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用变分同化方法,在整体观测资料下,对一类简单的"on-off"模式中的初值进行修正.研究观测误差对于变分同化方法的影响,对变分同化方法反演得到的最优初值的收敛性以及误差进行分析,从理论上分析"on-off"问题变分同化方法的有效性. 相似文献
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本文对线性抛物方程外区域问题,应用有限元与边界元的耦合方法,给出了其完整的数学理论分析,我们借助一条辅助公共边界,导出耦合问题分形式,证明了耦合变分问题解的适应性,且获得了逼近解的收敛性与误差估计。 相似文献
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系统分析了三维非稳态Boltzmann输运方程的谱有限元求解.根据球谐函数展开提出了关于处理方向变量的近似方法,导出了“扩散型”近似方程及其Galerkin变分形式,证明了变分问题解的存在唯—性。研制了对二维、三维都适用的有限元程序,实现了对稳态与非稳态问题的处理,计算实例表明此方法是可行的。 相似文献
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本文首先建立有阻尼线弹性动力学一类变量的简化Gurtin型变分原理,它能反映动力学初值一边值问题的全部特性。然后,以该简化Gurtin型变分原理为基础,提出时间域采用五次及七次一般Hermite插值多项式插值的时间子域法和空间域采用有限元法相结合的新方法,进行了平面问题的动力响应分析。同时本文还给出了五次及七次Hermite插值多而式无条件稳定的算法和算例。具体算例表明这种新方法的精度和计算效率都 相似文献
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A. Yu. Chirkov 《Strength of Materials》2008,40(2):253-268
We consider mixed variational formulations and the application of the mixed approximations of the finite element method to
the solution of problems on natural vibrations of elastic bodies. To solve the generalized spectral problem, three forms of
the mixed variational formulations are proposed. The correctness and stability of mixed variational formulations for displacements,
strains and stresses are investigated. Matrix equations of the mixed method are given whose solution is performed using the
modified algorithm of the steepest descent method. The results of calculations for natural frequencies of free vibrations
of a straight and a circular beam are presented that are obtained in the solution of the problem in a two-dimensional formulation
based on the classical and mixed finite-element method approaches.
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Translated from Problemy Prochnosti, No. 2, pp. 121–140, March–April, 2008. 相似文献
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Computational electro‐elasticity and magneto‐elasticity for quasi‐incompressible media immersed in free space 下载免费PDF全文
Jean‐Paul Pelteret Denis Davydov Andrew McBride Duc Khoi Vu Paul Steinmann 《International journal for numerical methods in engineering》2016,108(11):1307-1342
In this work, a mixed variational formulation to simulate quasi‐incompressible electro‐active or magneto‐active polymers immersed in the surrounding free space is presented. A novel domain decomposition is used to disconnect the primary coupled problem and the arbitrary free‐space mesh update problem. Exploiting this decomposition, we describe a block‐iterative approach to solving the linearised multiphysics problem, and a physically and geometrically based, three‐parameter method to update the free space mesh. Several application‐driven example problems are implemented to demonstrate the robustness of the mixed formulation for both electro‐elastic and magneto‐elastic problems involving both finite deformations and quasi‐incompressible media. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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Dr. A. Muc 《Acta Mechanica》1988,73(1-4):1-10
Summary The contact problem of an infinite cylindrical shell with an elastic or a rigid foundation is investigated. A shear deformation non-linear shell theory is used in setting up the governing differential equations and the functional of total potential energy. The variations of contact pressure and domains are discussed for different shell parameters, friction and rigidity coefficients of foundation. The obtained results are compared with the results for geometrically linear shell theory. Some problems connected with the variational inequality formulation of the analysed unilateral boundary problem are also discussed.With 7 Figures 相似文献
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Numerical solution of elastic bodies in contact by FEM utilising equilibrium displacement fields 总被引:1,自引:0,他引:1
Ľubor Fraštia 《Computational Mechanics》2007,41(1):159-174
In this paper a new effective formulation of the computation of the statics of elastic bodies in contact is described and
demonstrated. Line contact, plane strain, and negligible friction are assumed. The formulation is an extension of the standard
finite element method (FEM). With the aim to utilise the Hertz theory directly, we use the exact solution of the elastic 2-dimensional
halfspace loaded by Hertzian pressure distribution and enforce the contact condition by the method of Lagrange multipliers.
In numerical examples we have focussed on the demonstration and evaluation of the accuracy of the new formulation for selected
applications compared with the state of the art node-to-segment contact algorithm implemented in the software system ADINA.
Proposed formulation is more accurate for problems where Hertz contact dominates the strain state, especially for small number
of elements, whereas we obtained a fairly good agreement with ADINA for a more general bending problem. 相似文献
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The variational formulation of elastic contact problems leads to variational inequalities on convex subsets. These variational
inequalities are solved with the boundary element method (BEM) by making use of the Poincaré–Steklov operator. This operator
can be represented in its discretized form by the Schur-complement of the dense Galerkin-matrices for the single layer potential
operator, the double layer potential operator and the hypersingular integral operator. Due to the difficulties in discretizing
the convex subsets involved, traditionally only the h-version is used for discretization. Recently, p- and hp-versions have
been introduced for Signorini contact problems in Maischak and Stephan (Appl Numer Math, 2005) . In this paper we show convergence
for the quasi-uniform hp-version of BEM for elastic contact problems, and derive a-posteriori error estimates together with
error indicators for adaptive hp-algorithms. We present corresponding numerical experiments. 相似文献
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R. V. Goldstein V. M. Entov A. F. Zazovski 《International journal for numerical methods in engineering》1978,12(8):1213-1239
A direct variational method has been considered for solving mixed boundary value problems for linear elliptical equations. The main idea of the method consists in searching the unknown solution in a class of functions satisfying the differential equation and some of the boundary conditions. The functional to be minimized may be expressed in terms of the boundary values of the unknown solution, and thus the dimension of the variational problem is reduced. Reduction of the functional defined on the domain to a functional on its boundary corresponds to the common in the elsaticity theory of application of Clapeyron's theorem for the transformation of functionals of minimum elastic potential energy and complementary work. The reduced problem may be solved by the Ritz direct method. Some examples from the elasticity and seepage theories have been given to demonstrate the effectiveness of the method. Among the problems that have been solved by the method we may mention the plane elastic problem for a crack in a strip, three-dimensional elastic problems for a plane rectangular crack in an infinite elastic medium and the problem of a rectangular die in sliding contact with an elastic half-space (numerical solutions exhibit correct asymptotic behaviour in the neighbourhood of corners of cracks or die), and the plane and axisymmetric seepage problems. 相似文献
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H. G. Georgiadis 《Computational Mechanics》1998,21(4-5):347-352
The idea of considering tangential-displacement effects in a classical elastostatic contact problem is explored in this paper.
The problem involves the static frictionless indentation of a linearly elastic half-plane by a rigid wedge, and its present
formulation implies that the tangential surface displacements are not negligible and should thus be coupled with the normal
surface displacements in imposing the contact zone boundary conditions. L.M. Brock introduced this idea some years ago in
treating self-similar elastodynamic contact problems, and his studies indicated that such a formulation strongly influences
the contact-stress behavior at half-plane points making contact with geometrical discontinuities of the indentor. The present
work again demonstrates, by studying an even more classical problem, that the aforementioned considerations eliminate contact-stress
singularities and therefore yield a more natural solution behavior. In particular, the familiar wedge-apex logarithmic stress-singularity
encountered within the standard formulation of the problem (i.e. by avoiding the tangential displacement in the contact boundary
condition) disappears within the proposed formulation. The contact stress beneath the wedge apex takes now a finite value
depending on the wedge inclination angle and the material constants. By utilizing pertinent integral relations for the displacement/stress
field in the half-plane, an unusual mixed boundary-value problem results whose solution is obtained through integral equations. 相似文献
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In this paper we consider an algorithm of constrained optimization which arises from boundary variational principles of elastodynamics for bodies with cracks and unilateral constraints on the cracks edges. Variational formulation of unilateral contact problems with friction was considered, boundary variational functionals used with boundary integral equations were obtained and algorithm for solution of the unilateral contact problem with friction was developed. Some numerical results for 3-D elastodynamic unilateral contact problem for bodies with cracks are presented. 相似文献
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Henri Morand Roger Ohayon 《International journal for numerical methods in engineering》1979,14(5):741-755
The finite element method is used for the computation of the variational modes of the system composed of an elastic tank partially filled with a compressible liquied. We propose, on the one hand, a direct approcach based on a three field mixed variational formulation, and, on the other hand, a variational modal interaction scheme allowing the use of the acoustic eigenmodes of the liquid in a rigid motionless enclosure and the hydroelastic modes of the enclosure. Numerical results show the advantage of the second procedure. 相似文献