各向异性介质中SH波引起的裂纹扩展

本文利用Green函数法,求解各向异性介质中半无限长裂纹在SH波作用下,以任意速度扩展的问题。首先,利用Laplace变换和Cagniard-de Hoop反演法求解各向异性介质中反平面问题的Green函数,并利用它建立了求解裂纹扩展问题的积分方程。因为方程为Abel型的,所以可得到在SH波作用下,半无限长裂纹扩展问题的解析解。还可求得裂纹端点附近的应力和裂纹表面上位移的表达式。并对裂纹端点附近的奇异性进行讨论。最后讨论了裂纹尖端附近任一点的能量关系。并应用Griffith的能量准则,对裂纹扩展规律进行了讨论。     

SH波对双相介质界面附近圆形孔洞的散射

建立了求解平面SH波对双相介质界面附近圆形孔洞散射与动应力集中的一种分析方法．利用复变函数与多极坐标的方法构造了一个Green函数，它是在含有圆形孔洞的弹性半空间的水平面上任一点上作用时间谐和的出平面线源荷载的位移解．利用“契合”模型，并根据界面上位移连续性条件，建立了求解SH波对双相介质界面附近圆形孔洞散射的具有弱奇异性的第一类Fredholm型积分方程．给出了圆孔周边上动应力集中系数的表达式．作为算例，分析了在界面一侧或界面两侧附近具有圆形孔洞时SH波的散射，并讨论了入射波波数、不同的材料组合以及孔心至界面的距离对动应力集中的影响．     

双相介质参数反演的遗传算法

研究遗传算法在双相介质材料参数反演中的作用。将一维双相介质在动载荷下的表面位移响应的计算值与实测值进行拟合，以最小方差作为目标函数，把双相介质参数反演问题归结为非线性多峰函数的最优化问题。全局最优解的求解采用多点并行搜索的遗传算法，克服了传统梯度爬山法难于求得全局最优的困难。算例表明了遗传算法的可行性和稳健性。     

非均匀介质中流动和传热问题的有限分析法

数值求解非均匀介质中的输运问题广泛应用于科学计算和工程领域．介质的强非均匀性给相关问题的准确求解带来极大的困难．近年来，本课题组将有限分析法拓展到该领域，建立了非均匀介质中输运问题的有限分析法．该算法基于网格奇点邻域内类拉普拉斯方程局部解析解构建，算法具有很高的精度，且不依赖于介质的非均匀性强度．不管相邻网格传导率差异如何，仅需对原始网格进行很少地细分就可以获得非常准确的计算结果，因此与其他传统数值算法相比，可以大幅提高计算精度和效率．该算法可广泛应用于求解非均匀多孔介质中的渗流、复合材料中的热传导及电场分布等问题．     

非饱和多孔介质非线性有限元分析的一致性算法

在文[1]工作的基础上，对非饱和多孔材料非线性问题进行分析，给出分析的本构模型，模型中考虑了毛吸压力的影响。给出问题分析的求解技术与算法策略，在此基础上，为保证迭代算法的收敛性，文中给出适合于广义塑性本构模型分析的一致性算法与一致性切线刚度矩阵。给出的数值算例证实了理论与算法的正确与有效性。     

采空区流场非达西渗流一种新的迭代算法

对Bachmat非线性渗流方程求解问题，结合采空区问题的力学特点，提出基于变渗透率达西 (Darcy)渗流求解非线性渗流的迭代算法. 建立了冒落采空区非线性漏风流态的有限元数 值模型，通过对复杂边界采空区的漏风渗流的计算，得到与实际流态更接近的流动规律(风 压等值线和流函数线)和采空区漏风强度分布(速度场). 结果表明，迭代算法是振荡性收 敛的，收敛速度快；与Darcy渗流相比，采空区非线性渗流速度场趋向于平缓，在工作面附 近30\,m范围内最大风速降低到原来的0.61倍，其余大部分区域速度略有增加. 迭代方法满 足工程要求.     

非均匀介质散射问题的体积分方程数值解法

将非均匀介质视为某一均匀背景介质中的扰动，可建立用均匀背景介质格林函数作基本解的体积分方程．给出了配置法求解体积分方程的数值方法，首先解得扰动域内各点以速度扰动为权的波场函数，然后回代计算得到观测面上各接收点的散射波场．与边界元法和Ｂｏｒｎ近似法计算结果比较表明该方法具有很高的精度，可得到穿过非     

多介质流体非守恒律欧拉方程组的数值计算方法

对多介质流体在界面处满足的Euler方程进行了探讨,方程组中增加了描述材料参数间断性质的对流形式非守恒律方程组 .以波传播算法为基础,通过Roe方程近似求解Riemann问题,同时采用相同的数值差分格式求解流体动力学Euler方程组和界面方程组.该方法可以有效消除多介质流体在界面处压力、速度可能出现的非物理振荡.给出了部分典型一维和二维数值计算结果.     

弹塑性激波衰减规律的一种简便解法

本文提出了一个求解弹塑性激波衰减规律的级数解法,给出了各未知量级数展式的通项表达式。同时给出了塑性激波后方弹性卸载区内的应力和质点速度分布规律。该方法简单方便,级数收敛得很快。     

求解二维结构-声耦合问题的一种半数值半解析方法

基于传递矩阵法和虚拟源强模拟技术提出了一种求解在谐激励作用下二维结构-声相互作用问题的半数值半解析法．在足够小的积分步长内，文中对任意形状弹性环沿周向曲线坐标的非齐次状态微分方程组，建立了一种齐次扩容方法．对于外声场，采用多圆形虚拟源强配置方案。并在每一条圆形配置曲线上将源强密度函数用Fourier级数展开，同时结合快速Fourier变换法，提出了一种高精度、高效率求解任意形状二维孔穴Helmholtz外问题的快速算法．在耦合方程的求解方面，根据叠加原理，将外激励和虚拟源强的Fourier级数展开项作为广义力分别作用在弹性环上，借助齐次扩容方法和精细积分法求得弹性环的状态向量，再利用流固交接条件和最小二乘法直接建立了耦合系统的求解方程．文中给出了二个典型弹性环在集中谐激励力作用下声辐射算例，计算结果表明该文方法较通常采用的混合FE-BE法更为有效．     

层状饱和土Biot固结问题状态空间法

针对饱和多孔介质空间非轴对Biot固结问题，引入状态变量，构造了两组相比独立的状态变量方程，利用Fourier级数和Laplace-Hankel变换，将状态变量方程转换为两组一阶常微分方程组，提出了均质饱和多孔介质空间非轴对称Biot固结问题的传递矩阵，得到以状态变量和传递矩阵乘积的形式表示的均质饱和多孔介质空间非轴对称Biot固结问题的解，利用层间完全接触的条件，可得到N层饱和多孔介质空间非轴对称Biot固结问题的一般解析表达式，文中考虑几种不同的边界条件，分析了两个算例，数值结果表明该方法具有较高的计算精度和良好的计算稳定性。     

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.     

非均质流固耦合介质轴对称动力问题时域解

将地基视为流固两相介质并考虑其非均质成层特性，推导了多层地基动力问题时域解．文中首先建立了一组解耦的两相介质动力控制方程；而后利用Ｌａｐｌａｃｅ－Ｈａｎｋｅｌ变换推导了单层地基象空间初参数解答；再利用初参数法及传递矩阵技术导出了任意多层地基瞬态解的一般解析算式．本文获得的解答可方便地退化为现有理想弹性介质的解答     

层状层电介质空间轴对称问题的状态空间解

从横观各向同性压电介质空间轴对称问题的基本方程出发,建立了压电介质空间轴对称问题的状态变量方程,对状态变量方程进行Hankel变换,得到以状态变量表示的单层压电介质在Hankel变换空间中的解,讨论了3种不同特征根的情况,利用提出的解得到了半无限压电体在垂直集中载荷和点电荷作出下的Boussinesq解。利用传递矩阵方法导出了多层压电介质空间轴对称问题解一般解析式。     

The state vector methods for space axisymmetric problems in multilayered piezoelectric media

The state vector equations for space axisymmetric problems of transversely isotropic piezoelectric media are established from the basic equations. Using the Hankel transform, the state vector equations are reduced to a system of ordinary differential equations. An analytical solution of the problems in the Hankel transform space is presented in the form of the product of initial state vector and transfer matrix. The transfer matrices are given for the three distinct eigenvalues. Applications of the solutions are discussed. An analytical solution for the transversely isotropic semi-infinite piezoelectric media subjected to concerted point loads on the surface z=0 is presented in the Hankel transform space. Using transfer matrix and the continuity conditions at the layer interfaces, the general solution formulation of N-layered transversely isotropic piezoelectric media is given. A selected set of numerical solutions is presented for a layered semi-infinite piezoelectric solid.     

3-D CONSOLIDATION ANALYSIS OF LAYERED SOIL WITH ANISOTROPIC PERMEABILITY USING ANALYTICAL LAYER-ELEMENT METHOD

Starting with governing equations of a saturated soil with anisotropic permeability and based on multiple integral transforms,an analytical layer-element equation is established explicitly in the Laplace-Fourier transformed domain.A global matrix of layered soil can be obtained by assembling a set of analytical layer-elements,which is further solved in the transformed domain by considering boundary conditions.The numerical inversion of Laplace-Fourier transform is employed to acquire the actual solution.Numerical analysis for 3-D consolidation with anisotropic permeability of a layered soil system is presented,and the influence of anisotropy of permeability on the consolidation behavior is discussed.     

平面应变 Biot 固结的解析层元

提出用解析层元法有效地解决任意深度单层土的平面应变 Biot 固结问题. 从 Biot 固结问题的控制方程出发, 采用特征值法在 Laplace-Fourier 变换域内推导出一个精确对称的解析层元刚度矩阵. 通过表示单层土广义力和广义位移之间关系的解析层元, 并结合土层的边界条件, 推导出土层任意点的解答; 物理域内的真实解可以通过 Laplace-Fourier 数值逆变换进一步获得. 通过数值计算验证理论的正确性, 研究了土层性质及时间因素对固结的影响.}      

Exact solutions of multi-term fractional diffusion-wave equations with Robin type boundary conditions

General exact solutions in terms of wavelet expansion are obtained for multi- term time-fractional diffusion-wave equations with Robin type boundary conditions. By proposing a new method of integral transform for solving boundary value problems, such fractional partial differential equations are converted into time-fractional ordinary differ- ential equations, which are further reduced to algebraic equations by using the Laplace transform. Then, with a wavelet-based exact formula of Laplace inversion, the resulting exact solutions in the Laplace transform domain are reversed to the time-space domain. Three examples of wave-diffusion problems are given to validate the proposed analytical method.     

Exact solutions of multi-term fractional difusion-wave equations with Robin type boundary conditions

General exact solutions in terms of wavelet expansion are obtained for multiterm time-fractional difusion-wave equations with Robin type boundary conditions. By proposing a new method of integral transform for solving boundary value problems, such fractional partial diferential equations are converted into time-fractional ordinary diferential equations, which are further reduced to algebraic equations by using the Laplace transform. Then, with a wavelet-based exact formula of Laplace inversion, the resulting exact solutions in the Laplace transform domain are reversed to the time-space domain. Three examples of wave-difusion problems are given to validate the proposed analytical method.     

Simulation of elastic wave diffraction by multiple strip-like cracks in a layered periodic composite

The problem of numerical simulation of the steady-state harmonic vibrations of a layered phononic crystal (elastic periodic composite) with a set of strip-like cracks parallel to the layer boundaries is solved, and the accompanying wave phenomena are considered. The transfer matrix method (propagator matrix method) is used to describe the incident wave field. It allows one not only to construct the wave fields but also to calculate the pass bands and band gaps and to find the localization factor. The wave field scattered by multiple defects is represented by means of an integral approach as a superposition of the fields scattered by all cracks. An integral representation in the form of a convolution of the Fourier symbols of Green’s matrices for the corresponding layered structures and a Fourier transform of the crack opening displacement vector is constructed for each of the scattered fields. The crack opening displacements are determined by the boundary integral equation method using the Bubnov-Galerkin scheme, where Chebyshev polynomials of the second kind, which take into account the behavior of the solution near the crack edges, are chosen as the projection and basis systems. The system of linear algebraic equations with a diagonal predominance of components arising when the system of integral equations is discretized has a block structure. The characteristics describing qualitatively and quantitatively the wave processes that take place under the diffraction of plane elastic waves by multiple cracks in a phononic crystal are analyzed. The resonant properties of a system of defects and the influence of the relative positions and sizes of defects in a layered phononic crystal on the resonant properties are studied. To obtain clearer results and to explain them, the energy flux vector is calculated and the energy surfaces and streamlines corresponding to them are constructed.