横观各向同性饱和层状地基的三维稳态动力响应

首先引入状态向量,将直角坐标系下横观各向同性饱和土的Biot波动方程转化为一组状态方程,然后基于双重Fourier变换,求解了状态方程,得到传递矩阵.进而利用传递矩阵,并结合饱和地基的边界条件、排水条件及层间接触和连续条件,求解了横观各向同性饱和层状地基的稳态动力响应问题.     

弹性层内部有集中力的精确解

利用Ｈａｎｋｅｌ变换及矩阵理论，获得了位于水平刚性基础上的弹性层在其内部受垂直于边界的集中力作用了的精确率，推广了已有的结论。Ｋｅｌｖｉｎ解，Ｍｉｎｄｌｉｎ解及弹性层表面受集中的用的解都是其特殊情形下的结论。     

解析法求解成层渗透各向异性地基Biot固结轴对称问题

采用解析法研究成层渗透各向异性地基,该法从渗透各向异性Ｂｉｏｔ固结轴对称问题的基本方程（静力平衡方程,物理方程及渗透连续方程）出发,利用Ｌａｐｌａｃｅ～Ｈａｎｋｅｌ变换及有关矩阵理论等,得到Ｂｉｏｔ固结基本量不同深度之间的传递矩阵。利用传递矩阵,边界条件以及Ｌａｐｌａｃｅ～Ｈａｎｋａｌ逆变换技术可求解多层渗透各向异性地基体系,采用更为有效的Ｆ．Ｄｕｒｂｉｎ的方法实现Ｌａｐｌａｃｅ逆变换。编制了计算     

层状弹性半空间非轴对称动力问题的奇异解

在柱坐标系下，利用关于方位角的Ｆｏｕｒｉｅｒ变换及关于径向的Ｈａｎｋｅｌ变换，将弹性力学基本方程组转化为非齐次的一阶常微分方程组的标准形式．采用求解微分方程组的矩阵法，建立了介质层的传递矩阵．由层间完全接触条件，导出了在任意埋藏源作用下层状弹性半空间频域奇异解，时域奇异解可通过关于频率的Ｆｏｕｒｉｅｒ积分得到．该方法可应用到固体、流体层的情况     

层状横观各向同性饱和土的非轴对称动力响应

通过方位角的Fourier变换,将圆柱坐标系下横观各向同性饱和土的Biot非轴对称波动方 程转化为一组一阶常微分方程组. 然后基于径向Hankel变换,建立问题的状态方程;求解状态方程后,得到传递矩阵. 进而利用传递矩阵,结合饱和层状地基的边界条件、排水条件及层间接触和连续条件,求解 了任意震源力作用下层状横观各向同性饱和地基频域动力响应问题. 时域解可通过频率的Fourier积分得到.     

多层弹性半空间问题解的精确刚度矩阵法

利用二维Fourier积分变换和刚度矩阵法,得到了直角坐标系下多层弹性半空间问题的精确解.在推导的过程中,直接从空间弹性力学的基本方程出发,利用积分变换等数学手段,首先推导出了单层空间弹性问题的刚度矩阵,然后按有限元法组成总体刚度矩阵.通过求解由总体刚度矩阵所构成的代数方程和积分逆变换,就可解出在任意静荷载作用下多层弹性半空间问题的精确解.由于刚度矩阵中不含有正指数项,计算时不会出现溢出现象,从而克服了传递矩阵法的缺点.由于在推导过程中摒弃了应力函数的选择,使得问题的求解更加合理化.最后还给出了计算实例来证明推导结果的准确性.     

关于传递矩阵法分析饱和成层介质响应问题的讨论

水平成层土体的地震响应分析(自由场分析)是地震工程领域地震波散射问题的前提基础,由于饱和多孔方程的复杂性,以往的研究大多集中于干土情形,对于饱和土情形的研究相对较少.而实际工程中,地下水位以下,土体孔隙中充满流体,应考虑饱和多孔介质模型.基于Biot多孔介质模型,考虑饱和土中固液相对运动引起的衰减,采用Thomson--Haskell传递矩阵方法得到了饱和成层土体在地震波入射情形时的稳态反应,经傅里叶反变换,可得到时域暂态反应.通过SV波从基岩入射至上覆饱和土层的数值算例,验证了该方法的有效性.发现和初步阐明了计算中出现的两类违背因果律(即响应先于输入)的现象:(1)当SV波入射角度大于导致基岩中反射P波为非均匀波的临界角时,会使得计算结果违背因果律.因此,当入射角超过临界角时,非均匀波的表示尚需进一步完善;(2)由于P2波的衰减,当与稳态波衰减有关的渗透率、土层厚度、入射波频率等参数导致衰减系数超过计算机表示精度时,会出现结果违背因果律现象,并据此得到了满足因果律的参数范围,该范围可作为实际计算时的一个上界.该工作为采用传递矩阵法分析水平饱和土层自由场响应提供了指导依据,且地下水位以上可采用干土模型,水位以下采用饱和土模型,更符合实际情形.     

基于惯性参考系基准的快速传递对准方法

研究了以惯性参考系为基准的新型传递对准方法。推导了计算惯性坐标系和计算体坐标系传递对准动态误差模型,并给出了相应的"速度+姿态"观测方程。基于惯性参考系的对准方法通过链式法则将子惯导输出的姿态矩阵描述为三个变换矩阵之积,其中两个变换矩阵通过对准时间和主惯导提供的位置信息可得到精确求解,剩余的变换矩阵(子惯导体坐标系至惯性坐标系间的变换矩阵)通过子惯导陀螺仪的输出进行解算,其误差通过传递对准估计得到的失准角进行补偿。对提出的两种对准方法进行摇摆实验验证,方位对准误差优于4’(1)。与传统基于导航坐标系的方法相比,基于惯性坐标系的方法直接将误差定位到惯性坐标系上,具有算法简便的特点。     

单支开口薄壁梁屈曲分析的Riccati有限条传递矩阵法

针对单支开口薄壁梁屈曲问题,通过采用半解析有限条法推导薄壁梁的条元控制方程、传递矩阵基础形成单元传递方程、Riccati变换改善数值计算稳定性,提出了开口单支薄壁梁屈曲分析的Riccati有限条传递矩阵法。为了验证该方法的正确性与高效性,通过提出的Riccati有限条传递矩阵法和有限元法分析了一般支撑条件下两种不同截面形式的薄壁梁屈曲临界载荷与屈曲模态,计算发现两种方法的结果具有很好的一致性,且与传递矩阵法相比,Riccati有限条传递矩阵法数值稳定性好。因此,Riccati有限条传递矩阵法可计算广义边界条件的薄壁结构屈曲问题。     

Plane strain consolidation of a multi-layered soil with anisotrpic permeability and compressible constituents

对多层地基的平面应变固结问题进行了研究,并同时考虑了土体的渗透各向异性和孔隙 流体的可压缩性. 从平面应变Biot固结的控制方程出发,对时间t, 坐标z和x进行 Laplace和Fourier变换,建立了地基表面(z=0)和任意深度z处的基本量 在Laplace-Fourier变换域内的传递矩阵关系. 利用传递矩阵 法,结合土层连续条件和边界条件,并应用Laplace-Fourier逆变换技术,推导出渗透各向 异性可压缩多层地基平面应变固结的理论解. 基于该解,编制了计算程序,并进行了 数值计算. 讨论了土体的渗透各向异性、孔隙流体的可压缩性以及地基的分层特性对地基固 结的影响,分析结果表明：土体的渗透各向异性、孔隙流体的可压缩性,以及地基的分层特 性对地基的固结行为有着重要的影响.     

Generalized flow analysis of non-Newtonian visco-elastic fluid flow through fractal reservoir

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Visco-elastic effects on wave dispersion in three-phase acoustic metamaterials

This paper studies the wave attenuation performance of dissipative solid acoustic metamaterials (AMMs) with local resonators possessing subwavelength band gaps. The metamaterial is composed of dense rubber-coated inclusions of a circular shape embedded periodically in a matrix medium. Visco-elastic material losses present in a matrix and/or resonator coating are introduced by either the Kelvin–Voigt or generalized Maxwell models. Numerical solutions are obtained in the frequency domain by means of $\mathbf{k}\left(\omega \right)$-approach combined with the finite element method. Spatially attenuating waves are described by real frequencies ω and complex-valued wave vectors $\mathbf{k}$. Complete 3D band structure diagrams including complex-valued pass bands are evaluated for the undamped linear elastic and several visco-elastic AMM cases. The changes in the band diagrams due to the visco-elasticity are discussed in detail; the comparison between the two visco-elastic models representing artificial (Kelvin–Voigt model) and experimentally characterized (generalized Maxwell model) damping is performed. The interpretation of the results is facilitated by using attenuation and transmission spectra. Two mechanisms of the energy absorption, i.e. due to the resonance of the inclusions and dissipative effects in the materials, are discussed separately.It is found that the visco-elastic damping of the matrix material decreases the attenuation performance of AMMs within band gaps; however, if the matrix material is slightly damped, it can be modeled as linear elastic without the loss of accuracy given the resonator coating is dissipative. This study also demonstrates that visco-elastic losses properly introduced in the resonator coating improve the attenuation bandwidth of AMMs although the attenuation on the resonance peaks is reduced.     

模拟微可压粘弹性流体的WCCBS_SU方法

针对微可压缩粘弹性流动问题,发展了微可压缩流的WCCBS方法,详细推导了基于Oldroyd-B本构模型的WCCBS_SU方法的求解过程。在流场微可压的条件下,分别对平面Poiseuille流和4：1粘弹性收缩流进行了数值模拟。Poiseuille流在不同We数下数值结果与解析解的比较,验证了本文方法具有较高的精度和较好...     

Numerical simulation of tumor-induced angiogenesis influenced by the extra-cellular matrix mechanical environment

To investigate tumor-induced angiogenesis under the influence of the mechanical environments inside and outside the tumor, mathematical model of tumor angiogenesis was developed. In the model, extra-cellular matrix （ECM） was treated as a thin plane. The displacement of ECM is obtained from the force balance equation consisted of the ECs traction, the ECM visco-elastic forces and the exter- nal forces. Simulation results show that a layered capillary network is obtained with a well vascularized region at the periphery of the tumor. The present model can be used as a valid theoretical method in the basic researches in tumorinduced angiogenesis.     

瞬态温度场作用下冰载荷计算

给出了关于冰的粘弹性微分本构模型的广义变分原理和冰载荷计算的有限元方法。修正的增量粘弹性矩阵有效地加速了迭代过程，计算了瞬态温度场下冰内压应力分布及对结构物作用力。其结果与实测数据定性吻合。     

Visco-elastic flow due to a plate which starts oscillating in the presence of a parallel stationary plate

In this paper, the flow of a visco-elastic liquid between two parallel plates has been studied when one plate is stationary and the other plate suddenly starts oscillating. Both finite Fourier sine transform and Laplace transform technique have been employed to solve the basic differential equations. The flow phenomenon has been characterized by the parameters, and and the effects of these on the flow characteristics have been studied through several graphs.Late professor of the department, who died in an accident on 7th July 1978.     

Thermal effect on vibration of non-homogenous visco-elastic rectangular plate of linearly varying thickness

An analysis for vibration of non-homogenous visco-elastic rectangular plate of linearly varying thickness subjected to thermal gradient has been discussed in the present investigation. For visco-elastic, the basic elastic and viscous elements are combined. We have taken Kelvin model for visco-elasticity that is the combination of the elastic and viscous elements in parallel. Here the elastic element means the spring and the viscous element means the dashpot. The governing differential equation of motion has been solved by Galerkin’s technique. Deflection, time period and logarithmic decrement at different points for the first two modes of vibration are calculated for various values of thermal gradients, non homogeneity constant, taper constant and aspect ratio for non-homogenous visco-elastic rectangular plate which is clamped on two parallel edges and simply supported on remaining two edges. Comparison studies have been carried out with homogeneous visco-elastic rectangular plate to establish the accuracy and versatility.     

Flow due to non-coaxial rotation of a porous disk and a second grade fluid rotating at infinity

An exact solution for the three-dimensional flow due to non-coaxial rotation of a porous disk and a second grade fluid at infinity is obtained. It is shown that for uniform suction or uniform blowing at the disk, an asymptotic profile exists for the velocity distribution. The velocity depends on two parameters: one of them is the suction parameter or blowing parameter and the other is the visco-elastic parameter. Furthermore, it is found that when the value of the visco-elastic parameter is fixed, the velocity decreases with an increase in the value of the suction parameter and when the value of the suction parameter is fixed, the velocity increases with an increase in the value of the visco-elastic parameter.     

无网格方法在平面粘弹性力学问题中的应用

本文综合应用无网格方法(EFGM)、线性粘弹性与弹性力学之间的对应原理,Laplace变换和逆变换等方法求解了拟静态平面弹性和粘弹性力学问题。首先,利用Laplace变换和逆变换推导了平面问题的粘弹性本构关系,建立了拟静态粘弹性平面问题的边值问题;其次,利用粘弹性与弹性力学之间的对应原理得到了Laplace变换域中平面问题的基本方程,在Laplace变换域中建立了相应的泛函,并得到了用无网格方法离散的控制方程;同时,求解了几个拟静态弹性和粘弹性平面问题,给出了它们的表达式和数值结果;最后,采用Laplace逆变换和数值逆变换,得到了粘弹性力学平面问题在物理空间中的解,并比较了由解析解和无网格数值方法所得到的数值结果,可以看到它们是非常吻合的。说明本文方法的正确性和有效性。