共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper,a new analytical method of symplectic system.Hamiltonian system,is introduced for solving the problem of the Stokes flow in a two-dimensional rectangular domain.In the system,the fundamental problem is reduced to all eigenvalue and eigensolution problem.The solution and boundary conditions call be expanded by eigensolutions using ad.ioint relationships of the symplectic ortho-normalization between the eigensolutions.A closed method of the symplectic eigensolution is presented based on completeness of the symplectic eigensolution space.The results show that fundamental flows can be described by zero eigenvalue eigensolutions,and local effects by nonzero eigenvalue eigensolutions.Numerical examples give various flows in a rectangular domain and show effectivenees of the method for solving a variety of problems.Meanwhile.the method can be used in solving other problems. 相似文献
2.
3.
Stokes流问题中的辛本征解方法 总被引:8,自引:0,他引:8
通过引入哈密顿体系,将二维Stokes流问题归结为哈密顿体系下的本
征值和本征解问题. 利用辛本征解空间的完备性,建立一套封闭的求解问题方法. 研究结果
表明零本征值本征解描述了基本的流动,而非零本征值本征解则显示着端部效应影响特点.
数值算例给出了辛本征值和本征解的一些规律和具体例子. 这些数值例子说明了端部非规则
流动的衰减规律. 为研究其它问题提供了一条路径. 相似文献
4.
Symplectic solution system for reissner plate bending 总被引:3,自引:0,他引:3
Based on the Hellinger-Reissner variatonal principle for Reissner plate bendingand introducing dual variables, Hamiltonian dual equations for Reissner plate bending werepresented. Therefore Hamiltonian solution system can also be applied to Reissner platebending problem, and the transformation from Euclidian space to symplectic space and fromLagrangian system to Hamiltonian system was realized. So in the symplectic space whichconsists of the original variables and their dual variables, the problem can be solved viaeffective mathematical physics methods such as the method of separation of variables andeigenfunction-vector expansion. All the eigensolutions and Jordan canonical formeigensolutions for zero eigenvalue of the Hamiltonian operator matrix are solved in detail, and their physical meanings are showed clearly. The adjoint symplectic orthonormal relation of the eigenfunction vectors for zero eigenvalue are formed. It is showed that the alleigensolutions for zero eigenvalue are basic solutions of the Saint-Venant problem and theyform a perfect symplectic subspace for zero eigenvalue. And the eigensolutions for nonzeroeigenvalue are covered by the Saint-Venant theorem. The symplectic solution method is notthe same as the classical semi-inverse method and breaks through the limit of the traditional semi-inverse solution. The symplectic solution method will have vast application. 相似文献
5.
6.
Gyroscopic dynamic system can be introduced to Hamiltonian system.Based on an adjoint symplectic subspace iteration method of Hamiltonian gyroscopic system, an adjoint symplectic subspace iteration method of indefinite Hamiltonian function gy- roscopic system was proposed to solve the eigenvalue problem of indefinite Hamiltonian function gyroscopic system.The character that the eigenvalues of Hamiltonian gyroscopic system are only pure imaginary or zero was used.The eigenvalues that Hamiltonian function is negative can be separated so that the eigenvalue problem of positive definite Hamiltonian function system was presented,and an adjoint symplectic subspace iteration method of positive definite Hamiltonian function system was used to solve the separated eigenvalue problem.Therefore,the eigenvalue problem of indefinite Hamiltonian function gyroscopic system was solved,and two numerical examples were given to demonstrate that the eigensolutions converge exactly. 相似文献
7.
8.
基于二维弹性理论, 利用Hellinger-Reissner变分原理, 通过引入对偶变量, 推导
了双参数地基上正交各向异性梁平面应力问题的辛对偶方程组; 采用分离变量法和本征展
开方法, 将原问题归结为求解零本征值本征解和非零本征值本征解, 得到了适用于任意横纵
比的梁的解析解. 由于在求解过程中不需要事先人为地选取试函数, 而是从梁的基本方程出
发, 直接利用数学方法求出问题的解, 使得问题的求解更加合理化. 其中, 地基对梁的力学
行为的影响看作是侧边边界条件, 类似于外载, 可通过零本征解的线性展开来评价, 非零本
征值本征解对应圣维南原理覆盖的部分. 还利用哈密顿变分原理, 给出了两端固支梁的
一种新的改进边界条件. 编程计算了细梁和深梁等算例, 研究了地基上梁的变形沿着厚度方
向的变化特性, 验证了辛方法的有效性. 相似文献
9.
10.
11.
According to the Hellinger-Reissner variational principle and introducing proper transformation of variables , the problem on elastic wedge dissimilar materials can be led to Hamiltonian system, so the solution of the problem can be got by employing the separation of variables method and symplectic eigenfunction expansion under symplectic space, which consists of original variables and their dual variables . The eigenvalue - 1 is a special one of all symplectic eigenvalue for Hamiltonian system in polar coordinate . In general, the eigenvalue - 1 is a single eigenvalue, and the classical solution of an elastic wedge dissimilar materials subjected to a unit concentrated couple at the vertex is got directly by solving the eigenfunction vector for eigenvalue - 1. But the eigenvalue - 1 becomes a double eigenvalue when the vertex angles and modulus of the materials satisfy certain definite relationships and the classical solution for the stress distribution becomes infinite at this moment, that is, the para 相似文献
12.
13.
14.
辛弹性力学已广泛应用于弹性学中各种边值问题的精确解、计算表面波模式以及预测多层超弹性薄膜中的表面褶皱。本文展示了辛分析框架还可应用于受约束介电弹性体中的表面褶皱。机械和电位移向量是两个基本变量来描述介电弹性体中机械变形与电场紧密耦合。褶皱的临界电压可以通过引入基本变量的对偶变量来从辛本征值问题中解决。本文采用扩展的W-W(Wittrick-Williams)算法和精确的积分方法,准确而高效地解决制定的辛本征值问题的本征值。通过将褶皱电压和波数与有无表面能的褶皱基准结果进行比较,验证了辛分析的有效性。辛分析框架简洁且适用于其他不稳定问题,如分层电介质弹性体、磁弹性不稳定性以及层压复合结构的微观和宏观不稳定性。 相似文献
15.
16.
电磁波导的半解析辛分析 总被引:18,自引:1,他引:18
根据电磁波导的Hamilton体系,辛几何可用于任意各向异性材料,而且便于处理不同区段的界面条件,横向的电场和磁场构成了对偶向量.基于Hamilton变分原理用半解析法进行横向离散应当保持体系的辛结构.离散后可以运用应用力学的有效算法,求解其辛本征值问题.每段波导可以引入两端Riccati矩阵,用精细积分法求解其方程组. 相似文献
17.
The eigenvalue problem of the Hamiltonian operator associated with plane elasticity problems is investigated.The eigenfunctions of the operator are directly solved with mixed boundary conditions for the displacement and stress in a rectangular region.The completeness of the eigenfunctions is then proved,providing the feasibility of using separation of variables to solve the problems.A general solution is obtained with the symplectic eigenfunction expansion theorem. 相似文献
18.
The two-dimensional (2D) transient heat conduction problems with/without heat sources in a rectangular domain under different combinations of temperature and heat flux boundary conditions are studied by a novel symplectic superposition method (SSM). The solution process is within the Hamiltonian system framework such that the mathematical procedures in the symplectic space can be implemented, which provides an exceptional direct rigorous derivation without any assumptions or predetermination of the solution forms compared with the conventional inverse/semi-inverse methods. The distinctive advantage of the SSM offers an access to new analytic heat conduction solutions. The results obtained by the SSM agree well with those obtained from the finite element method (FEM), which confirms the accuracy of the SSM. 相似文献
19.
With the help of the coordinate transformation technique, the symplectic dual solving system is developed for multi-material wedges under antiplane deformation. A virtue of present method is that the compatibility conditions at interfaces of a multi-material wedge are expressed directly by the dual variables, therefore the governing equation of eigenvalue can be derived easily even with the increase of the material number. Then, stress singularity on multi-material wedges under antiplane deformation is investigated, and some solutions can be presented to show the validity of the method. Simultaneously, an interesting phenomenon is found and proved strictly that one of the singularities of a special five-material wedge is independent of the crack direction. 相似文献