二维振荡机翼可压缩绕流IA型反命题变域变分有限元解

In this paper, on the basis of the variational principles developed the finite element method (FEM) is employed for numerical solution of the inverse problem of 2-D unsteady compressible flow around oscillating airfoils by incorporating the non-reflecting far-field boundary conditions and a new unsteady Kutta condition. All unknown boundary (airfoil contour) and discontinuities(shocks and free trailing vortex sheets) are determined via the functional variation with variable domain and artificial density concept. For the numerical realization of the variable-domain variation, a special finite element with self-adjusting nodes is also suggested herein. The numerical results show that the present method is effective for the design of unsteady airfoil.     

命题还原与评价审视:高考语文命题过程的二维视角 ——以2021年新高考全国卷Ⅰ为例

基于必备知识、关键能力、学科素养、核心价值的2021年新高考尘埃落定.本文以语文全国卷Ⅰ信息文本阅读、文学文本阅读两大板块为例,尝试建立一个在课程目标与高考评价体系基础上,以"命题还原—评价审视"为二维视角的高考试题研究框架.     

Unsteady Inverse Problem of Type B for 2 D Transonic Flow: A Variational Formulation

１　Ｉｎｔｒｏｄｕｃｔｉｏｎ　Ｉｎｔｈｅｌａｓｔｔｗｏｄｅｃａｄｅｓｅｖｅｒｉｎｃｒｅａｓｉｎｇｉｎｔｅｒｅｓｔｏｆｓｃｉｅｎｔｉｓｔｓａｎｄｅｎｇｉｎｅｅｒｓｈａｓｂｅｅｎａｔｔｒａｃｔｅｄｔｏｉｎｖｅｒｓｅａｎｄｏｐｔｉｍｉｚａｔｉｏｎｐｒｏｂｌｅｍｓｏｆａｅｒｏｄｙｎａｍｉｃｓ,ｂｕｔｕｐｔｏｎｏｗｉｎｔｈｅｌｉｔｅｒａｔｕｒｅａｌｌｐａｐｅｒｓｏｎｉｎｖｅｒｓｅ／ｈｙｂｒｉｄｐｒｏｂｌｅｍｓａｒｅｓｔｉｌｌｃｏｎｆｉｎｅｄｔｏｓｔｅａｄｙｆｌｏｗ［１－３］．　ＩｎＲｅｆ．［５］,ｔｈ…     

基于变域变分有限元的翼型气动设计

Designing airfoils according to given pressure (or velocity) distribution is one kind of free boundary problems. Free boundary condition can be coupled with the flow governing equations by variable-domain variational calculus, which makes it possible to calculate simultaneously the flow field and the free boundary. An accurate deduction of the variable-domain variational principles is taken herein to design airfoils in compressible and incompressible flows. Furthermore, two grid types (H and O) are used in the calculation with better results for the O-type grid. It is shown that convergence is accelerated and good results can be obtained even if the initial guessed airfoil shape is a triangle, demonstrating the strong adaptability of this method.     

具有表面电极的二维压电力学的广义变分原理

1　Ｉｎｔｒｏｄｕｃｔｉｏｎ　Ｐｉｅｚｏｅｌｅｃｔｒｉｃｃｅｒａｍｉｃｓｈａｖｅｂｅｅｎｗｉｄｅｌｙｕｓｅｄｉｎｅｎｇｉｎｅｅｒｉｎｇ.ＡｃｏｍｐｒｅｈｅｎｓｉｖｅｌｉｓｔｏｆｗｏｒｋｓｉｎｔｈｉｓａｒｅａｍａｙｂｅｆｏｕｎｄｉｎＲｅｆｓ.[1,2]ａｎｄｔｈｅｒｅｆｅｒｅｎｃｅｓｃｉｔｅｄｔｈｅｒｅｉｎ.Ｉｎｏｒｄｅｒｔｏａｐｐｌｙｔｈｅｆｉｎｉｔｅｅｌｅｍｅｎｔｍｅｔｈｏｄｓｔｏｔｈｅｎｕｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎｏｆｔｈｅｐｉｅｚｏｅｌｅｃｔｒｉｃｉｔｙ,ｉｔｉｓｎｅｃｅｓｓａｒｙｔｏｅｓｔ…     

Variable Domain Variational Finite Element Solution of I A Inverse Problem of 2 D Unsteady Compressible Flow around Oscillating Airfoils

１ＩｎｔｒｏｄｕｃｔｉｏｎＵｐｔｏｎｏｗ,ａｌｔｈｅｐａｐｅｒｓｂｕｔＲｅｆ．［１］ｏｎｔｈｅｉｎｖｅｒｓｅａｅｒｏｄｙｎａｍｉｃｐｒｏｂｌｅｍａｒｅｓｏｌｅｌｙｃｏｎｆｉｎｅｄｔｏｓｔｅａｄｙｆｌｏｗ．ＩｎＲｅｆ．［１］ｔｈｅａｕｔｈｏｒｃａｒｉｅ...     

一类Jacobi矩阵特征值反问题的新算法

In this paper, an inverse problem on Jacobi matrices presented by Shieh in 2004 is studied. Shieh’s result is improved and a new and stable algorithm to reconstruct its solution is given. The numerical examples is also given.     

一类分裂变分不等式问题及其算法

引入一种新的分裂变分不等式问题,提出两种迭代算法并得到了相应的弱收敛定理和强收敛定理.     

关于中心厄米特矩阵的广义反特征值问题

1　Introduction　AmatrixA∈Cn×missaidtobecentrohermitianifA =Jn AJm,andskewcentrohermitianifA =-Jn AJm,where Adenotetheconjugateofthema trixAandJlisthepermutationmatrixoforderlwithonesonthecrossdiagonal(bottomlefttotopright)andzeroselsewhere .ThehermitianToeplitzmatricesformanimportantsubclassofcentrohermi tianmatriceswhichoccurnaturallyindigitalsignalprocessingandotherareas ,seeforinstance[1] andreferencetherein .Thecentrohermitianandrelatedmatricesrecentlyplayanimportantroleinthesolu…     

Equivalent theorem of Hellinger-Reissner and Hu-Washizu variational principles

The paper has proved that Hellinger-Reissner and Hu-Washizu variational principles are but equivalent principles in elasticity by following three ways: 1) Lagrange multiplier method. The paper points out that only a new independent variable can be introduced when one constraint equation has been eliminated by one Lagrange multiplier, which must be expressed as a function of the original variable(s) and/or the new introduced variable after identification. In using Lagrange multiplier method to deduce Hu-Washizu principle from the minimum potential energy principle, which has only one kind of independent variable namely displacement, by eliminating the constraint equations of stress-displacement relations, one can only obtain a principle with two kinds of variables namely displacement and stress; 2) involutory transformation, with such method Hu-Washizu variational principle can be deduce directly from the Hellinger-Reissner variational principle under the same variational constraints of stress-strain relation, and vice verse; 3)semi-inverse method, by which both of the above variational principles can be deduced from the minimum potential energy principle with the same variational constraints. So the three kinds of variational functions in Hu-Washizu variational principle are not independent to each other, the stress-strain relationships are still its constraint conditions.     

北江大堤渗流分析的一个反问题

北江大堤石角段堤基为强透水深砂层,是经常出险情的堤段．根据该堤段的地形地质情况,以测压管资料作为依据,反求出二维渗流分析的边界条件,通过有限元计算得到与实际情况相符的结果,也与三维数值计算结果一致