两种圆形双层辐射式悬挂结构的优化计设

本文考虑了有内拉环和无内拉环两种形式结构的优化设计,三个设计变量,十个约束条件,以结构造价为目标函数。对约束条件处理后,用Powell方法进行了优化,结果表明,内环垂直变位约束[Dp]对造价与结构选型影响十分大,当[Dp]较小时,有内拉环的结构经济性较好,当[Dp]较大时,则无内拉环的结构更经济,结构总造价随[Dp]的增大而明显下降,在一定范围内对造价影响不大,本文可为此类结构造型,决定结构初步设计尺寸及为规定合理的[Dp]尺寸提供参考依据。     

分区函数法在加权残数法中的应用

本文提出了一个分区函数法的概念.即根据边界形状或刚度、荷载的变化,将原受力体分成若干个分区.在每个分区中设定不同的试函数,并在各分区的交界上考虑了连续协调条件.这样共建立了内部平衡、外部边界和交线协调三种残数方程.文中给出了公式和例题.     

SOLUTION FOR FREE VIBRATION PROBLEM OF MEMBRANE WITH UNEQUAL TENSION IN TWO DIRECTIONS

In this paper,we obtain the analytic solution of free vibra-tion frequency and mode shapes of rectangle,circle and ellip-tic membranes.The approximate solution of membrane with arbi-trary boundary is also obtained.All of these membranes areacted on by unequal tension in two directions.For the rectangle membrane,in this paper we transform itsvibration equation into one of usual membranes by trnasformingthe coordinate,thus it is easy to get the solution.For thecircle membrane,first we transform the coordinate in the sameway we deal with the rectangle membrane.Next we transform thevibration equation into the Mathieu equation,then we get a for-mula of frequeney of that membrane with some Mathieu function’sproperty.In the solution the elliptic membrane is similar tothat of the circle membrane.Finally,some examples are given.     

Application of subregion function method in the method of weighted residuals

In this paper, a new concept of subregion function method is suggested. According to the boundary shape and the stiffness and loading conditions of the structure, the original zone of the structure is divided into some subregions, in each of which different trial functions may be adopted. Conditions of compatibilities between subregions are considered. Finally residual equations consisted of interior residuals, boundary residuals and coboundary residuals between subregions are given.A numerical example to illustrate the theory of this method is given.     

二向受力不等的平面薄膜自由振动问题解

本文中求解了双向受力不等的矩形、圆形、椭圆形平面薄膜的自振频率与振型,还给出了任意外形边界的平面薄膜的近似解.矩形薄膜,先经过坐标变换将方程变换成常见的薄膜振动方程,因此很容易求得解.圆形薄膜.先将坐标作与上述同样的变换,再把它变换成椭圆坐标,将方程化为马丢(Mathieu)方程,这样利用马丢函数的性质,不难求得其解.椭圆形薄膜解法与圆形薄膜相似.文末还给出了例题.     

APPLICATION OF SUBREGION FUNCTION METHOD IN THE METHOD OF WEIGHTED RESIDUALS

In this paper,a new concept of subregion function method is suggested.According tothe boundary shape and the stiffness and loading conditions of the structure,the originalzone of the structure is divided into some subregions,in each of which different trialfunctions may be adopted.Conditions of compatibilities between subregions are considered.Finally residual equations consisted of interior residuals,boundary residuals and co-boundary residuals between subregions are given.A numerical example to illustrate the theory of this method is given.