考虑地基耦合效应含裂纹中厚矩形板的非线性振动分析

基于Reissner板理论和Hamilton变分原理,建立了双参数地基上具有表面横向贯穿裂纹的中厚矩形板的非线性运动控制方程.在周边自由的条件下,提出了一组满足问题全部边界条件和裂纹处连续条件的试函数.且利用Galerkin法和谐波平衡法对方程进行求解,分析了考虑地基耦合效应的中厚矩形裂纹板的非线性振动特性.数值计算中,讨论了不同裂纹位置、裂纹深度、板的结构参数和地基物理参数对弹性地基上具裂纹的四边自由中厚矩形板的非线性幅频响应的影响.     

关于求解弹性力学平面问题的功的互等定理法

本文推广功的互等定理法于求解具有复杂边界条件矩形板的弹性力学平面问题.首先,我们给出了作为基本系统的四边固定矩形板平面问题的基本解,然后基于在具有复杂边界条件的实际系统与基本系统之间应用功的互等定理,从而求得实际系统的位移表达式.当只存在位移边界条件时,用功的互等定理法求得的位移表达式就是真实的.但是在另一些情况下,当有静力边界条件或混合边界条件时,所求得的位移是容许的.为求得真实位移.必须应用最小势能原理.一些计算表明.对于求解具有复杂边界条件的矩形板弹性力学平面问题,功的互等定理法是一简便通用的方法.显然,这是一个新方法.     

与线弹性结构连接的弹性基础圆板大挠度问题

本文处理边界与线弹性结构连接的弹性基础圆板的轴对称大挠度问题.用混合边界条件方法[1]建立了问题的确定积分方程组,并进行了简化.用摄动法给出了解答.计算了圆板与圆柱壳组合问题的例子.     

万因斯坦-钱伟长法的应用——简支与固支混合边界矩形板基频上下限

本文将边界条件放松法[1][2]应用于简支与固支混合边界矩形板,求得此类板的基频下限值.文中还设计了一种能满足位移边界条件的多项式作为振型试函数,从而用里兹法得到相应的上限值.具体算例得到了满意的结果.最后本文指出,通常用力法迭加法得到的此类板的所谓精确解,若考虑实际计算的级数截断误差,本质上是一种下限解.     

双参数弹性地基上自由边矩形板

本文以迭加法[1]给出在V. Z. Vlazov双参数弹性地基上自由边矩形板的精确解.文中导出了在各种边界条件下的基本解式,迭加这些基本解式,求得了在双参数弹性地基上自由边矩形板的最一般的精确解.它严格满足双参数弹性地基上板的控制微分方程和自由边的边界条件和角点条件.给出了数值结果.计算结果表明:当板的平面尺寸一定,地基深度与板厚度之比H/h=15时,双参数弹性地基与Winkler弹性地基相接近,证明了Winkler地基模式适用于压缩尺寸比较薄的弹性地基.     

弹性地基上的自由边矩形板

本文讨论了在弹性地基上的自由边矩形板的弯曲问题.我们讨论了两种情形,诸如在板的中心受到一集中力作用和在板的四个角点上各受到一相等的集中力作用.文中选择了一个挠曲函数,它不但能满足所有自由边上的全部几何边界条件,而且也满足所有的内力边界条件.同时,我们应用了变分法,从而得到了较好的近似解答.     

板弯曲断裂计算的边界配置解法

采用复变函数理论和边界配置方法,分析计算了Kirchhoff板的弯曲断裂问题.假设了位移及内力的复变函数式,它们能满足一系列的基本方程和支配条件,例如域内的平衡方程、裂纹表面的边界条件、裂纹尖端的应力奇异性质.这样,仅板边界的边界条件需要考虑.它们可用边界配置法和最小二乘法近似满足.对不同边界条件和载荷情形进行了分析计算.数值算例表明,本文方法精度较高,计算量小,是一种有效的半解析、半数值计算方法.     

面内功能梯度三角形板等几何面内振动分析

基于平面应变理论,利用等几何有限元方法分析了弹性边界条件下面内功能梯度三角形板的面内振动特性.板的材料属性沿厚度方向呈均匀分布,而在面内方向呈任意指数梯度变化.采用非均匀有理B样条(NURBS)基函数对三角形结构进行等几何建模和位移描述,实现了三角形板几何设计和振动分析的无缝衔接.在三角形板边界上引入虚拟弹簧约束并通过调节虚拟弹簧刚度,实现任意边界条件的施加.通过不同的单元细化方案和对比算例,验证了等几何方法的灵活性、准确性和快速收敛性.系统研究了边界条件、材料属性和几何参数对三角形板振动特性的影响.同时给出了弹性边界条件下面内功能梯度三角形板的振动特性解,具有重要参考价值.     

应用虚拟功的互等定理求解均载悬臂厚矩形板的弯曲

悬臂矩形板的弯曲问题一直是平板经典理论中的著名难题,利用中厚板虚拟功的互等定理,借助付宝连提出的角点静力边界条件,得到了均布载荷作用下悬臂厚矩形板弯曲的封闭解析解,并采用现代数值方法和计算软件对所得解析解进行了数值计算.结果表明功的互等法是求解中厚板弯曲问题的一个简明有效的方法.     

无限域拉普拉斯方程问题的高阶边界条件及其应用

对无限域Laplace方程问题,推导出了高阶边界条件.在采用数值方法的有限域的外边界上应用高阶边界条件,可以在保证计算精度的前提下缩小数值求解域,从而减小计算工作量和少占用计算机内存.数值算例表明,一阶边界条件近似于精确边界条件,它明显地优于经典边界条件和二阶边界条件.     

Analysis of free-edge effects by boundary finite element method

The scaled boundary finite element method is a novel semi-analytical analysis technique that combines the advantages of the finite element method and the boundary element method. Only a part of the boundary of the considered domain has to be discretized but nevertheless the method is solely finite element based. The governing equations are solved in the so-called scaling direction analytically, whereas a finite element approximation of the solution is performed in the circumferential directions, which form the boundary of the considered domain. Thus, the numerical effort can be reduced considerably when handling stress concentration problems such as e.g. the free-edge effect in laminated plates. In order to analyze the free-edge effect in a semi-infinite half plane, some kinematic coupling equations have to be introduced, that not only couple the degrees of freedom on the boundary, but also within the non-discretized domain. The implementation of kinematic coupling equations within the method is presented. Finally, the efficiency of the new approach is shown in some benchmark examples. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An Iterative FEM for Solving Wave Problems of a Halfspace

An iterative finite element method for solving wave problems of a halfspace is presented in this paper. The halfspace is first truncated by introducing a fictive finite boundary on which some fictive boundary conditions must be imposed. A finite computational domain is in each iteration subjected to actual boundary conditions on real boundary and to fictive Dirichlet or Neumann boundary conditions on the fictive boundary. The radiation condition is satisfied by using DtN operator. The DtN operator is not introduce in the finite element formulation on the fictive boundary so any finite elements can be used. The method is simple and specially useful for computing higher harmonics.     

Numerical solution for the model of vibrating elastic membrane with moving boundary

In this work, we are interested in obtaining an approximated numerical solution for the model of vibrating elastic membranes with moving boundary. The model is an extension of Kirchhoff’s model, which takes into account the change of size during the vibration. We apply the finite element method with a finite difference method in time to obtain an approximated numerical solution. Some numerical experiments are presented to show the effect of moving boundary effects in vibrating elastic membranes.     

Convergence of a Bakhvalov grid adaptation method for singularly perturbed boundary value problems

In this paper, a Galerkin finite element method for non-self-adjoint boundary value problems on Bakhvalov grids is considered. Using the Galerkin projectionmethod, the convergence of a sequence of computational grids with an unknown boundary of the boundary layer is proved. Some numerical examples are presented.     

边界层问题的小波—有限元解

本文将小波分析与有限元法结合起来，建立了一种小波－有限元计算格式，并用该算法计算了一个典型的边界层问题，探讨了寻找边界层位置的过程以及计算边界层区的内部解及外部解的步骤。计算结果表明，用该法寻找的边界层位置以及所求得的内部解与真实结果完全符合。     

A finite element method for granular flow through a frictional boundary

A finite element method for the flow of dry granular solids through a domain involving a frictional contact boundary is formulated. The granular material is assumed as a compressible viscous-elastic–plastic continuum. Based on the principles of continuum mechanics, a complete set of equations is developed. The resulting boundary value problem is solved by the finite element method in space and by the finite difference method in time. The derivation of the finite element equations and the mathematical framework of the numerical technique are presented, together with two illustrative examples to demonstrate the validity of the technique.     

A full multigrid method for nonlinear eigenvalue problems

We introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of the nonlinear eigenvalue problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and nonlinear eigenvalue problems on the coarsest finite element space. The linearized boundary value problems are solved by some multigrid iterations. Besides the multigrid iteration, all other efficient iteration methods for solving boundary value problems can serve as the linear problem solver. We prove that the computational work of this new scheme is truly optimal, the same as solving the linear corresponding boundary value problem. In this case, this type of iteration scheme certainly improves the overfull efficiency of solving nonlinear eigenvalue problems. Some numerical experiments are presented to validate the efficiency of the new method.     

求解Brinkman方程的修正弱有限元方法

本文针对Brinkman方程引入了一种修正弱Galerkin(MWG)有限元方法.我们通过具有两个离散弱梯度算子的变分形式来逼近模型. 在MWG方法中, 分别用次数为$k$和$k-1$的不连续分段多项式来近似速度函数$u$和压力函数$p$. MWG方法的主要思想是用内部函数的平均值代替边界函数. 因此, 与WG方法相比, MWG方法在不降低准确性的同时, 具有更少的自由度, 对于任意次数不超过$k-1$ 的多项式,MWG方法均可以满足稳定性条件. MWG 方法具有高度的灵活性, 它允许在具有一定形状正则性的任意多边形或多面体上使用不连续函数. 针对$H^1$和$L^22$范数下的速度和压力近似解, 建立了最优阶误差估计. 数值算例表明了该方法的准确性, 收敛性和稳定性.     

Energetic BEM-FEM coupling for the numerical solution of the damped wave equation

Time-dependent problems modeled by hyperbolic partial differential equations can be reformulated in terms of boundary integral equations and solved via the boundary element method. In this context, the analysis of damping phenomena that occur in many physics and engineering problems is a novelty. Starting from a recently developed energetic space-time weak formulation for the coupling of boundary integral equations and hyperbolic partial differential equations related to wave propagation problems, we consider here an extension for the damped wave equation in layered media. A coupling algorithm is presented, which allows a flexible use of finite element method and boundary element method as local discretization techniques. Stability and convergence, proved by energy arguments, are crucial in guaranteeing accurate solutions for simulations on large time intervals. Several numerical benchmarks, whose numerical results confirm theoretical ones, are illustrated and discussed.     

THE BOUNDARY INTEGRO-DIFFERENTIAL EQUATIONS OFA BIHARMONIC BOUNDARY VALUE PROBLEM

1.IntroductionWeconsiderahomogeneousisotropicandlinearelasticKirchhoffplateunderlateralloaddistributedovertheplatefix[--t,t].ThedomainfiERZisboundedwiththesmoothboundaryr.Inthestaticequilibrium,weconsiderthefreetypeboundaryconditiononr.Thenthedeflectionusatisfiesthefollowingproblem:whereD~--E0h'.12(1--ac,isthebendingstiffnessoftheplatewithhbeingtheplatethicknessandEOandu(0相似文献