查询词典 variational equation

However,authors still do not find the relevant references on convergence and symmetric problems of the semi-analytical solution.Based on the semi-analytical solution for Hamilton canonical equation theory,the formulations of the clamp and simply supported and symmetric boundary conditions on the Hamiltonian element are derived by the variational principle.Several numerical examples show that with increase of meshes,the convergence rate of the semi-analytical solution is faster than the convergent rate of traditional finite element method based on displacement.

①在厚度上没有任何位移和应力模式的假设，由于传递矩阵方法的引入，从理论上讲，不受板壳厚度或层合板壳层数的限制；②采用弹性力学的Hamilton正则方程半解析法，可以克服边界的局部化效应[8]；③由于在平面内或圆柱壳的曲面内采用了有限元法，所以一般的板壳问题不受结构侧面边界条件的限制，在复杂工程板壳问题上具有广泛的应用领域。

Firstly, the modified H-R variational principle for elastic material was briefly presented, then the quadratic interpolation functions were used to express the out-plane stresses and displacements variables, consequently the formulation of 8-node isoparametric element for Hamilton canonical equation was derived in detail.

首先简要地介绍了弹性材料修正后的H-R变分原理，然后用二次插值函数表示平面外应力和位移变量，并详细地推导了Hamilton正则方程的八节点等参元列式。

These problems include the selfadjointness of the coefficient matrix operator, the functional of the matrix operator equation, the equivalence between variational problem and boundary value problem of eddy-current fields, and the extreme value principle of the functional.

本文首先从求解时谐涡流场的〓-ψ法与〓-Ω法的矩阵算子方程出发，提出了时谐涡流场的统一矩阵算子方程，进而系统地讨论了该方程的系数矩阵算子的自伴性、矩阵算子方程的泛函、涡流场边值问题与对应变分问题的等价性以及泛函的极值原理。

In cylindrical coordinate system,a modified mixed variational principle with viscous damping force is established and the corresponding state-vector equation is derived.

建立了圆柱坐标系下包含粘滞阻尼力的修正后的Hellinger-Reissner变分原理，推导了对应的状态向量方程。

In this paper a new variational method for approximating the semilinear singular parabolic equation is given by using continuous finite elem...

本文利用连续时空有限元法对半线性奇异抛物方程进行了研究，利用线性化方法给出了有限元解的存在性证明和理论误差估计。

We study the existence of nonlinear elliptic equation by variational method and critical point theory, combined with sub- and sup-solution method.

第二章我们考虑非线性椭圆方程和带有局部p-凹凸非线性项的p-Laplace方程解的存在性，其中λ是正参数，0＜p＜1＜q。

Keywords: meshless method;adaptive algorithm;elliptic equation; variational inequality.

中文关键词：无网格方法；自适应算法；椭圆型方程；变分不等式

In this paper, a semilinear elliptic equation with critical Sobolev-Hardy exponents is studied, the existence of nontrival solutions for which is proved by the linking theorem in variational calculus.

该文研究了一类带有Sobolev-Hardy临界指数的半线性椭圆方程，运用变分理论中的环绕定理证明了方程非平凡解的存在性。

Using the first order shear deformation theory for plate and mechanical-electro coupled variational equation, the two dimensional dynamic finite element formulation containing the effect of pressure in the cavity was derived.

数值分析了在不同的结构和声腔共振频率下主动控制效果，结果表明通过合适地布置压电片，能够很好地控制腔体的声压与位移。

This method is variational method, which will be much faster and more efficiency than other method.Firstly we use gauss integral method to disperse the least potential energy of barrette pile group, with the help of vertical settlement finite series and Mindlins equation, we derived vertical load-settlement solution of barrette pile group.

另外，目前有关壁板桩群桩水平承载特性的研究也比较少，因此，为了加深对壁板桩群桩承载特性的理解，本文利用变分法对壁板桩群桩竖直或水平受荷情况下的承载特性进行了初步的研究，通过变分法直接得出荷载位移显式方程，较之以往方法更加快捷。

Objective:To explore the feasibility of laparoscopy in diagnosing and treating of abdominal diseases.

目的：探讨腹腔镜用以诊断腹部外科疾病及选择治疗方案的可行性。

The lifetime of nylon 1010 and nylon 1010/POSS composites decreased with increasing temperature.

热重-红外联用分析表明尼龙1010在氮气气氛下的降解产物主要为小分子的低聚物，POSS并不改变尼龙1010降解产物的组成。