of thin shells including geometrical non-linearities[J],Comput Methods Appl Mech Engrg,1997,140:361-381.
[147]Oden J.T.,Finite element of nonlinear continua[M],McGraw-Hill,1972.
[148]Bathe K.J.,Finite element procedures in engineering analysis[M],Prentice-Hall,1982.
[149]陈至达,杆、板、壳大变形理论[M],科学出版社,1994.
[150]陈至达,有理力学,中国矿业大学出版社[M],1986.
[151]李尧臣,圆截面杆在曲线井中的屈曲问题[J],力学季刊,2002,32(2):265-271.
[152]Liu Y.Z.,Stability and bifurcation of helical equilibrium of a thin elastic rod[J],Acta Mechanica,2004,167:29-39.
[153]刘延柱,弹性杆基因问题的力学问题[J],力学与实践,2003,25(1):1-5.
[154]Angelides and Roesset,Nonlinear lateral dynamic stiffness of pile[J],Journal of the Geotechnical Engineering Division,1981,107(GT110):1443-1460.
[155]程昌钧,朱媛媛,弹性力学(修订版)[M],上海,上海大学出版社,2005.
[156]Randolph M F.,Analysis of deformation of vertically loaded piles[C],Proc,J,GT DIV,ASCE,1978,104(12):1465-1488.
[157]Cooke R W,Price G,Tarr K,Jacked piles in London clay:a study of load transfer and settlement under working conditions,Geotechnique,1979,29(2):113-147.
[158]Shen W.Y.,Chow Y.K.and Yong K.Y.,Variational solution for loaded pile groups in an elastic half-space,Geotechnique,1999,49(2):119-213.
[159]谢贻权,何福保,弹性和塑性力学的有限单元法[J],机械工业出版社,1983.
[160]Makris N.,Rigidity-plasticity-viscosity:can electrorheological dampers protect base-isolated structures from near-source ground motions?[J],Earthquake Engineering and Structural Dynamics 1997,26:571-591.
[161]Randolph M F.,Wroth C P,Analysis of deformation of vertically deformation of pile groups[J],Geotechnique,1979,29(4):423-439.
[162]Lee C Y.,Settlement of Pile Group-Practical Approach[J],J.Geotech Engng Div.ASCE,1993,119(9):149-1461.
[163]Reese L.C.,Cox W.R.and Koop F.D.,Field testing and analysis of laterally loaded piles in stiffclay[C],Proc.7~(th) Offshore Tech.C.onf.,ASCE et al.,1975,671-690.
[164]Briaud,J L,Tucker,L M.& Ng,E,Axially loaded 5 pile group and single pile in sand[C],Proc.of 12th Int.Conf.Soil Mech.Fdn Engng,Rio de Janeiro,1989,2,1121-1124.
[165]Wolf,J P.,Impedance Function of a group of vertical piles[M],Erzmetll,1978,2:1024-1041
[166]Gazetas G.and Makris N.,Dynamic pile-soil-pile interaction,Part Ⅰ:analysis of axial vibration[J],Earthquake Engineering and Structural Dynamics,1991,20:115-132.
[167]Cook,R.W.,Price,G.,Jacked piles in London clay:interaction and group behavior under working conditions[J],Geotechnique,1980,30(2):449-471.
[168]Berezantzev,V.G.,Khristoforov,Load bearing capacity and deformation of piled foundation[C],Proc.5~(th) Int.Conf.Soil Mech.Fdn Engng,Paris,1961,2,11-15.
[169]Boit M A.,General theory of three-dimensional consolidation[J],J Appl Phys,1941,12:155-164.
[170]Boit M A.,Theory of propagation of elastic waves in a fluid-saturated porous media,I.Low frequency range[J],J Acoust Soc Am,1956,28(2):168-178.
[171]Bowen R M.,Compressible porous media models by use of the theory of mixtures[J],Int J Engng Sci,1982,20:693-735
[172]de Boer R.,Theory of porous media:Highlights in the historical development and current state[M],Springer-Verlag,2000,Berlin,Heidelberg.
[173]Schrefler B A.,Mechanics and thermodynamics of saturated/unsaturated porous material and quantitative solution[J],Appl Mech Rev,2002,5:351-380.
[174]Schrefler B A.,Zhang X,Simoni L.,A coupled model for water flow,air flow and heat flow in deformable porous media[J],Int,J Num meth Fluid Flow,1995,5:531-547.
[175]Edelman I.,Wilmanski K.,Asymptotic analysis of surface waves at vacuum/porous medium and liquid/porous medium interfaces[J],Continuum Mech Thermody,2002,14:25-44.
[176]de Boer R.,Theoretical poroelasticity-a new approach[J],Chaos Solitons & Fractals,2005,25:861-878.
[177]de Boer R.,Ehlers W.,Liu Z.,One-dimensional transient wave propagation in fluid-saturated incompressible porous media[J],Archive Appl Mech,1993,63:59-72.
[178]Breuer S.,Reflection and refraction of longitudinal waves in a fluid-saturated porous solid,in Problems of Environmental and Damage mechanics[C],IPPT PAN.Warszawa,Proceedings of SoilMec'96 Conference,Mierki,September 9-14,1996,Poland,27-37
[179]Breuer S.,Quasi-static and dynamic behaviors of saturated porous media with incompressible constituents[J],Transport in Porous Media,1999,34:285-303.
[180]Wilmansld,K.,A thermodynamic model of compressible porous materials with the balance equation of porosity[J],Transport in Porous Media,1998,32:21-47.
[181]Diebels S.,Ehlers W.,Dynamical analysis of a fully saturated porous media accounting for geometrical and material non-linearities[J],Int J Numer Meth Engng,1996,39:81-97.
[182]Aboustit B L.,Advani S H.,Lee J K.,Variational principles and finite element simulations for thermo-elastic consolidation[J],Int J Numer Meth Engng,1985,9:49-69.
[183]杨骁,程昌钧,流体饱和多孔介质动力学Gurtin型变分原理和有限元模拟[J],固体力学学报,2003,24(3):267-276.
[184]Yang Xiao,He Lu-wu,Variational principles of fluid-saturated incompressible porous media[J],兰州大学学报(自然科学版),2003,39(6):24-39.
[185]Yao,S.,et al.,Interactive behavior of soil-pile-structure system in transient state to liquefaction by means of large shake table tests[J],Soil.Dyn.Earthquake Eng.,2004,24:297-409.
[186]克里斯坦森R M,老亮译,粘弹性力学引论[M],北京:科学出版社,1990.
[2]林天健,熊厚金,王利群,桩基础设计指南[M],中国建筑工业出版社,1999.
[3]Novak,M.,Dynamic stiffness and damping of pile[J],Canad.Geotech.J.1974,11:574-598.
[4]Novak,M.,Soil-pile interaction in horizontal vibration[J],Earthquake Engineering and Structure Dynamics,1977,5:263-281.
[5]Novak,M.,Piles under dynamic loads[C],Proceedings:Second International Conference on Recent Advances in Geotechnical Earthquake Engineering and Sore Dynamics,1991:2433-2456.
[6]Anestis,S.,Impedances of soil layer with disturbed boundary zone[J],Journal of Geotechnical Engineering,1985,112(3):363-369.
[7]Anestis,S.,Vertical and torsional of foundations in inhomogeneous media[J],Journal of Geotechnical Engineering,1987,114(9):1002-1021.
[8]Poulos,H.G.,Behavior of laterally loaded piles:I-single piles[J],Soil Mech.and Found.Div.,ASCE,1971,97(5):711-731.
[9]Wong S.C.,Poulos,H.G.,Approximate pile-to-pile interaction factor between two dissimilar piles[J],Computers and Geothechnics,2005,32:613-618.
[10]Poulos,H.G.,and Davis,E.H.,Pile foundation analysis and design[M].Gohn Wiley and Sons,New York,N.Y,1980.
[11]Chow,Y.K.,Axial and lateral response of pile groups embedded in nonhomogeneous soils[J].Int.G.Nuner.Anal.Methods Geomech.,1987,11(3):621-638.
[12]宫全美,基于Mindlin位移解的群桩沉降计算[J],地下空间,2001,21(3):167-177.
[13]Roesset,J.M.,Dynamic stiffness of pile groups[M],Analysis and Design of Pile Foundations.J.R.Meyer,ed.,ASCE,New York,N.Y.,263-286,1984.
[14]Xu,K.J.,Poulos,H.G.,General elastic analysis of piles and pile groups[J],Int J Numer Anal Method Geomech,2000,24:1109-1138.
[15]Koo,K.K.,Chau,K.T.,Yang X.,Lam,S.S.and Wong,Y.L.,Soil-pile-structure interactions under SH waves[J],Earthquake Engineering and Structural Dynamics[J],2003,32(3):395-415.
[16]Chau,K.T.,Yang X.,Nonlinear Interaction of Soil-Pile in Horizontal Vibration[J],J.Eng.Mech.2005,131(8):847-858.
[17]程昌钧,胡育佳,受轴力作用的桩基在水平振动时的抗力,上海大学学报(自然科学版)[J],2005,11(3):275-281.
[18]Hu Yu-jia,Cheng Chang-jun,Characteristics of piles under horizontal vibration,Applied Mathematics and Mechanics[J],2005,26(6):700-708.
[19]Hu Yu-jia,Zhu Yuan-yuan,Cheng Chang-jun,EFGM for Nonlinear Mechanical Behaviors of Single Pile and Pile Group[C],ICNM-5,2008,429-437.
[20]Hikmet,H.H.,Free vibration of semi-rigid connected and partially embedded piles with the effects of the bending moment,axial and shear force[J],Engineering Structures,2006,28:1911-1918.
[21]Apirathvorakij V.,Quasi-static bending of a cylindrical elastic bar partially embedded in a saturated elastic half-space[J],Int.J.Soil and Stru,1980,16(7):625-644.
[22]Zeng,X.,Rajapakse,R.K.N.D.,Dynamic axial load transfer from elastic bar to poroelastic medium[J],J.Eng.Mech.ASCE,1999,125(9):1048-1055.
[23]王建华,陆建飞,沈为平,层状地基中考虑固结和流变的垂直桩的理论分析[J],水利学报,2001,4:57-61.
[24]李强,王奎华,谢康和,饱和土桩纵向振动引起土层复阻抗分析研究[J],土工程学报,2004,26(5):679-683.
[25]Jin,B.,Zhou,D.Zhong,Z.,Lateral dynamic compliance of pile embedded in poroelastic half space[J],Soil.Dyn.Earthquake Eng.,2001,21:519-525.
[26]陆建飞,王建华,考虑固结和流变的层状地基中的水平单桩的理论分析[J],岩土力学与工程学报,2001,20(3):386-390.
[27]陆建飞,频率域半空间饱和土中水平受荷桩的动力分析[J],岩土力学与工程学报,2002,21(4):577-581.
[28]杨军,宋二祥,陈肇元,桩在饱和土中水平振动的辐射阻尼简化算法[J],岩土力学,2002,23(2):179-183.
[29]Wang,J.H.,Zhou,X.L.,Dynamic response of pile groups embedded in a poroelastic medium[J],Soil.Dyn.Earthquake Eng.,2003,23:235-242.
[30]Maeso,O.,Aznarez,J.J.,Garcia,F.,Dynamic impedances of piles and groups of piles in saturated soils[J],Computers and Structures,2005,83:769-782.
[31]Nogami,T.,Novak,M.Time domain axial response of dynamically loaded single piles [J].J.Geotech.Engg.Div.ASCE,1987,112(11):1241-1252.
[32]El Naggar,M.H.,Novak,M.Nonlinear analysis for dynamic lateral pile response[J].Soil Dynamics and Earthquake Engineering,1996,15(4):233-244.
[33]胡安峰,谢康和,水平载荷下单桩动力反应分析[J],浙江大学学报,2003,37(4):420-425.
[34]黄茂松,吴志明,任青,层状地基中群桩的水平振动特性[J],岩土工程学报,2007,29(1):32-38.
[35]胡春林,程昌钧,非线性粘弹性桩基纵向混沌运动[J],岩土力学,2005,26(10):1541-1544.
[36]胡春林,程昌钧,陈中学,桩基非线性轴向振动的多时间尺度分析[J].振动与冲击,2007,26(5):54-59.
[37]任九生,程昌钧,非线性粘弹性桩耦合运动中的混沌分析[J],振动与冲击,2006,25(5):21-23.
[38]任九生,程昌钧,纵向振动粘弹性桩的分叉和混沌运动[J],振动与冲击,2005,24(5):11-13.
[39]Cai S.,Wang S.,A simple estimation of the force exerted by internal solitons on cylindrical piles[J],Ocean Engineering,2006,33:974-980.
[40]Matlock H.,Correlation for design of lateral loaded piles in soft clay[C],Proc.2~(nd)Offshore Technology Conference,Vol.1,Houston,TX.OX.C 1204,1970:577-594.
[41]Reese,L.C.,Cox,W.R.,and Koop,F.D.Field testing and analysis of laterally loaded piles in stiff clay[C],Proc.7th Offshore Tech.Conf.,ASCE et al.,1975:671-690.
[42]O'Neill,M.W.,Hawkins,R.A.and Mahar,L.J.Load transfer mechanisms in piles and pile groups[J],J.Geotech.Engrg.Div.,ASCE,1982,108(12):1605-1623.
[43]O'Neill,M.W.,Ghazzaly,O.I.,and Ha,H.B.Analysis of three-dimensional pile groups with non-linear soil response and pile-soil-pile interaction[C],Proc.9th Offshore Tech.Conf.,ASCE et al.,1977:245-256.
[44]Bogard,D.and Matlock,H.Procedures for analysis of laterally loaded pile groups in soft clay[M],Geotechnical practice in offshore engineering,S.G.Wright,ed.,ASCE,New York,N.Y.,1983:499-535.
[45]Brown,D.A.,Morrison,C.and Reese,L.C.Lateral load behavior of pile group in sand[J],J.Geotech.Engig.,ASCE,1988,114(11):1261-1276.
[46]Kraft Jr.L.M.,Ray,R.P.and Kagawa,T.Theoretical t-z curves[J],J.Geotech.Engrg.Div.,ASCE,1981,107(11):1543-1562.
[47]Gazioglou,S.M.and O'Neill,M.W.Evaluation of p-y relationships in cohesive soils.Analysis and design of pile foundations[M],J.R.Meyer,ed.,ASCE,New York,N.Y.,1984:192-213.
[48]Nogami,T.and Chen,H.L.Simplified approach for axial pile group response analysis[J],J.Geotech.Engrg.,ASCE,1984,110(9):1239-1255.
[49]Nogami,T.and Paulson,S.K.Transfer matrix approach for nonlinear pile group response analysis[J],Int.J.Numer.Anal.Methods Geomech.,1985,9(4):299-316.
[50]Focht J A,and Koch K J.,Rational analysis of lateral performance of offshore pile groups[C],Proceeding of the 5th offshore technology conference 1973,Dallas,Texas,1997;701-708.
[51]田平,王惠初,粘土中横向周期性荷载桩的P-Y曲线统一法[J],河海大学学报,1993,(1):9-14.
[52]王惠初,武冬青,田平,粘土中横向静载桩P-Y曲线的一种新的统一法[J],河海大学学报,1991,(1):9-17.
[53]章连洋,陈竹昌,粘性土中P-Y曲线的计算新方法[J],港口工程,1991,(2):29-35.
[54]程泽坤,关于P—Y曲线法分析横向力作用下高桩结构物的讨论[J],港工技术,1997,(3):53-57.
[55]程泽坤,基于P-Y曲线法考虑桩土相互作用的高桩结构物分析[J],海洋工程,1998,(2):5-9.
[56]胡立万,郝军,陈鹭缨.用P-Y曲线法计算板桩结构[J],港工技术,2001,(1):24-26.
[57]杨国平,张志明.对大变位条件下横向受力桩P-Y曲线的研究[J],水运工程,2002,(7):40-45.
[58]Ellison,R.D.,D'Appoionia,E.and Thiers,G.R.Load-deformation mechanism for bored piles[J],J.Soil Mech.And Found.Div.,ASCE,1971,97(4):661-679.
[59]Christiano,P.,Rergstad,G.,and Ellison,R.,Behavior of driven piles partel:Numerical analysis,part Ⅱ:Deformation and failure mechanisms[C],Proc.2nd Iranian Conf.On Civ.Engrg.,Iran society of Civil Engineers,1976,3:1778-1834.
[60]Randolph,M.F.,The response of flexible piles to lateral loading[J],Geothecnique,Loadon,England,1981,31(2):247-259.
[61]Faruque,M.O.and Desai,C.S,3-D material and geometric nonlinear analysis of piles[C],Proc.Second Int.Conf.on Numerical Methods in Offshore Piling.Univ.of Texas.1982:553-575.
[62]Muqtadir,A.and Ddsai,C.S.,Three-dimensional analysis of a pile-group foundation[J],Int.J.Numer.Anal.Methods Geomech.,1986,10(1):41-58.
[63]Kuhlemeyer,R.L.,Vertical vibration of pile[J],ASCE J.Geotech.Engry.Div.,1979,105(GT2):273-288.
[64]Aristonous M.,Three-dimensional nonlinear study of pile[J],Journal of the Geotechnical Engineering,1991,117:429-447.
[65]傅旭东,称晓平,单桩承载力可靠度的非线性摄动随机有限元分析[J],岩土力学与工程学报,2003,22(1):103-109。
[66]Butterfield,R.and Banerjee,P.K.,The elastic analysis of compressible piles and pile groups[J].Geotechnique,1971,21:43-60.
[67]Semih K.,Time domain dynamic analysis of piles under impact loading[J],Soil Dynamics and Earthquake Engineering,2002,22:97-104.
[68]周常春,邓安福,水平载荷下群桩前后土抗力分布的数值计算[J],地下结构,2003,23(1):17-21.
[69]赵明华,吾鸣,轴、横向载荷下桥梁基桩的受力分析及试验研究[J],中国公路学报, 2002,15(1):50-54.
[70]Mizuno,H.,Pile damage during earthquakes in Japan(1923-1983)[J],Dynamic Response of Pile Foundations.ASCE,Geotech.Special Publ.11(Edited by T.Nogami),1987,53-78.
[71]Miura F.,Lessons from Damage to Pile Foundation Caused by Past Earthquake in Japan and the Necessity of Nonlinear Analyses of Pile foundation[C],Proceedings of the 4~(Th)International Conference on Nonlinear Mechanics,Shanghai:Shanghai University Press,2002,109-115.
[72]Miyasaka,T.,Study on the effectiveness of the high ductility aseismatic joint spliced pile subjected to liquefaction-induced large ground displacement[D],Doctor Thesis of Yamaguchi-University,1997(in Japanese).
[73]Izumi,H.,Dynamic behavior of high ductility aseismatic joint spliced pile foundations during strong earthquake motions[D],Doctor Thesis of Yamaguchi University,1999(in Japanese).
[74]三浦房纪,朱媛媛,在弹性基础上具有初始水平位移的桩基的临界载荷[M],日本土木学会论文集(日文),682/1-56,2001,143-153.(Miura F.and Zhu Y.,Critical Load of a Single Pile with Initial Horizontal Displacement iIl Elastic Ground,J.JSCE,No.682/I-56,2001,143-153)
[75]三浦房纪,朱媛媛,桩头的边界条件对受侧向基础位移桩临界载荷的影响[M],日本土木学会论文集(日文),682/1-56,2001,155-164.(Miura Eand Zhu Y,The Effect of Boundary Condition at Pile Head of a Pile on the Critical Load subjected to Lateral Ground Displacement,J.JSCE,No.682/I-56,2001,155-164)
[76]朱媛媛,三浦房纪,朱正佑,弹性地基上HDAJ接头桩的非线性稳定性分析[J],力学季刊,26(2),2005,216-223.
[77]朱媛媛,胡育佳,弹性基础上具有初始缺陷的桩基的大变形分析[J],力学季刊,2007,28(2):310-319.
[78]Yuan-yuan Zhu,Yu-jia Hu,Large Deformation Analysis of Piles with Elastic Joints[C],ICNM-5,2008:588-595.
[79]朱媛媛,胡育佳,求解具有弹性铰接头的桩基大变形动力学问题的微分—代数方法[C],上海市力学学会2007年年会论文集,2007:180-187.
[80]张雄,刘岩,无网格法[M],北京:清华大学出版社,2004.
[81]Belytschko T.,Krongauz Y.,Organ D et al.,Meshless methods:An overview and recent developments[J],Comput.Methods Appl.Mech.Engrg.,1996,139:3-47.
[82]Li S,Liu W K.Meshfree and partical methods and their applications[J],Appl.Mech.Rev.,2002,55(1):1-34.
[83]张雄,宋康祖,陆明万,无网格法的研究进展及其应用[J],计算力学学报,2003(20):731-742.
[84]Liszka T.,Orkisz J.,Finite difference method for arbitrary irregular meshes in nonlinear problems of applied mechanics[M],In:Ⅳ SmiRT,San Francisco,1997.
[85]Luo Y,Haussler-Combe U.,A generalized finite-difference method based on minimizing globle residual[J],Comput.Methods Appl.Mech.Engrg.,2002,191:1421-1438.
[86]Lucy L B.,A numerical approach to the testing of the fission hypothesis[J],The Astron.J.,1997,8(12):1013-1024.
[87]Gingold R.A.,Monaghan J.J.,Smoothed particle hydrodynamics:theory and applications to non-spherical stars[J],Mon.Not.Roy.Astrou.Soc.,1997,18:375-389.
[88]Johnson G.R.,Beissel S.R.,Normalized smoothing functions for SPH impact computations[J],Int.J.Num.Meth.Engrg.,1996,39:2725-2741.
[89]Lancaster P.,Salkauskas K.,Surfaces generated by moving least squares methods[J],Math,Comput.,1981,37(155):141-158.
[90]Nayroles B.,Touzot G.,Villon P.,Generalizing the finite element method:diffuse approximation and diffuse elements[J],Comput.Mech.,1992,10:307-318.
[91]Belytschko T.,Liu Y.Y.,Gu L.,Element free Galerkin methods[J],Int.J.Num.Mech.Engrg.,1994,37:229-256.
[92]Chung H.J.,Belytschko T.,An error estimate in the EFG method[J],Comput.Mech.,1998,21:91-100.
[93]Dolbow J.,Belytschko T.,Numerical integration of the Galerkin weak form in mesh-free methods[J],Comput.Mech.,1999,23:219-230.
[94]Belytschko T.,Krongauz Y.,Organ D et al.Smoothing and accelerated computations in the element free Galerkin method[J],J.Comput.Appl.Math,1996,74:111-126.
[95]Krongauz Y.,Belytschko T.,EFG approximation with discontinuous derivatives[J],Int.J. Num.Meth.Engrg.,1998,41 1215-1233.
[96]周维垣,寇晓东,无单元法及其工程应用[J],力学学报,1998,30(2):193-202.
[97]寇晓东,周维垣,应用无单元法近似计算拱坝开裂[J],水利学报,2000,28-35.
[98]庞作会,葛修润,郑宏等,一种新的数值方法——无网格伽辽金法(EFGM)[J],计算力学学报,1999,16(3):320-329.
[99]朱媛嫒,胡育佳,程昌钧,无网格方法在平面粘弹性力学问题中的应用[J],力学季刊,2006,27(3):404-412.
[100]Liu W K.,Jun S,Zhang Y F.,Reproducing Kernel Partical methods[J],Int.J.Numer.Meth.Fluids.,1995,20:1081-1106.
[101]Ohs R R.,Aluru N R.,Meshless analysis of piezoelectric devices[J],Comput.Mech.,2001,27:23-36.
[102]Duarte C A.,Oden J T.,An h-p adaptive method using clouds[J],Comput.Methods Appl.Mech.Engrg.,1996,139:237-262.
[103]Onate E.,Idelsohn S.,Zienkiewicz O C.et al.,A finite point method in computational mechanics:Applications to convective transport and fluid flow[J],Int.J.Num.Meth.Engrg.,1996,39:3839-3866.
[104]Atluri S N.,Zhu T.,A new meshless local Petrov-Galerkin(MLPG) approach in computational mechanics[J],Comput.Mech.,1998,22:117-127.
[105]Wendland H.,Meshless Galerkin method using radial basis functions.Math[J],Comput.,1999,68(228):1521-1531.
[106]尹华杰.无网格法及其在电磁场计算中的应用展望[J],电机与控制学报,2003,(7):107-111,132.
[107]Singh I.V.,A numerical solution of composite heat transfer problems using meshless method[J],International Journal of Heat and Mass Transfer,2004,47:2123-2138.
[108]Hua Lia,Wang QX,Lam KY,A variation of local point interpolation method(v LPIM)for analysis of microelectromechanical system(MEMS) device[J],Engineering Analysis with Boundary Elements.2004,28:1261-1270.
[109]Fleming M.,Rahman S.,An efficient element free galerkin methods for crack tip fields[J],Int.J.Num.Meth.Engng.,1997,40:1483-1504.
[110]Liu W.K.,Chen Y.,Aziz UR et al.,Generalized multiple scale reproducing kernel particle methods[J],Comput.Methods Appl.Mech.Engrg.,1996,139:91-157.
[111]周小平,周瑞忠,对无单元法插值函数的几点研究[J],福州大学学报(自然科学版).2000,28:52-56.
[112]Bellmam,R.E.,Kashef,B.G.,Casti,J.,Differential quadrature:A technique for the rapid solution of nonlinear partial differential equations[J],J.Comput.Phys.1972,10:40-52.
[113]Bert,C.W.,Jang,S.K.,Striz,A.J.,New methods for analyzing vibtation of structural components[C].Proc.AIAA Dynamics Specialist Conference,Monterey,CA,USA,Part2,1987:936-943.
[114]Bert,C.W.,Malik M.,Differential quadrature method in computational mechanics:a review[J],Applied Mechanics Reviews,1996,49:1-28.
[115]Civan,F.,Slepcevich,C.M.,Differential quadature for multidimensional problem[J],J.Math.Appl.,1984,101:423-443.
[116]Quan,J.R.,Chang,C.T.,New insights in solving distributed system equations by the quadrature methods-Ⅰ[J],Comput.Chem.Engrg.,1989,13:779-788.
[117]Quan,J.R.,Chang,C.T.,New insights in solving distributed system equations by the quadrature methods-Ⅱ[J],Comput.Chem.Engrg.,1989,13:1017-1024.
[118]Shu,C.,Richards,B.E.,parallel simulation of incompressible viscous flows by generalized differential quadrature[J],Computing Systems in Engineering,1992,(3):271-281.
[119]Striz,A.G.,Wang,X.,Bert,C.W.,Harmonic Differential Method and Applications to Structure Components[J],Acta Mechanica,1995,111:85-94.
[120]Chang,C.T.,Tasi,C.S.,Lin,T.T.,Modified differential quadrature and their application to structure components[J],Acta Mechanica,1995,111:85-94.
[121]Wang,X.,Bert,C.W.,A new approach in applying differential quadrature to static and free vibrational analyses of beams and plates[J],J.Sound & Vibration,1993,162:566-572.
[122]王鑫伟,调和微分求积法权系数矩阵的一种显式计算式[J],南京航空航天大学学报,1995;027(004):496-501.
[123]Hong z.z.,Triangular differential quadrature[J],Communications for Numerical Methods in Engineering,2000,16(4):401-408.
[124]聂国隽,仲政,用微分求积法求解梁的弹塑性问题[J],工程力学,2005,22(1):59-62.
[125]吕朝锋,陈伟球,边祖光,状态空间微分求积分法分析Winkler地基梁的自由振动,浙江大学学报(工学版)[J],2004,38(11):1451-1454.
[126]杨杰,彭建设,组合载荷作用下层合板非线性弯曲的半解析摄动DQ法[J],计算力学学报,2002,19(3):373-375.
[127]Li Jing-Jing,Cheng,Chang-Jun,Differential quadrature method for bending of orthotropic plates with finite deformation and transverse shear effect[J],Appl.Math and Mech.,2004,25(8):878-886.
[128]Li J.J.,Cheng C.J.,Differential quadrature method for nonlinear vibration of orthotropic plates with finite deformation and transverse shear effect[J],Journal of Sound and Vibration,2005,281:295-305.
[129]李晶晶,程昌钧,盛冬发,考虑高阶横向剪切正交各向异性板振动的微分求积分析方法[J],振动与冲击,2004;22(4):8-11.
[130]Sun Jian-An,Zhu Zheng-You,Application of differential quadrature method to solve entry flow of viscoelastic second-order fluid[J],Int.J.of Numer.Mech.Fluids,1999,30(8):1109-1117.
[131]Sun Jian-an,Zhu Zheng-you,Upwind local differential quadrature method for solving incompressible viscous flow[J],Compute.Methods in Appl.Mech.Engng,2000,188:495-504.
[132]Striz,A.G..,Chen,W.L.,Bert,C.W.,Free vibration of plates by the high accuracy differential quadrature element method[J],Journal of Sound and Vibration,1997,202:689-702.
[133]Han,J.B.,Liew,K.M.,Static analysis of Mindlin plates:the differential quadrature element method(DQEM),Comput.Methods Appl.Mech.Engrg,1999,177:51-75.
[134]王永亮,微分求积法和微分求积单元法——原理与应用[D],南京航空航天大学.2001.
[135]Liu,F.L.,Liew,K.M.,Static analysis of Reissner-Mindlin plates by the differential quadrature element method[J],J.Applied Mechanics,1998,65:705-710.
[136]Liu,F.L.,Liew,K.M.,Analysis of vibrating thick rectangular plates with mixed boundary constraints using differential quadrature element method[J].Journal of Sound and Vibration.1999,25(5):915-934.
[137]Liu F.L.and Liew K.M.,Vibration analysis of discontinuous Mindlin plates by differential quadrature element method[J],Vibration and Acoustics,1999,121:204-208.
[138]Yu-jia Hu,Yuan-yuan Zhu,Chang-jun Cheng,Differential-algebraic approach to large deformation analysis of frame structures subjected to dynamic loads[J],Applied Mathematics and Mechanics.2007,29(4):441-452.
[139]Yu-jia Hu,Yuan-yuan Zhu,Chang-jun Cheng,DQEM for Large Deformation Analysis of Structures with Discontinuity Conditions and Initial Displacements[J],Engineering Structures,2008,30:1473-1487.
[140]Wang X.W.,Wang Y.L.and Chen R.B.,Static and free vibrational analysis of rectangular plates by the differential quadrature element method[J],Commun.Numer.Meth.Engrg.,1998,14:1133-1141.
[141]Chen C N.,The two -dimensional frames model of the differential quadrature element method[J],Computers & Structures,1997,62(3):555-571.
[142]聂国隽,仲政,变截面门式刚架结构分析的微分求积单元法[J],力学季刊,2005,26(2):198-203.
[143]Bisshopp K.E.and Drucker D.C.,Large deflections of a cantilever beam[J],Quart.Appl.Math.,1945,3:272-275.
[144]Jenkins J.A.,Large deflection of diamond shaped frames[J],Int.Soils Struct.,1966,2:591-603.
[145]Bathe K.J,Large displacement analysis of three dimensional beam Structures[J],Internal J Number Methods Engrg,1979,4:961-986.
[146]Arregui I.,Destuynder P.,Salaun M.,An Eulerian approachfor large displacements of thin shells including geometrical non-linearities[J],Comput Methods Appl Mech Engrg,1997,140:361-381.
[147]Oden J.T.,Finite element of nonlinear continua[M],McGraw-Hill,1972.
[148]Bathe K.J.,Finite element procedures in engineering analysis[M],Prentice-Hall,1982.
[149]陈至达,杆、板、壳大变形理论[M],科学出版社,1994.
[150]陈至达,有理力学,中国矿业大学出版社[M],1986.
[151]李尧臣,圆截面杆在曲线井中的屈曲问题[J],力学季刊,2002,32(2):265-271.
[152]Liu Y.Z.,Stability and bifurcation of helical equilibrium of a thin elastic rod[J],Acta Mechanica,2004,167:29-39.
[153]刘延柱,弹性杆基因问题的力学问题[J],力学与实践,2003,25(1):1-5.
[154]Angelides and Roesset,Nonlinear lateral dynamic stiffness of pile[J],Journal of the Geotechnical Engineering Division,1981,107(GT110):1443-1460.
[155]程昌钧,朱媛媛,弹性力学(修订版)[M],上海,上海大学出版社,2005.
[156]Randolph M F.,Analysis of deformation of vertically loaded piles[C],Proc,J,GT DIV,ASCE,1978,104(12):1465-1488.
[157]Cooke R W,Price G,Tarr K,Jacked piles in London clay:a study of load transfer and settlement under working conditions,Geotechnique,1979,29(2):113-147.
[158]Shen W.Y.,Chow Y.K.and Yong K.Y.,Variational solution for loaded pile groups in an elastic half-space,Geotechnique,1999,49(2):119-213.
[159]谢贻权,何福保,弹性和塑性力学的有限单元法[J],机械工业出版社,1983.
[160]Makris N.,Rigidity-plasticity-viscosity:can electrorheological dampers protect base-isolated structures from near-source ground motions?[J],Earthquake Engineering and Structural Dynamics 1997,26:571-591.
[161]Randolph M F.,Wroth C P,Analysis of deformation of vertically deformation of pile groups[J],Geotechnique,1979,29(4):423-439.
[162]Lee C Y.,Settlement of Pile Group-Practical Approach[J],J.Geotech Engng Div.ASCE,1993,119(9):149-1461.
[163]Reese L.C.,Cox W.R.and Koop F.D.,Field testing and analysis of laterally loaded piles in stiffclay[C],Proc.7~(th) Offshore Tech.C.onf.,ASCE et al.,1975,671-690.
[164]Briaud,J L,Tucker,L M.& Ng,E,Axially loaded 5 pile group and single pile in sand[C],Proc.of 12th Int.Conf.Soil Mech.Fdn Engng,Rio de Janeiro,1989,2,1121-1124.
[165]Wolf,J P.,Impedance Function of a group of vertical piles[M],Erzmetll,1978,2:1024-1041
[166]Gazetas G.and Makris N.,Dynamic pile-soil-pile interaction,Part Ⅰ:analysis of axial vibration[J],Earthquake Engineering and Structural Dynamics,1991,20:115-132.
[167]Cook,R.W.,Price,G.,Jacked piles in London clay:interaction and group behavior under working conditions[J],Geotechnique,1980,30(2):449-471.
[168]Berezantzev,V.G.,Khristoforov,Load bearing capacity and deformation of piled foundation[C],Proc.5~(th) Int.Conf.Soil Mech.Fdn Engng,Paris,1961,2,11-15.
[169]Boit M A.,General theory of three-dimensional consolidation[J],J Appl Phys,1941,12:155-164.
[170]Boit M A.,Theory of propagation of elastic waves in a fluid-saturated porous media,I.Low frequency range[J],J Acoust Soc Am,1956,28(2):168-178.
[171]Bowen R M.,Compressible porous media models by use of the theory of mixtures[J],Int J Engng Sci,1982,20:693-735
[172]de Boer R.,Theory of porous media:Highlights in the historical development and current state[M],Springer-Verlag,2000,Berlin,Heidelberg.
[173]Schrefler B A.,Mechanics and thermodynamics of saturated/unsaturated porous material and quantitative solution[J],Appl Mech Rev,2002,5:351-380.
[174]Schrefler B A.,Zhang X,Simoni L.,A coupled model for water flow,air flow and heat flow in deformable porous media[J],Int,J Num meth Fluid Flow,1995,5:531-547.
[175]Edelman I.,Wilmanski K.,Asymptotic analysis of surface waves at vacuum/porous medium and liquid/porous medium interfaces[J],Continuum Mech Thermody,2002,14:25-44.
[176]de Boer R.,Theoretical poroelasticity-a new approach[J],Chaos Solitons & Fractals,2005,25:861-878.
[177]de Boer R.,Ehlers W.,Liu Z.,One-dimensional transient wave propagation in fluid-saturated incompressible porous media[J],Archive Appl Mech,1993,63:59-72.
[178]Breuer S.,Reflection and refraction of longitudinal waves in a fluid-saturated porous solid,in Problems of Environmental and Damage mechanics[C],IPPT PAN.Warszawa,Proceedings of SoilMec'96 Conference,Mierki,September 9-14,1996,Poland,27-37
[179]Breuer S.,Quasi-static and dynamic behaviors of saturated porous media with incompressible constituents[J],Transport in Porous Media,1999,34:285-303.
[180]Wilmansld,K.,A thermodynamic model of compressible porous materials with the balance equation of porosity[J],Transport in Porous Media,1998,32:21-47.
[181]Diebels S.,Ehlers W.,Dynamical analysis of a fully saturated porous media accounting for geometrical and material non-linearities[J],Int J Numer Meth Engng,1996,39:81-97.
[182]Aboustit B L.,Advani S H.,Lee J K.,Variational principles and finite element simulations for thermo-elastic consolidation[J],Int J Numer Meth Engng,1985,9:49-69.
[183]杨骁,程昌钧,流体饱和多孔介质动力学Gurtin型变分原理和有限元模拟[J],固体力学学报,2003,24(3):267-276.
[184]Yang Xiao,He Lu-wu,Variational principles of fluid-saturated incompressible porous media[J],兰州大学学报(自然科学版),2003,39(6):24-39.
[185]Yao,S.,et al.,Interactive behavior of soil-pile-structure system in transient state to liquefaction by means of large shake table tests[J],Soil.Dyn.Earthquake Eng.,2004,24:297-409.
[186]克里斯坦森R M,老亮译,粘弹性力学引论[M],北京:科学出版社,1990.