基于Wilson-θ和Newmark-β法的非线性动力学方程改进算法

Wilson-θ法和Newmark-β法是非线性动力学方程求解的常用方法。它们的一个基本步骤是,将方程改写为增量平衡的形式,在每一个积分步长内用状态参量修正平衡方程的系数矩阵,其本质是在单个步长内对系统的非线性环节进行了线性化处理。本文基于增量思想分别改进了Wilson-θ法和Newmark-β法,根据即时解给出下一步的猜测解,然后对猜测解进行迭代校正,最终得到收敛的近似解。算例表明,改进算法的精度更高,且收敛准则简单。更为重要的是,本文方法无须对非线性项进行线性化处理,因而计算效率更高,适应范围更广。     

内时弹塑性力学边界积分理论和边界元计算(一)

本文根据贝蒂理论,应用拟弹性方法,建立了内时弹塑性力学的适于数值计算的边界积分方程,其中包括空间问题和平面问额。而后根据它们给出了球壳问题的增量解析解计算式。我们在“内时弹塑性力学边界积分理论和边界元计算(二)”中依据(一)所建立的方程给出了几个轴对称问题的全量解析解。从比较结果可知本文建立的方程是有效且有用的。对于难于求得解析解的复杂问题我们将在以后的文章中进行边界元数值计算。     

基于Wilson-θ和Newmark-β法的非线性动力学方程改进算法

Wilson-θ法和Newmark-β法是非线性动力学方程求解的常用方法。它们的一个基本步骤是,将方程改写为增量平衡的形式,在每一个积分步长内用状态参量修正平衡方程的系数矩阵,其本质是在单个步长内对系统的非线性环节进行了线性化处理。本文基于增量思想分别改进了Wilson-θ法和Newmark-β法,根据即时解给出下一步的猜测解,然后对猜测解进行迭代校正,最终得到收敛的近似解。算例表明,改进算法的精度更高,且收敛准则简单。更为重要的是,本文方法无须对非线性项进行线性化处理,因而计算效率更高,适应范围更广。     

虚功原理的变分不等方程及在物理非线性问题中的应用

文中给出了虚功原理的另一形式——适应于不同本构关系的物理非线性和边界非线性的变分不等式,使用增量理论可以归结为求解线性互补方程的数值计算方法,     

变厚度板弯曲的边界元分析法

由于变厚度板弯曲问题的控制分方程复杂，直接求解其基本解推导边界积分方程建立边界元分析法较为困难，本文通过引入等效荷载，等效刚度，将此问题的控制微分方程化成与普通薄板弯曲问题基本方程相同的形式，利用求解通板弯曲问题的边界元迭代求解，建立了分析变厚度板弯曲问题的蛤法，算例表明本方法理正确，精度良好。     

利用格林函数方法数值求解不可压粘性流非线性问题的研究

1.概述 本文对格林函数方法用以计算不可压粘性流非线性问题的能力进行了研究.该方法将定常运动的边值问题化为求解速度和边界应力的非线性积分方程,由于积分方程系完全精确推得,且在方程中可利用格林公式将速度、应力等物理量的微商转移为对基本解的微商,因而在数值计算中处理比较容易,且精度较高.     

正交各向异性弹性问题的规则化边界元法

本文致力于平面正交各向异性弹性问题的规则化边界元法研究,提出了新的规则化边界元法的理论和方法。对问题的基本解的特性进行了研究,确立基本解的积分恒等式,提出一种基本解的分解技术,在此基础上,结合转化域积分方程为边界积分方程的极限定理,建立了新颖的规则化边界积分方程。和现有方法比,本文不必将问题变换为各向同性的去处理,从而不含反演运算,也有别于Galerkin方法,无需计算重积分,因此所提方法不仅效率高,而且程序设计简单。特别是,所建方程可计算任何边界位移梯度,进而可计算任意边界应力,而不仅限于面力。数值实施时,采用二次单元和椭圆弧精确单元来描述边界几何,使用不连续插值逼近边界函数。数值算例表明,本文算法稳定、效率高,所取得的边界量数值结果与精确解相当接近。     

内时弹塑性力学边界积分理论和边界元计算（二）

本文在文[1]的基础上应用边界积分方程求得了球壳和简体弹塑性问题的全量解析解。首先求出其增量形式的解,然后对内时标度积分求得其最终解。与经典解比较可知本文结果是较为精确和理想的。     

弹性力学中一种新的边界轮廓法

利用基本解的特性,将面力积分方程化成仅含有Ｃａｕｃｈｙ主值积分的形式,基于这种边界积分方程,提出了一种新的边界轮廓法,对于三维问题,该方法只须计算沿边界单元界线的线积分,对二维问题,则只需计算边界单元两点的热函数之差,无须进行数值积分计算,实例计算说明该方法是有效的。     

增量罚有限元位移法分析非线性橡胶类材料

本文基于增量驻值势能原理,用罚函数的概念,建立适用于不可压缩的非线性橡胶类材料的增量形式的罚有限元位移法的计算列式.这种方法能克服混合法中存在的问题.实例计算表明,罚有限元位移法的计算结果与精确解符合得很好.文中还讨论了罚数的选择方法. ...     

非均质问题中的无网格边界单元法

介绍了一种不需要内部网格计算非均匀介质问题的边界元算法.该算法是建立在一种能将任何区域积分转换成边界积分的径向积分转换法基础上,首先用对应各向同性问题的基本解来建立以正规化位移表示的非均质问题的积分方程,然后用径向积分转换法将出现在积分方程中的区域积分转换成边界积分,从而形成不需要使用内部网格来计算区域积分的纯边界元算法.与其它无网格法相比,此方法需要很少的内部点,有些问题甚至不需要内部点都能得到满意的结果,因此,可以计算大型的三维非均匀介质工程问题.由于此方法继承了边界元和无网格算法的优点,因而具有广阔的发展前景.     

Vibration of fluid-conveying pipe with nonlinear supports at both ends

The axial fluid-induced vibration of pipes is very widespread in engineering applications. The nonlinear forced vibration of a viscoelastic fluid-conveying pipe with nonlinear supports at both ends is investigated. The multi-scale method combined with the modal revision method is formulated for the fluid-conveying pipe system with nonlinear boundary conditions. The governing equations and the nonlinear boundary conditions are rescaled simultaneously as linear inhomogeneous equations and linear inhomogeneous boundary conditions on different time-scales. The modal revision method is used to transform the linear inhomogeneous boundary problem into a linear homogeneous boundary problem. The differential quadrature element method (DQEM) is used to verify the approximate analytical results. The results show good agreement between these two methods. A detailed analysis of the boundary nonlinearity is also presented. The obtained results demonstrate that the boundary nonlinearities have a significant effect on the dynamic characteristics of the fluid-conveying pipe, and can lead to significant differences in the dynamic responses of the pipe system.

     

Boundary element analysis for bending elastic plates with three generalized displacements

In this paper, the two fundamental differential equations for bending elastic plates with three generalized displacements are transformed into a set of boundary integral equations by Green formula. Three kinds of boundary conditions on edges have been strictly derived. So this paper gives a satisfactory method of boundary element analysis for solving the problem of bending elastic plates.     

Variational principles for hydrodynamic impact problems

We first establish the rigorous field equations of the two continuous stages before and after entering water. Then correspondently, we obtain the specific variational principles, bounded theorems, and boundary integral equations of the second stage problems. The existence of solutions are proved and the scheme of solving the solutions are provided. Finally, as a numerical example, the ship's wave resistence problem is used to demonstrate the specific application of the second stage problems and its accuracy. Then we provide a rigorous and sound theoretical basis of variational finite element method and boundary element method for calculating the accurately fundamental equations.     

Penalty finite element method for Navier–Stokes equations with nonlinear slip boundary conditions

The penalty finite element method for Navier–Stokes equations with nonlinear slip boundary conditions is investigated in this paper. Since this class of nonlinear slip boundary conditions include the subdifferential property, the weak variational formulation is a variational inequality problem of the second kind. Using the penalty finite element approximation, we obtain optimal error estimates between the exact solution and the finite element approximation solution. Finally, we show the numerical results which are in full agreement with the theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.     

Complex variable bem solution for half-plane problems with straight boundary clamped

In this paper, a new complex variable fundamental solution which satisfies the clamped boundary conditions of half-plane problem has been derived by use of Riemann-Schwarz symmetric principle and the mathematical theory of elasticity. The correspondent complex variable boundary integral equations for elastic analysis have been given. Numerical procedure shows more efficiency and advantages of the present method over conventional boundary element method.     

Transient heat conduction analysis using the NURBS-enhanced scaled boundary finite element method and modified precise integration method

The Non-uniform rational B-spline(NURBS)enhanced scaled boundary finite element method in combination with the modified precise integration method is proposed for the transient heat conduction problems in this paper.The scaled boundary finite element method is a semi-analytical technique,which weakens the governing differential equations along the circumferential direction and solves those analytically in the radial direction.In this method,only the boundary is discretized in the finite element sense leading to a reduction of the spatial dimension by one with no fundamental solution required.Nevertheless,in case of the complex geometry,a huge number of elements are generally required to properly approximate the exact shape of the domain and distorted meshes are often unavoidable in the conventional finite element approach,which leads to huge computational efforts and loss of accuracy.NURBS are the most popular mathematical tool in CAD industry due to its flexibility to fit any free-form shape.In the proposed methodology,the arbitrary curved boundary of problem domain is exactly represented with NURBS basis functions,while the straight part of the boundary is discretized by the conventional Lagrange shape functions.Both the concepts of isogeometric analysis and scaled boundary finite element method are combined to form the governing equations of transient heat conduction analysis and the solution is obtained using the modified precise integration method.The stiffness matrix is obtained from a standard quadratic eigenvalue problem and the mass matrix is determined from the low-frequency expansion.Finally the governing equations become a system of first-order ordinary differential equations and the time domain response is solved numerically by the modified precise integration method.The accuracy and stability of the proposed method to deal with the transient heat conduction problems are demonstrated by numerical examples.     

敷设多孔吸声材料声腔特征值分析的径向积分边界元法

由于Helmholtz方程的基本解是频率的函数,因此传统边界元法在处理声场特征值问题时具有天生的缺陷。本文采用Laplace方程基本解生成积分方程,通过径向积分法将在此过程中产生的域积分项转化为边界积分。此方法克服了传统边界元法系数矩阵对频率的依赖,同时克服了特解积分法对特解的依赖,并通过对表面声导纳的多项式逼近,将敷设多孔吸声材料声腔特征值问题转化为矩阵多项式,从而避免了复杂的非线性求解。通过数值算例验证了算法的有效性。     

PERTURBATION FINITE ELEMENT METHOD FOR SOLVING GEOMETRICALLY NONLINEAR PROBLEMS OF AXISYMMETRICAL SHELL

In analysing the geometrically nonlinear problem of an axisymmetrical thin-walled shell, the paper combines the perturbation method with the finite element method by introducing the former into the variational equation to obtain a series of linear equations of different orders and then solving the equations with the latter. It is well-known that the finite element method can be used to deal with difficult problems as in the case of structures with complicated shapes or boundary conditions, and the perturbation method can change the nonlinear problems into linear ones. Evidently the combination of the two methods will give an efficient solution to many difficult nonlinear problems and clear away some obstacles resulted from using any of the two methods solely. The paper derives all the formulas concerning an axisym-metric shell of large deformation by means of the perturbation finite element method and gives two numerical examples,the results of which show good convergence characteristics.     

Unsymmetrical nonlinear bending problem of circular thin plate with variable thickness

Introduction Manystructuralelements(pole,plate,shell)withunevenandvariablethicknessarewidely usedinallkindsofengineeringfields.Engineerscansavematerialswhentheydesignbecause theseelementshavebetteroptimizedshapeofstructuralfeature,butthisaddsdifficultytotheanalysisoftheirmechanicalcapability.Manypreviouspapers[1-4]havesolvedtheproblemof symmetricalaxis,butnobodyhassolvedtheunsymmetricalnonlineardeformationproblemof circularthinplatewithvariablethicknessandunsymmetricalaxisuptonow,afewworkonly …