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1.
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   

2.
压电材料变分原理逆问题的研究   总被引:10,自引:2,他引:8       下载免费PDF全文
研究了压电材料变分原理的逆问题, 采用文献[ 8 ]提出的变积方法, 系统地建立了压电材料的变分原理及其广义变分原理, 除得到文献中已有的结果外, 还得到了一些新的变分原理, 为建立压电材料的有限元分析模型提供了依据。  相似文献   

3.
研究了压电材料耦合动态场中Hamilton 型和Gurtin 型变分原理的逆问题。采用变积方法, 建立了各级变分原理和广义变分原理, 为建立横观各向同性压电材料的动力学有限元分析模型提供了依据。  相似文献   

4.
广义变分不等式及其应用   总被引:1,自引:0,他引:1  
本文对广义变分不等式进行了进一步研究。得到了几个不等式的存在性定理,并讨论了一个非线性互补问题。  相似文献   

5.
拉压不同模量材料的参变量变分原理和有限元方法   总被引:2,自引:0,他引:2  
张洪武  张亮  高强 《工程力学》2012,(8):22-27,38
对具有拉伸和压缩不同模量的材料,建立了平面静力问题的参变量变分原理。基于参变量变分原理,并结合有限元方法,将拉压不同模量平面问题转化为互补问题求解。经典的Lemke算法被用于求解此互补问题。该方法避免了应力状态的假设和刚度矩阵的更新,算法稳定,且收敛速度快。  相似文献   

6.
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   

7.
用一种新的方法对Franco等在1978年文中所提出的一类混合变分不等式进行了分析,首先用凸分析中的有关定理证明了连续问题的存在唯一性,然后提出了一种新的等价变分和较为简洁,有效的方法,获得了与上文相同的有限元逼近结果。  相似文献   

8.
提出了一类求解单调变分不等式问题的连续型牛顿法。方法采用不精确的线性搜索以确保整体收敛性,从本质上改进了TajiK等(1993)只能求解强单调变分不等式问题的局限性,同时又保持局部二次收敛率,最后用数值例子验证了算法的有效性和稳定性。  相似文献   

9.
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   

10.
罗志国  佘慧 《工程力学》2000,3(A03):24-28
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   

11.
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. __________ Translated from Problemy Prochnosti, No. 2, pp. 121–140, March–April, 2008.  相似文献   

12.
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   

13.
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   

14.
基于实际问题对通量较低的正则性要求,本文建立了椭圆型方程的一种新型混合变分形式.在鞍点问题框架下,通过验证LBB条件,证明了该混合形式解的存在唯一性.由于压力空间不再是传统的H(div),而是平方可积空间,因此混合元的选取变得简单容易.同时本文给出了相应的有限元逼近形式,并对于由分片常数速度元和分片线性压力元构成的协调...  相似文献   

15.
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   

16.
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   

17.
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   

18.
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   

19.
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   

20.
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   

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