共查询到18条相似文献,搜索用时 297 毫秒
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微分求积法已在科学和工程计算中得到了广泛应用。然而,有关时域微分求积法的数值稳定性、计算精度即阶数等基本特性,仍缺乏系统性的分析结论。依据微分求积法的基本原理,推导证明了微分求积法的权系数矩阵满足V-变换这一重要特性;利用微分求积法和隐式Runge-Kutta法的等值性,证明了时域微分求积法是A-稳定、s级s阶的数值方法。在此基础上,为进一步提高传统微分求积法的计算精度,利用待定系数法和Padé逼近,推导出了一类新的s级2s阶的微分求积法。数值计算对比结果验证了所提出的新微分求积法比传统的微分求积法具有更高的计算精度。 相似文献
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利用混合微分求积法,对任意荷载作用下不同材料梯度分布的功能梯度材料平板柱形弯曲问题进行了分析。针对广义微分求积法求解集中荷载问题精度不高的缺点,本文利用小波微分求积法进行了改进。由于小波对突变信号具有良好的自适应描述能力,因此在平板宽度方向上,利用小波微分求积法可以有效地处理集中荷载;而在材料梯度变化的板厚方向上,则利用广义微分求积法计算量小且精度高的特点进行离散计算。计算表明,混合微分求积法不仅保留了广义微分求积法高效的特点,而且能有效地求解任意荷载作用的问题。通过算例,分析了在机械荷载作用下,材料不同梯度形式、平板上下表面材料性质差异对功能梯度平板结构响应的影响。 相似文献
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微分求积法具有数学概念简单、精度高和计算时间少等优点,是一种不断受到重视的数值方法.目前微分求积法在方法本身的研究已经相当充分和成熟,而应用方面的研究则大多集中在边值问题的求解,本文的研究集中在采用微分求积法求解动力学初值问题方面.先介绍了一种新近提出的逐步积分方法,该方法基于一种特殊的节点分布的微分求积法.然后通过理论分析与几种常用的时间积分方法进行了稳定性、精确性和计算量的比较.最后计算了一个双质点系在强迫力下的瞬态响应.比较结果表明新近提出的逐步积分方法具有无条件稳定、高精度和计算量少的优点. 相似文献
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框架结构P-△效应分析的微分求积单元法 总被引:1,自引:1,他引:1
采用一种新的数值方法——微分求积单元法分析框架结构的P-△效应。微分求积单元法采用微分求积法直接求解微分方程的技术,并结合有限分割技术而形成。首先建立考虑剪切变形和轴力二阶效应的框架结构单元平衡微分方程,通过微分求积离散而得到梁单元的一般弹性刚度方程;同时考虑变形后节点的平衡条件和变形协调条件,导出框架结构整体二阶分析的微分求积单元法力学模型。由于该分析模型中包括了单元及结构的所有离散形式的控制方程,因此采用该模型进行结构分析可得出较为精确的解。数值算例的分析比较,表明了该法用于框架结构P-△效应分析的正确性和有效性。本文导出的框架结构二阶分析的微分求积单元法力学模型可用于框架结构剪切变形与几何非线性的耦合效应分析。 相似文献
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微分求积单元法在结构工程中的应用 总被引:3,自引:0,他引:3
微分求积法(Differential Quadrature Method)是求鳃偏微分方程和积分-微分方程的一种数值方法,该法具有计算简便、精度较高和易于实现等优点。微分求积单元法(Differential Quadrature Element Method)是在微分求积法的基础上结合区域分割和集成规则而形成的一种新的数值计算方法,能通过自适应地选取微分求积网点数目正确模拟构件的刚度和荷载性质,其精度可通过细分单元或增加离散点数目加以提高。微分求积单元法是一种可供选择的、性能优越的数值计算方法。本文将详细论述这一数值方法的基本原理,并通过数值算例说明该方法的应用过程及其优越性,为这一方法在结构工程中的推广应用提供参考。 相似文献
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本文提出了新型带虚点的径向基函数微分求积法,并将其应用于模拟薄板弯曲问题。带虚点的径向基函数微分求积法是一种基于传统径向基函数微分求积法的新型无网格方法,传统方法只将中心点放在计算域内,而该方法扩展了中心点的区域,使其既位于计算域内又位于计算域外,在不增加计算量和存储量的基础上,显著提高计算精度。本文首次尝试将此方法应用于求解薄板弯曲问题,并与解析解和传统方法进行对比,验证了此方法的优越性 相似文献
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拟谱方法和微分求积法是两类重要的无网格法,二者都已在科学和工程计算中获得了广泛应用。采用拉格朗日插值多项式作为二者的试函数,且采用同一种网格点分布,指出了在空间域上,微分求积法是拟谱方法的一种特殊形式。在此基础上,结合二者各自的特点,提出了拟谱-微分求积混合方法用于求解一类双曲电报方程。理论分析和数值测试表明,新方法在空间域上具有谱精度收敛性,在时间域上是A-稳定的,比较适合于求解多维电报方程。 相似文献
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无网格方法与有限元法或边界元法耦合是无网格方法处理边界条件的方法之一,在无网格方法中研究无网格方法与有限元法或边界元法耦合的研究显得非常重要.本文在无单元Galerkin法和边界元法的基础上,基于无单元Galerkin法子域和边界元法子域的界面上位移连续和面力平衡条件,提出了一种新的无单元Galerkin法和边界元法的直接耦合方法,对弹性力学问题详细推导了在整个求解域上的耦合公式.与以往的耦合法相比,这种方法简单直观,不需要增加新的耦合区域,也不需要建立新的逼近函数来保证界面位移的连续性.算例结果表明,该方法具有较好的计算精度. 相似文献
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The present paper deals with the dynamic behaviour of a clamped beam subjected to a sub-tangential follower force at the free end. The aim of this work is to obtain the frequency–axial load relationship for a beam with a variable circular cross-section. In this way, one can identify both divergence critical loads – where the frequency goes to zero – and the flutter critical load – in correspondence with two frequencies coalescence. The numerical approach adopted for solving the partial differential equation of motion is the differential quadrature method (henceforth DQM). This method was proposed by Bellmann and Casti [Bellmann, R.E., Casti, J., 1971. Differential quadrature and long-term integration. J. Math. Anal. 34, 235–238] and has been employed recently in the solution of solid mechanics problems by Bert and Malik [Bert, C.W., Malik, M., 1996. Differential quadrature method in computational mechanics: a review. Appl. Mech. Rev., ASME, 49 (1), 1–28] and Chen et al. [Chen, W., Stritz, A.G., Bert, C.W., 1997. A new approach to the differential quadrature method for fourth-order equations. Int. J. Numer. Method Eng. 40, 1941–1956]. More precisely, a modified version of this method has been used, as proposed by De Rosa and Franciosi [De Rosa, M.A., Franciosi, C., 1998a. On natural boundary conditions and DQM. Mech. Res. Commun. 25 (3), 279–286; De Rosa, M.A., Franciosi, C., 1998b. Non classical boundary conditions and DQM. J. Sound Vibrat. 212(4), 743–748] to satisfy all the boundary conditions.Some frequencies–axial loads relationships are reported in order to show the influence of tapering on the critical loads. 相似文献
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Bo WANG 《应用数学和力学(英文版)》2018,39(5):717-732
The dynamic stability of axially moving viscoelastic Rayleigh beams is presented. The governing equation and simple support boundary condition are derived with the extended Hamilton’s principle. The viscoelastic material of the beams is described as the Kelvin constitutive relationship involving the total time derivative. The axial tension is considered to vary longitudinally. The natural frequencies and solvability condition are obtained in the multi-scale process. It is of interest to investigate the summation parametric resonance and principal parametric resonance by using the Routh-Hurwitz criterion to obtain the stability condition. Numerical examples show the effects of viscosity coefficients, mean speed, beam stiffness, and rotary inertia factor on the summation parametric resonance and principle parametric resonance. The differential quadrature method (DQM) is used to validate the value of the stability boundary in the principle parametric resonance for the first two modes. 相似文献
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《International Journal of Solids and Structures》1999,36(8):1149-1168
This paper presents an application of the differential quadrature (DQ) method for three-dimensional buckling analysis of rectangular plates. The governing equations of the plate model are first presented in terms of displacement, stress displacement relationship, and boundary conditions with three-dimensional flexibility. These equations are then normalised and discretised using the DQ procedure. Example problems pertaining to the buckling of rectangular plates with generic boundary conditions are selected to illustrate the efficiency and simplicity of implementing the DQ procedure. The convergence characteristics of the method are first conducted based on numerical studies. The DQ solutions are then compared, where possible, with exact or approximate solutions. It is found that the differential quadrature method yields accurate results for the plate problems under the current investigation. In addition to the above, some parametric studies are carried out by varying the plates aspect ratio, boundary conditions and thickness to width ratio under axial and biaxial loading. 相似文献
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《International Journal of Solids and Structures》1999,36(33):5101-5123
In this paper, a new numerical technique, the differential quadrature element method (DQEM) , has been developed for static analysis of the two-dimensional polar Reissner–Mindlin plate in the polar coordinate system by integrating the domain decomposition method (DDM) with the differential quadrature method (DQM) . The detailed formulations for the sectorial DQEM plate bending element and the compatibility conditions between each element are presented. The convergence properties and the accuracy of the DQEM for bending of thick polar plates are investigated through a number of numerical computations. Consequently, the DQEM has been successfully applied to analyze several annular sector plates with discontinuous loading and boundary conditions and cutouts to illustrate the simplicity and flexibility of this method for solving Reissner–Mindlin plates in polar coordinate system which are not solvable directly using the differential quadrature method. The numerical results are verified by the existing exact solutions or the FEM solutions obtained using the software package ANSYS (Version 5.3) . 相似文献