| 1. | A class of variational equations and the boundednes of its solution
一类变分方程解的有界性 |
| 2. | The explict structure of solution of a class of symmetric variational equation by stationary topy
一类平稳型对称变分方程解的显式结构 |
| 3. | Connexion of first integrals with particular solution to the variational equations for birkhoffian systems
系统的第一积分与其变分方程特解的联系 |
| 4. | In this paper , the boundary problem of laplace equation is changed into the variational equation which is equivalent to the boundary integral equation . using linear element , it is solved by galerkin boundary element method
本文把laplace方程的边值问题转化为边界积分方程后，通过与边界积分方程等价的变分形式，采用线性单元，利用galerkin边界元方法求解。 |
| 5. | In efgm , in order to get a numerical solution for a partial differential equation , the shape function is constructed by moving least squares ( mls ) , the control equation is derived from the weak form of variational equation and essential boundary conditions are imposed by penalty function method
它采用移动最小二乘法构造形函数，从能量泛函的弱变分形式中得到控制方程，并用罚函数法施加本质边界条件，从而得到偏微分方程的数值解。 |
| 6. | Applying variational method we analyze the existence and uniqueness for the solution of the corresponding boundary variational equation , truncated mrm boundary variational equation , and approximation truncated mrm boundary variational equation in detailed . we obtain the error estimation for various approximation solutions and construct the boundary integral method with constraint . we explain the principle for choosing the mesh size and the truncated number in mrm . finally the numerical examples show that the theoretical analysis is accord with the numerical experiment result
采用变分方法系统分析了相应问题的边界变分方程，截断的mrm边界变分方程与近似截断mrm边界变分方程解的存在唯一性，解释了网格宽度与mrm方法中截断数的选取原则，讨论了mrm方法中的迭代误差估计，给出了数值算例。 |
| 7. | The governing equations , the corresponding variational equations and equivalent constitutive equations with the numerical expressions of initial stress were developed and applied to the analysis of the deformation of a bar . the conclusions related to the influences of initial stress on the additional deformation , especially to the natural frequency and were obtained
第四章在平截面假设下，用变分原理建立了包含初应力数值表征在内的附加变形支配方程及相应的边界条件、给出了广义应力、广义应变及等效本构方程，凸显了初应力各数值表征对附加变形的影响。 |
| 8. | Therefore it is started with the derivation of variational equation , full formulations including contact boundary conditions , internal forces of shell element are given , and the algorithms for contact - surfaces searching , contact - force computation , and even time integration for the response computation are listed as well
为此，文中从推导变分方程开始，给出了包括接触边界条件、壳单元内力计算在内的全部列式，并列出了识别接触界面的搜索算法，接触力计算以及动力响应计算的时间积分算法的有关公式等等。 |
| 9. | In the buckling question under nonconservation force , a simply example ( the dynamic stability question under the uniformly follower forces with small deformation % linear elastic , straight normal . ) is considered . the variational equation of braid composite cylindrical shells subjectd to uniformly follower forces is deduced based on the variation principle of quasinatural frequency of elastic nonconservative system self - excited vibration . the calculated formulas of the flutter load and quasinatural frequency of shells are obtained . the program for calculating the flutter load is developed . the numerical example is given and some useful conclusions are obtained
对非保守力作用下的屈曲问题，具体研究了圆柱壳在比较简单的情况，即小变形、线弹性、直法线假设下在随动力作用下的壳屈曲问题，由拟固有频率变分原理推出了圆柱壳受随从力作用的变分方程，得到了颤振载荷与壳弯曲的固有频率的计算公式，编制了相应的计算机程序，并给出了具体算例，得到了一些有益的结论。 |
| 10. | According to the stress and displacement variational principle , the mixed variational equations are established from which the state equation is established . thus , the theory of state space is combined with variational principle and the variational solutions are presented under arbitrary loads for transverse isotropic orthortropic bodies on general boundary conditions . thick plates on winkler ' s foundations are researched thoroughly
本文根据应力变分原理和位移变分原理，导出混合变分方程，并将其转换成状态方程，使状态空间理论和变分原理相结合，给出了一般边界条件下横观各向同性和正交各向异性体在任意荷载作用下的变分解。 |
