饱和土埋置力源的三维动力Lamb问题解答

基于一组弹性土波动方程，应用Fourier级数展开和Hankel积分变换，得到了三维问题饱和土骨架与孔隙水的应力及位移分量在变换域内的积分形式通解．考虑地基表面透水情形，由边界条件导出了半空间饱和土体在埋置力源作用下的三维动力Lamb问题的解答．给出了埋置水平力作用下地基表面竖向位移、径向位移及周向位移的数值解．该研究为运用边界元法求解饱和地基的动力响应课题奠定了理论基础．     

考虑在地基固结和流变的上部结构和地基基础的共同作用问题

本文提出一种能同时考虑地基的瞬时变形,团结变形和流变的地基基础与上部结构共同作用的一种新的计算方法,在这种方法中,土的计算考虑了Biot固结理论和流变,上部结构利用子结构法进行凝聚可得边界刚度矩阵和边界力,利用位移协讯条件则可以得到共同作用的控制方程,对上述方程进行Laplace变换,可以得到Laplace变换域内的控制方程,在Laplace变换域内对上述方程进行数值求解并进行相应的Laplace逆变换则可以得到时间境内任意时刻的解。     

A PRECISE INTEGRATION APPROACH FOR THE DYNAMIC-STIFFNESS MATRIX OF STRIP FOOTINGS ON A LAYERED MEDIUM 1）

提出应用精细积分算法计算多层地基的动力刚度问题.精细积分是计算层状介质中波传播的高效而精确的数值方法.利用傅里叶积分变换将层状地基的波动方程转换为频率-波数域内的两点边值问题的常微分方程组,运用精细积分方法求解格林函数,最后再将得到的频率-波数域内地基表面的动力刚度矩阵转换到频率-空间域内,进而得到刚性条带基础频率域的动力柔度或刚度矩阵.所建议的精细积分算法,可以避免一般传递矩阵计算中的指数溢出问题,对各种情况有广泛的适应性,计算稳定,在高频段可以保障收敛性,并能达到较高的计算精度.     

边界元分析薄板自由振动问题的一个近似方法

本文提出边界元法分析域内具有支承及集中质量的薄板自由振动问题的近似方法，该方法在利用基本解的基础上，将域内积分化为边界积分来处理，节省了工作量，文中计算实例结果表明，该方法的精度满足实际工程的要求。．     

多层地基条带基础动力刚度矩阵的精细积分算法

提出应用精细积分算法计算多层地基的动力刚度问题. 精细积分是计算层状介质中波传播的高效而精确的数值方法. 利用傅里叶积分变换将层状地基的波动方程转换为频率-波数域内的两点边值问题的常微分方程组, 运用精细积分方法求解格林函数, 最后再将得到的频率-波数域内地基表面的动力刚度矩阵转换到频率-空间域内, 进而得到刚性条带基础频率域的动力柔度或刚度矩阵. 所建议的精细积分算法, 可以避免一般传递矩阵计算中的指数溢出问题, 对各种情况有广泛的适应性, 计算稳定, 在高频段可以保障收敛性, 并能达到较高的计算精度.      

考虑离心体力的直线单元的解析法

对于体积力问题，可将体积力的域内积分转换为边界上的积分运算[1]，这将减少域内划分单元，使边界元法处理体积力时更简秉方便，本文在文[1]和[2]的基础上，提出用单元的解析积分取代数值积分，计算离心体力问题，推导了相应的直线单元即常单元和线性单元的解析式，算例表明，本文方法数值精度高，尤其在造近边界的内点时，效果迹较好。     

流体晃动时域双协边界元法分析

利用双协边界元法在时域内对流体晃动问题进行分析,推导出边界积分方程及相应的边界条件。分析过程中考虑流体的粘性,自由面上的动力学条件为法向正应力和切向剪应力为零。固壁面上采用流体质点与固壁质点速度相等的条件。时域的离散采用差分法,并利用时间步迭代,逐步追踪流体自由面,在流体的不断变动的边界上考虑其边界条件。数值结果表明本文的双协边界元法是可行的。     

弹性动力学的双互易杂交边界点法

将双互易法同杂交边界点法相结合,提出了求解弹性动力问题的新型数值方法------双互易杂交边界点方法. 该算法在求解弹性动力问题时,将控制方程非齐次项的域内积分转化为边界积分. 该方法将问题的解分为通解和特解两部分,通解使用杂交边界点法求得,特解则使用局部径向基函数插值得到,从而实现了使用静力问题的基本解来求解动力问题. 计算时仅仅需要边界上离散点的信息,无论积分还是插值都不需要网格,域内节点仅用来插值非齐次项,因此该算法仍是一种边界类型的无网格方法. 数值算例表明,该方法后处理简单,计算精度高,适合于求解弹性动力问题.      

薄体位势问题边界元法中的解析积分算法

薄体结构的数值分析是边界元法的难点问题之一。该文导出了一种完全解析积分算法，用这种算法计算了薄体平面位势问题边界元法中出现的几乎弱奇异、强奇异和超奇异积分。当边界离散为一系列线性单元，边界积分方程离散计算的积分可归纳为三种形式。对薄体问题，源点与积分单元距离通常相距很近，这些积分产生显著几乎奇异性，直接采用常规高斯积分不能有效计算。为此该文导出了这些几乎奇异积分的全解析计算公式。按源点与单元的距离是否为零，公式分两种情况。新算法采用全解析积分公式处理几乎奇异积分，首先精确计算出薄体问题边界未知位势和法向位势梯度，然后再进一步计算了域内点的物理参量。算例表明该文算法可处理狭长比为1．E-08的薄体问题，显示了边界元法分析薄体问题具有独特的优势。     

物体边界层域内位移及应力的边界元法新公式

1.前言当分析塑性加工工具表层剥落破坏原因和求解断裂力学强度因子或其他工程问题时,仅计算物体表面应力是不够的,还需要计算边界层域内的位移及应力场。用边界元法计算上述工程问题时,当域内点和边界积分点距离足够小时,基本解中     

双参数弹性地基板计算新方法

弹性地基板的弯曲问题,尤其是自由边板,一直是学者和工程师们所十分关切的问题。本文用无单元法研究双参数弹性地基板的弯曲问题,由最小二乘法和变分原理导出了双参数弹性地基板的无单元法刚度短阵,编制相应的无单元法计算程序,并给出计算实例。结果表明本方法精度良好,可求出任意荷载作用下板中任一点的挠度、转角、弯矩和扭矩,且有广泛的工程应用前景。     

梯度弹性基础上正交异性薄板的弯曲

基于能量法和变分原理,采用双参数弹性基础模型,研究了梯度弹性基础上正交异性薄板在分布载荷作用下的弯曲问题。首先,根据能量法与变分原理,给出了梯度弹性基础上正交异性薄板的弯曲微分平衡方程,并得到了梯度弹性基础刚度系数 与 的计算表达式;进而,假设 向正应力在厚度方向上均匀分布,推导了弹性基础 向位移衰减函数 的计算式。在算例中,通过将梯度弹性基础退化为均质基础,并与Vlazov模型对比,证明了本文理论的正确性;最后,求解了弹性模量呈幂律分布的梯度基础上薄板的挠度分布,分析了基础上下表层材料弹性模量比 与体积分数指数 对薄板挠度分布的影响。     

Iterative technique for circular thin plates on Gibson elastic foundation using modified Vlasov model

In this paper, to investigate the influence of soil inhomogeneity on the bending of circular thin plates on elastic foundations, the static problem of circular thin plates on Gibson elastic foundation is solved using an iterative method based on the modified Vlasov model. On the basis of the principle of minimum potential energy, the governing differential equations and boundary conditions for circular thin plates on modified Vlasov foundation considering the characteristics of Gibson soil are derived. The equations for the attenuation parameter in bending problem are also obtained, and the issue of unknown parameters being difficult to determine is solved using the iterative method. Numerical examples are analyzed and the results are in good agreement with those form other literatures. It proves that the method is practical and accurate. The inhomogeneity of modified Vlasov foundations has some influence on the deformation and internal force behavior of circular thin plates. The effects of various parameters on the bending of circular plates and characteristic parameters of the foundation are discussed. The modified model further enriches and develops the elastic foundations. Relevant conclusions that are meaningful to engineering practice are drawn.     

Analysis of bending, vibration and stability for thin plate on elastic foundation by the multivariable spline element method

I.IntroductionTheplatestructuresonelasticfoundationareofpracticalimportanceinwide-spreadapplicationsinengineering.Basedonrapidprogressofscienceandtechnologyaswellasengineeringconstructions,differentmodelsofeIasticfoundationaredeve1oped,sucha,Winkler,Vlazo…     

Modeling and analysis of micro-sized plates resting on elastic medium using the modified couple stress theory

Analytical solutions for bending, buckling, and vibration of micro-sized plates on elastic medium using the modified couple stress theory are presented. The governing equations for bending, buckling and vibration are obtained via Hamilton’s principles in conjunctions with the modified couple stress and Kirchhoff plate theories. The surrounding elastic medium is modeled as the Winkler elastic foundation. Navier’s method is being employed and analytical solutions for the bending, buckling and free vibration problems are obtained. Influences of the elastic medium and the length scale parameter on the bending, buckling, and vibration properties are discussed.     

The exact solution for the general bending problems of conical shells on the elastic foundation

The general bending problem of conical shells on the elastic foundation (Winkler Medium) is not solved. In this paper, the displacement solution method for this problem is presented. From the governing differential equations in displacement form of conical shell and by introducing a displacement function U(s,θ), the differential equations are changed into an eight-order soluble partial differential equation about the displacement function U(s,θ) in which the coefficients are variable. At the same time, the expressions of the displacement and internal force components of the shell are also given by the displacement function U(s θ). As special cases of this paper, the displacement function introduced by V.S. Vlasov in circular cylindrical shell^[5], the basic equation of the cylindrical shell on the elastic foundation and that of the circular plates on the elastic foundation are directly derived.Under the arbitrary loads and boundary conditions, the general bending problem of the conical shell on the elastic foundation is reduced to find the displacement function U(s,θ).The general solution of the eight-order differential equation is obtained in series form. For the symmetric bending deformation of the conical shell on the elastic foundation, which has been widely usedinpractice,the detailed numerical results and boundary influence coefficients for edge loads have been obtained. These results have important meaning in analysis of conical shell combination construction on the elastic foundation,and provide a valuable judgement for the numerical solution accuracy of some of the same type of the existing problem.     

CC series solution for bending of rectangular plates on elastic foundations

The analytical solution for the bending problem of the rectangular plates on an elastic foundation is investigated by using the Stockes' transformation of a double variables function. The numerical results for the rectangular plates with free edges on the elastic foundations under a concentrated force are given in the example. First Received Dec. 14 1993     

The general solution for axial symmetrical bending of nonhomogeneous circular plates resting on an elastic foundation

In this paper,a new method,the exact analytic method,is presented on the basis of stepreduction method.By this method,the general solution for the bending of nonhomogenouscircular plates and circular plates with a circular hole at the center resting,on an elastfcfoundation is obtained under arbitrary axial symmetrical loads and boundary conditions.The uniform convergence of the solution is proved.This general solution can also be applieddirectly to the bending of circular plates without elastic foundation.Finally,it is onlynecessary to solve a set of binary linear algebraic equation.Numerical examples are givenat the end of this paper which indicate satisfactory results of stress resultants anddisplacements can be obtained by the present method.     

基于无网格法的非均匀弹性地基上变厚度加筋板弯曲与固有频率分析

采用基于移动最小二乘近似的无网格方法并结合一阶剪切变形理论,分析了非均匀弹性地基上变厚度加筋板的弯曲和固有频率问题.首先,用节点对变厚度板和筋条分别进行离散,导出变厚度板和筋条的势能;其次,利用筋条与变厚度板之间的位移协调条件将筋条的节点参数转换为板的节点参数,再将两者的势能进行叠加得到变厚度加筋板的总势能,并根据能量法得到其动能;最后,利用最小势能原理及Hamilton原理分别得到弯曲控制方程与振动控制方程.由于采用的方法不能直接施加位移边界,故采用完全转换法处理位移边界.本文先计算变厚度板的弯曲及非均匀弹性地基板的固有频率,与文献对比验证方法的有效性;然后对非均匀弹性地基上变厚度加筋板弯曲与 自由振动进行了计算,并将计算结果与有限元结果进行了对比.结果表明,本文方法计算所得结果与文献解及有限元结果之间的误差均小于5％,验证了该方法在计算非均匀弹性地基上变厚度加筋板弯曲与固有频率问题的有效性.     

Nonlinear bending behavior of orthotropic Mindlin plate resting on orthotropic Pasternak foundation using GDQM

Rectangular plates resting on elastic foundations are operational activities of large transportation aircraft on runways, footings, foundation of spillway dam, civil building in cold regions, and bridge structures. Hence, in the present work, nonlinear bending analysis of embedded rectangular plates is investigated based on orthotropic Mindlin plate theory. The elastic medium is simulated by orthotropic Pasternak foundation. Adopting the nonlinear strain–displacement relation, the governing equations are derived based on energy method and Hamilton’s principle. The generalized differential quadrature method is performed for the case when all four ends are clamped supported. The influences of the plate thickness, shear-locking, elastic medium constants, and applied force on the nonlinear bending of the rectangular plate are studied. Results indicate that increasing the plate thickness decreases the deflection of the plate. It is also observed that increasing the applied force increases the deflection of the plate. Furthermore, considering elastic medium decreases deflection of the plate, and the effect of the Pasternak-type is higher than the Winkler-type on the maximum deflection of the plate. Also, it is found that the present results have good agreement with previous researches.