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The thermomechanical bending of an elastic sandwich ring plate with light core on an elastic foundation is considered. To
describe the kinematics of the plate that is asymmetric across the thickness, broken-normal hypotheses are accepted. The foundation
reaction is described by Winkler's model. A system of equilibrium equations is derived and solved for displacements. Numerical
results for a sandwich ring plate in a temperature field are presented
Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 94–103, September 2008. 相似文献
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薄板小波有限元理论及其应用 总被引:1,自引:0,他引:1
利用样条小波尺度函数构造了常用的三角形和矩形薄板单元的位移函数,得到了利用小波函数表示的形函数。采用合理的局部坐标,对单元进行压缩,使单元在局部坐标区间上有其值,成功地推导出了分域的三角形和矩形薄板小波有限元列式。在此基础上,提出了弹性地基薄板的小波有限元求解方法。通过两个算例对薄板的挠度和弯矩进行了计算,数值结果表明,求解结果具有收敛快、精度高的特点。 相似文献
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纪振义 《应用数学和力学(英文版)》1991,12(11):1065-1074
In this paper,based on the step reduction method and exact analytic method,a new method,the exact element method for constructing finite element,is presented.Since the new method doesn’t need variational principle,it can be applied to solve non-positive and positive definite partial differential equations with arbitrary variable coefficients.By this method,a triangle noncompatible element with15 degrees of freedom is derived to solve the bending of nonhomogenous Reissner’s plate.Because the displacement parameters at the nodal point only contain deflection and rotation angle.it is convenient to deal with arbitrary boundary conditions.In this paper,the convergence of displacement and stress resultants is proved.The element obtained by the present method can be used for thin and thick plates as well,Four numerical examples are given at the end of this paper,which indicates that we can obtain satisfactory results and have higher numerical precision. 相似文献
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The theoretic solution for rectangular thin plate on foundation with four edges free is derived by symplectic geometry method. In the analysis proceeding, the elastic foundation is presented by the Winkler model. Firstly, the basic equations for elastic thin plate are transferred into Hamilton canonical equations. The symplectic geometry method is used to separate the whole variables and eigenvalues are obtained simultaneously. Finally, according to the method of eigen function expansion, the explicit solution for rectangular thin plate on foundation with the boundary conditions of four edges frees are developed. Since the basic elasticity equations of thin plate are only used and it is not need to select the deformation function arbitrarily. Therefore, the solution is theoretical and reasonable. In order to show the correction of formulations derived, a numerical example is given to demonstrate the accuracy and convergence of the current solution. 相似文献
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为更精确地求解弹性地基薄板的动力响应,发展了一种分段时域自适应算法,通过变量在离散时段内的展开,将时空耦合的初边值问题转化为一系列递推的基于有限元(FEM)的空间问题求解,通过自适应计算保持稳定的计算精度。数值算例表明:本文解与解析解相比最大相对误差不超过3.59%;当步长较大时四阶Runge-Kutta法和Newmark法均失效,本文所提算法仍可得到满意的计算结果。 相似文献
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The mill roller bearing is made up of an internal ring, middle rolls and an external ring, the analysis of which is a multi-bodies
contact problem. In this paper, based on the three-dimensional elastic contact BEM without friction, and using the structural
characteristics of roller bearings, middle rolls are described by elastic plate units of different shapes, which is placed
on the internal ring. The discontinuous traction problem of the contact element can be dealt with by the traction sub-element
method. Therefore the contact problem can be changed from one of multi-bodies to one of two-bodies. As an elastic deformation
of the plate element, it can be calculated by an elastic contact formula and is regarded as an equivalent gap to be put into
the total matrix equality. The face-to-face contact condition of displacement and traction on the element will serve as the
convergence judging condition. So convergence solution can be obtained before any geometry inconsistent on the contact element
may take place. Therefore, the three-dimensional distribution of load of the mill roller bearing can be achieved. It has been
proved that the calculating model of this method is visualized and simple, has fast convergence solution and higher accuracy,
making it an effective numerical method of designing and analyzing load characteristics of the mill roller bearing.
Project supported by the National Natural Science Foundation of China (50075075). 相似文献
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Analytical solutions of steady vibration of free rectangular plate on semi-infinite elastic foundation 总被引:1,自引:0,他引:1
The method of double Fourier transform was employed in the analysis of the semi-infinite elastic foundation with vertical load.And an integral representations for the displacements of the semi-infinite elastic foundation was presented.The analytical solution of steady vibration of an elastic rectangle plate with four free edges on the semi-infinite elastic foundation was also given by combining the analytical solution of the elastic rectangle plate with the integral representation for displacements of the semi- infinite elastic foundation.Some computational results and the analysis on the influence of parameters were presented. 相似文献
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Some further results of the boundary element method for the Kirchhoff type plate bending problems are given. The direct boundary integral equation-boundary element scheme with higher conforming properties is used for several computation examples. The results of computation show that the numerical scheme seems to be more economical in computer time and with better accuracy in comparison with some previous results. 相似文献
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In this paper, based on the step reduction method, a new method, the exact element method for constructing finite element, is presented. Since the new method doesn't need the variational principle, it can be applied to solve non-positive and positive definite partial differential equations with arbitrary variable coefficient. By this method, a triangle noncompatible element with 6 degrees of freedom is derived to solve the bending of nonhomogeneous plate. The convergence of displacements and stress resultants which have satisfactory numerical precision is proved. Numerical examples are given at the end of this paper, which indicate satisfactory results of stress resultants and displacements can be obtained by the present method. 相似文献
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基于一种板的修正变分泛函,将杂交边界点法与双互易法结合,用于薄板弯曲问题的分析。该方法将问题的解分为齐次方程的通解和非齐次的特解两部分,特解采用径向基函数插值得到,而通解则使用杂交边界点法求解。在杂交边界点法用于求解通解的列式过程中,边界变量采用移动最小二乘近似,域内变量则采用基本解插值。与有限元法相比,该方法仅需要边界上离散点的信息,无论插值还是积分都不需要网格,域内点仅用来插值非齐次项,因而仍是一种纯边界类型的无网格方法。数值算例表明,本文方法能以很少的计算自由度获得与其它方法同样的计算精度,且具有前后处理简单、收敛速度快等优点,适合于求解工程中各种薄板的弯曲问题。 相似文献
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Equivalent Boundary Integral Equations with indirect unknowns for thin elastic plate bending theory 总被引:4,自引:0,他引:4
Zhang Yao-ming Associate Professor Doctor Sun Huan-chun Yang Jia-xin 《应用数学和力学(英文版)》2000,21(11):1246-1255
Equivalent Boundary Integral Equations (EBIE) with indirect unknowns for thin elastic plate bending theory, which is equivalent
to the original boundary value problem, is established rigorously by mathematical technique of non-analytic continuation and
is fully proved by means of the variational principle. The previous three kinds of boundary integral equations with indirect
unknowns are discussed thoroughly and it is shown that all previous results are not EBIE.
Paper from SUN Huan-chun, Member of Editorial Commitee, AMM
Biography: ZHANG Yao-ming (1962-) 相似文献
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IntroductionWhenthestructuresaresubjectedtotransientloadssuchasbomb_load,earthquakeandsoon,engineerspayspecialattentiontothesafetybehaviorofstructures.Thereislotsofresearchworkontheconventionalmethodofdynamicresponseanalysisforstructuralengineeringbot… 相似文献
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用拉压不同模量理论分析弯曲板 总被引:12,自引:0,他引:12
材料的拉压不同弹性模量性对结构计算的影响是一个不容忽视的问题,本文对不同模量弯曲板进行了较系统的分析,构造了相应的有限元算法,通过算例分析,得出了一些较有价值的结论。 相似文献
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Two sets of trial functions with different variables are constructed for the admissible space of the finite element analysis. The trial functions satisfy the equilibrium differential equation inside elements, while the deflections and rotations on the edges of the elements are approximated by the Peano hierarchical interpolation functions. Then, a generalized variational principle is applied to set up the p-version hybrid analytical finite element method for plate bending problems. The accuracy of finite element computation can be improved by increasing the order of the interpolation polynomials with fixed mesh. In the finite element formulation, to obtain the stiffness matrices and the load vectors, it is only necessary to perform quadrature over the edges of the elements. These matrices and vectors possess an embedding structure. The conformability between the elements can be controlled automatically.This work is supported by the Natural Science Foundation of China and the Aeronautical Science Foundation of China. 相似文献
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XIAO Yong-gang 《应用数学和力学(英文版)》2005,26(8):963-972
IntroductionThe moderate thickness plates on elastic foundation are a kind of important structure instructural engineering. The mechanic characters of the plates on elastic foundation withdifferent boundary conditions have been received considerable atten… 相似文献
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ELASTIC ANALYSIS OF ORTHOTROPIC PLANE PROBLEMS BY THE SPLINE FICTITIOUS BOUNDARY ELEMENT METHOD 总被引:5,自引:0,他引:5
IntroductionIntheconventionalboundaryelementmethod (BEM) ,singularpointsaredistributedalongtheboundaryofthedomainunderstudy ,whichleadstosingularintegralequationsduetothesingularityoffundamentalsolutions .Therefore ,singularintegrationmustbehandledwhensol… 相似文献