共查询到20条相似文献,搜索用时 203 毫秒
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在康托洛维奇方法和Kerr方法的基础上,本文提出了改进的康托洛维奇方法。本方法在不提高方程阶数的基础上,能获得较Kerr方法精度更高的解;能解决工程中更广泛的问题。本文将改进康托洛维奇方法应用于薄板弯曲和稳定性问题以及膜的振动问题,充分说明了本方法的特点和优越性。 相似文献
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平行四边形弯曲板的康托洛维奇法 总被引:1,自引:0,他引:1
康托洛维奇、克雷洛夫提出了康托洛维奇近似变分法,用来处理多变量函数的泛函变分问题。钱伟长胡海昌以及各国学者对于康托洛维奇法都很注意它的演变与各种实际应用。胡海昌指出:“用康托洛维奇法解题的算例,文献上发表的不多。”因此,本文一个方向用里兹法求近似解。另一个方向用常微分方程求精确解。本文是将康氏法从矩形板推广到平行四边形板中应用。 相似文献
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基于数值流形方法和有限覆盖技术,提出了适用于Biot固结分析的三节点平面协调流形元。由于土骨架位移和孔隙水压力的节点覆盖函数(Lagrange插值函数)阶次可分别任意选择,该单元是一组满足位移和孔压插值阶次不同且所有节点具有相同自由度数的新型u-p混合模式单元,并且更加方便编程。数值分析表明,位移和孔压的节点覆盖函数阶次分别取一次和零次的流形单元(T1-0)是该组单元中最为有效的。与等价四边形等参元相比,T1-0流形元能给出精度更高的初期孔压和位移。 相似文献
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热传导问题的非协调数值流形方法 总被引:2,自引:0,他引:2
数值流形方法通过引入数学与物理双重网格,将插值域与积分域分别定义在两个不同的覆盖上,其优点是网格划分随意,不受复杂边界形状和材料界面的限制,是较之于有限元方法更一般化的数值模拟方法。在计算精度方面,数值流形方法远远高于有限元法。但它的精度还是不够理想。为此本文在单元总体位移场上附加非协调位移基本项,使单元位移函数趋于完全,构造了非协调流形单元来改善流形单元的计算精度和计算效率,并将其应用于热传导问题,推导了势问题的非协调数值流形方法。 相似文献
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弹性力学中的一种非协调数值流形方法 总被引:1,自引:0,他引:1
通过引入数学和物理双重网格,将插值域与
积分域分别定义在不同的覆盖上,即在数学网格上进行插值函数的构造,物理网格上完成
系统能量泛函积分运算,最后通过覆盖权函数将二者联结在一起. 它的优点是单元网格划
分随意,不受复杂边界形状和二相材料界面的限制,单元可以是任意形状,是较之于有限
元方法更一般的数值模拟方法. 在4节点四边形数值流形方法中,由于单元总体位移函数
包含的完全多项式不完全,使得计算精度不够精确,为此,在单元总体位移函数上附
加非协调位移基本项,使之趋于完全,提出了弹性力学问题的一种改进的数值流形
方法------非协调数值流形方法. 通过内部自由度静力凝聚处理,导出了消除内参后的单元应变矩阵
和单元刚度矩阵,使得在不增加广义节点自由度的前提下,大大提高了数值流形方法的计
算精度和计算效率. 同时对非协调项进行了显式处理,可以对工程实践起到更切实的帮助.
数值试验表明,它们能够保证收敛,有较高的精度,对畸变不敏感,从而证明了该方法的
可行性. 相似文献
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利用模态综合法分析车辆与桥梁之间的相互作用时,合理地构造桥梁的插值振型函数可以大幅提高计算精度.其中,分段三次Hermite插值函数和三次样条插值函数较为常用.为研究二者的异同,以简支梁桥为例分别采用这两种插值函数构造结构梁单元模型的一维插值振型函数和板单元模型的二维插值振型函数.基于以上两类插值振型函数,分析单自由度簧上质量匀速过桥时,桥梁的跨中位移、跨中梁底正应力和轮-桥接触力时程响应.结果表明:无论是一维问题还是二维问题,由三次样条插值法构造的插值振型函数与结构的实际振型较为吻合,计算结果具有较高的收敛性和精度.而要达到相同的精度,分段三次Hermite插值法则须加密单元网格,但其误差仅存在于独立网格内,不会累积放大. 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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Sutthisak Phongthanapanich Suthee Traivivatana Parinya Boonmaruth Pramote Dechaumphai 《Acta Mechanica Sinica》2006,22(2):138-147
Based on flux-based formulation, a nodeless variable element method is developed to analyze two-dimensional steady-state and
transient heat transfer problems. The nodeless variable element employs quadratic interpolation functions to provide higher
solution accuracy without necessity to actually generate additional nodes. The flux-based formulation is applied to reduce
the complexity in deriving the finite element equations as compared to the conventional finite element method. The solution
accuracy is further improved by implementing an adaptive meshing technique to generate finite element mesh that can adapt
and move along corresponding to the solution behavior. The technique generates small elements in the regions of steep solution
gradients to provide accurate solution, and meanwhile it generates larger elements in the other regions where the solution
gradients are slight to reduce the computational time and the computer memory. The effectiveness of the combined procedure
is demonstrated by heat transfer problems that have exact solutions. These problems are: (a) a steady-state heat conduction
analysis in a square plate subjected to a highly localized surface heating, and (b) a transient heat conduction analysis in
a long plate subjected to a moving heat source.
The English text was polished by Yunming Chen. 相似文献
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An analytical solution for bending of composite sector plates is presented using multi-term extended Kantorovich method (MTEKM). The governing equations are derived using the displacement field of the first-order shear deformation theory and converted into two sets of coupled ordinary differential equations (ODEs) utilizing MTEKM. Next, an analytical iterative procedure is presented for solving the derived sets of ODEs based on state-space method. Numerous examples are studied by the present method, and as special cases, solid sector and rectangular plates are also investigated. Next, the results obtained by the present method are compared to those of finite element method and other results available in the literature. It is found that the present method has a high convergence rate as well as good accuracy in all cases. 相似文献
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In this paper,a 13-node pyramid spline element is derived by using the tetrahedron volume coordinates and the B-net method,which achieves the second order completeness in Cartesian coordinates.Some appropriate examples were employed to evaluate the performance of the proposed element.The numerical results show that the spline element has much better performance compared with the isoparametric serendipity element Q20 and its degenerate pyramid element P13 especially when mesh is distorted,and it is comparable to the Lagrange element Q27.It has been demonstrated that the spline finite element method is an efficient tool for developing high accuracy elements. 相似文献
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This work presents a two‐grid stabilized method of equal‐order finite elements for the Stokes problems. This method only offsets the discrete pressure space by the residual of pressure on two grids to circumvent the discrete Babu?ka–Brezzi condition. The method can be done locally in a two‐grid approach without stabilization parameter by projecting the pressure onto a finite element space based on coarse mesh. Also, it leads to a linear system with minimal additional cost in implement. Optimal error estimates are obtained. Finally, some numerical simulations are presented to show stability and accuracy properties of the method. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
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《European Journal of Mechanics - A/Solids》2008,27(3):378-388
Applicability and performance of the extended Kantorovich method (EKM) to obtain highly accurate approximate closed form solution for bending analysis of a cylindrical panel is studied. Fully clamped panel subjected to both uniform and non-uniform loadings is considered. Based on the Love–Kirchhoff first approximation for thin shallow cylindrical panels, the governing equations of the problem in terms of three displacement components include a system of two second order and one forth order partial differential equations. The governing PDE system is converted to a double set of ODE systems by assuming separable functions for displacements together with utilization of the extended Kantorovich method. The resulted ODE systems are solved iteratively. In each iteration, exact closed form solutions are presented for both ODE systems. Rapid convergence and high accuracy of the method is shown for various examples. Both displacement and stress predictions show close agreement with other analytical and finite element analysis. 相似文献
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A comparative study of the bi‐linear and bi‐quadratic quadrilateral elements and the quadratic triangular element for solving incompressible viscous flows is presented. These elements make use of the stabilized finite element formulation of the Galerkin/least‐squares method to simulate the flows, with the pressure and velocity fields interpolated with equal orders. The tangent matrices are explicitly derived and the Newton–Raphson algorithm is employed to solve the resulting nonlinear equations. The numerical solutions of the classical lid‐driven cavity flow problem are obtained for Reynolds numbers between 1000 and 20 000 and the accuracy and converging rate of the different elements are compared. The influence on the numerical solution of the least square of incompressible condition is also studied. The numerical example shows that the quadratic triangular element exhibits a better compromise between accuracy and converging rate than the other two elements. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
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In this paper a new finite element method is presented, in which complex functions are chosen to be the finite element model
and the partitioning concept of the generalized variational method is utilized. The stress concentration factors for a finite
holed plate welded by a stiffener are calculated and the analytical solutions in series form are obtained. From some computer
trials it is demonstrated that the problem of displacement compatibility and continuity of tractions between the holed plate
and the stiffener is successfully analysed by using this method. Since only three elements need to be formulated, relatively
less storage is required than the usual finite element methods. Furthermore, the accuracy of solutions is improved and the
computer time requirements are considerably reduced. Numerical results of stress concentration factors and stresses along
the welded-line which may be referential to engineers are shown in tables. 相似文献
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Based on combination of two variational principles, a nonconforming stabilized finite element method is presented for the Reissner-Mindlin plates. The method is convergent when the finite element space is energy-compatible. Error estimates are derived. In particular, three finite element spaces are applied in the computation. Numerical results show that the method is insensitive to the mesh distortion and has better performence than the MITC4 and DKQ methods. With properly chosen parameters, high accuracy can be obtained at coarse meshes. 相似文献
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单元微分法是一种新型强形式有限单元法. 与弱形式算法相比, 该算法直接对控制方程进行离散, 不需要用到数值积分. 因此该算法有较简单的形式, 并且其在计算系数矩阵时具有极高的效率. 但作为一种强形式算法, 单元微分法往往需要较多网格或者更高阶单元才能达到满意的计算精度. 与此同时, 对于一些包含奇异点的模型, 如在多材料界面、间断边界条件、裂纹尖端等处, 传统单元微分法往往得不到较精确的计算结果. 为了克服这些缺点, 本文提出了将伽辽金有限元法与单元微分法相结合的强?弱耦合算法, 即整体模型采用单元微分法的同时, 在奇异点附近或某些关键部件采用有限元法. 该策略在保留单元微分法高效率与简洁形式等优点的同时, 确保了求解奇异问题的精度. 在处理大规模问题时, 针对关键部件采用有限元法, 其他部件采用单元微分法, 可以在得到较精确结果的同时, 极大提高整体计算效率. 在本文中, 给出了两个典型算例, 一个是具有切口的二维问题, 一个是复杂的三维发动机问题. 针对这两个问题, 分析了该耦合算法在求二维奇异问题和三维大规模问题时的精度与效率. 相似文献