符拉索夫板弯曲问题的通解

 针对符拉索夫板弯曲问题的基本方程, 给出了两个形式简洁 的通解定理.     

定常温度热弹性梁中精化理论和分解定理的等价性

根据分解定理,把自由表面热弹性梁内的应力状态分解为三部分:内应力状态、热应力状态和Papkovich-Fadle应力状态(简称P-F应力状态)。随后给出了定常温度热弹性Biot通解的一种新的简化形式。不作预先假设,从热弹性理论出发,利用热弹性通解和Lur'e算子方法构造了梁的精化理论,得出了自由表面热弹性梁的三个精确方程:四阶方程、温度方程和超越方程。最后分别证明了分解定理的三个应力状态与精化理论的三个方程一一等价。     

Papkovich-Neuber(P-N)通解的互逆公式及其它

本文构造出了P-N解的互逆公式从而较简捷地证明了P-N解的完备性。利用互逆公式中自动包含的反映零位移场的任意调和函数,可以自然地引出“E-S 凸域定理”,此外,平面应变问题通解也是互逆公式的直接结果。     

弹性力学空间轴对称问题通解的研究

本文证明了横观各向同性弹性力学空间轴对称问题的通解是完备的.这里φ满足同时得到了轴对称问题一个新的完备通解这里φ满足     

无限板分布圆孔的级数叠加法

对于平面弹性体孔口问题,已经建立了一些完整的研究方法,通过曲线坐标变换或复变函数影射等方法,求得了某些孔口问题的精确解,并提出了近似的计算方法。本文试图通过极坐标下单孔问题的通解,对于多个圆孔进行通解叠加,然后利用边界条件确定通解中的 ...     

关于“弹性力学平面问题位移函数的研究”的讨论

本文通过Ｌｏｖｅ位移函数导出了各向同性弹性力学平面问题的位移通解，从而证明了文［１］中结论只是空间问题位移通解的一种特例．     

关于弹性扁薄壳问题的通解

本文证明了BπacoB提出的扁壳混合函数方程确是常曲率非球面扁壳问题的通解(混合函数形式)。从而解决了专著[2]指出的疑题。本文导出了球面扁壳问题的通解。 此外,从扁壳位移法基本方程出发,导出了扁壳的位移函数,证明了用位移函数表示的位移连同位移函数方程一起也代表了扁壳问题的通解。     

弹性力学平面问题位移函数的研究

本文推导出各向同性弹性力学平面问题位移的完备通解，该位移通解的导出，使求解任何边界条件的平面问题成为现实     

弹性力学广义平面应力的精化理论

从Papkovich-Neuber通解出发，导出了弹性力学广义平面应力问题的精化理论控制方程．若取零阶近似表示，方程即为通常弹性力学平面应力问题的平衡方程．对略去h^2及以上高阶项的八阶方程给出了通解．     

任意边界条件下双模量矩形薄板的弯曲

将双模量板等效为两个各向同性小矩形板组成的层合板,假定该层合板的中性面即为两个小矩形板的交界面。根据中性面上应力为零且薄板全厚度上应力的代数和为零,推导了双模量矩形薄板的中性面位置。本文采用严宗达提出的带补充项的双重正弦傅里叶级数通解,该通解可以适用于任意边界条件的矩形薄板且不需要叠加或者重新构造。联立边界条件和控制方程,求得通解中的待定系数并代入到通解中,即可得到任意边界条件下双模量矩形薄板的弯曲解析解。与有限元结果比较,本文结果符合工程精度要求。     

ON A CLASS OF NEW KKM THEOREM WITH APPLICATIONS

ＯＮＡＣＬＡＳＳＯＦＮＥＷＫＫＭＴＨＥＯＲＥＭＷＩＴＨＡＰＰＬＩＣＡＴＩＯＮＳＺｈａｎｇＳｈｉｓｈｅｎｇ（张石生），ＺｈａｎｇＸｉａｎ（张宪）（ＲｅｃｅｉｖｅｄＭａｙ１５，１９９５）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ，ａｃｌａｓｓｏｆｎｅｗＫＫ...     

NEW VERSION OF KKMTHEOREM IN PROBABILISTIC METRIC SPACES WITH APPLICATIONS

ＮＥＷＶＥＲＳＩＯＮＯＦＫＫＭＴＨＥＯＲＥＭＩＮＰＲＯＢＡＢＩＬＩＳＴＩＣＭＥＴＲＩＣＳＰＡＣＥＳＷＩＴＨＡＰＰＬＩＣＡＴＩＯＮＳＺｈａｎｇＳｈｉｓｈｅｎｇ（张石生）ＹｅｏｌＪｅＣｈｏ（赵烈济）ＷｕＸｉａｎｇ（吴鲜）（ＲｅｃｅｉｖｅｄＭａｙ７，１９９...     

NOTES ON A STUDY OF VECTOR BUNDLE DYNAMICAL SYSTEMS (Ⅱ)─PART 2

In the part 2, theorem 3.1 studied in part 1^[15] is proved first. The proof is obtained via a way of changing variables to reduce the original system of differential equations to a form concerning standard systems of equations in the theory of differentiable dynamical systems. Then by using theorem 3.1 together with the preliminary theorem 2.1, the main theorem of this paper announced in part 1 is proved. The definition of admissible perturbation is contained in the appendix of part 2. The meanings of the main theorem is described in the introduction of part 1.     

An existence theorem for the limit analysis problem

The limit analysis problem has been considered. The statical and kinematical formulation are summarised, and it is noted that while an existence theorem for the statical problem can obtained by the results of convex analysis, similar theorem for the kinematical problem must be obtained independently. We illustrate the main reasons that lead to a Suquet's relaxed version of the original kinematical problem, and we prove an existence theorem showing that the functional of dissipation is lower semicontinuous. This theorem is compared with an analogous theorem existing in the literature.     

Some new fixed point theorems in probabilistic metric spaces

ＳＯＭＥＮＥＷＦＩＸＥＤＰＯＩＮＴＴＨＥＯＲＥＭＳＩＮＰＲＯＢＡＢＩＬＩＳＴＩＣＭＥＴＲＩＣＳＰＡＣＥＳｚｈｕＣｈｕａｎ－ｘｉ（朱传喜）（ＭａｔｈｅｍａｔｉｅｓＤｉｖｉｓｉｏｎ,Ｎａｎｃｈａｎｇ．Ｕｎｉｖｅｒｓｉｔｙ,Ｎａｎｃｈａｎｇ）（Ｒｅｃｅｉｖ...     

On Averaging of Difference Equations on an Infinite Interval

The averaging method on a semiaxis is justified for systems of difference equations. A theorem on the closeness of the corresponding solutions of the exact and averaged systems on a semiaxis is proved. This theorem is analogous to the second Bogolyubov theorem on the averaging method for systems of difference equations.     

A solving method for a system of partial differential equations with an application to the bending problem of a thick plate

Ｓｏｍｅｅｎｇｉｎｅｅｒｉｎｇｐｒｏｂｌｅｍｓｃａｎｂｅｅｘｐｒｅｓｓｅｄｂｙｓｕｃｈａｓｙｓｔｅｍｏｆｌｉｎｅａｒｎｏｎ＿ｈｏｍｏｇｅｎｅｏｕｓｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓａｓＬ１［ｕ１（ｑ）］＝Ｆ１（ｑ）,Ｌ２［ｕ２（ｑ）］＝Ｆ２（ｑ）＋ｆ２［ｕ１（ｑ）］,…Ｌｎ［ｕｎ（ｑ）］＝Ｆｎ（ｑ）＋ｆｎ［ｕ１（ｑ）,ｕ２（ｑ）,…,ｕｎ－１（ｑ）］,（１）ａｎｄｔｈｅｉｒｉｎｉｔｉａｌａｎｄｂｏｕｎｄａｒｙｃｏｎｄｉｔｉｏｎｓ,ｗｈｅｒｅｑｉｓｔｈｅｓｅｔｏｆａｌｌａｒｇｕｍｅｎｔｓｗ…     

ON THE MODIFIED CASTIGLIANO’S THEOREM

This paper gives the modified Castigliano’s theorem, which is more convenient and more extensive for applications than the classical Castigliano’s theorem.The modifications to the classical Castigliano ’s theorem are in following two respects, the first respect is that the expression of the partial derivative with respect to the concentrated load p of the complementary energy density in the clasical Castigliano ’s theorem is replaced by the expressions with teh products of the external loads and influence functions, the modification brings us greatest simplicity and greatest convenience for calculations under various loads; the second respect is that the expressions with the products of the inhomogeneous boundary displacements and the influence functions are introduced into the classical Castigliano’s theorem, the modification provides the theoretical fundamental for solving the problems of various boundary conditions.We show also the method of how to apply the modified Castigliano’s theorem to solve the problems of the surface structural mechanics.Finally, as a calculated example of the applications of the modified Castigliano’s theorem we solved the equation of the deflection surface of the rectangular plate with two adjacent edges built-in and other two adjacent edges free.     

时间尺度上Hamilton系统的Noether理论

提出并研究时间尺度上Hamilton系统的Noether对称性与守恒量问题．建立了时间尺度上Hamilton原理,导出了相应的Hamilton正则方程．基于时间尺度上Hamilton作用量在群的无限小变换下的不变性,建立了时间尺度上Hamilton系统的Noether定理．定理的证明分成两步：第一步,在时间不变的无限小变换群下给出证明;第二步,利用时间重新参数化技术得到了一般无限小变换群下的定理．给出了经典和离散两种情况下Hamilton系统的Noether守恒量．文末举例说明结果的应用．     

NOTES ON A STUDY OF VECTOR BUNDLE DYNAMICAL SYSTEMS (Ⅱ)──PART 2

IV.ChangingVariablesTheproofofthemaintheoremstatedinSectionIofthepaperwillbecompletedinSectionVI.Now,withthesystem.)giveninSectionill,letuswritesimplyTheexistenceofsuchf(k)followsfromtheproperty(II)ofthesystem.).Theexistenceisunique.Thenbytheproperty(II)o…