The out - of - plane stability of bending beam , which is made up with 2 beams and loaded by non - directional force , is studied . the bending and torsional deflection differential equation of each beam is established in critical condition . according to compatibility conditions of deformation , the characteristic equation is obtained to calculate out - of - plane stability of the cantilever bending beam 对两节梁组成的弯曲梁在非保向力作用下的平面外失稳问题进行了研究,通过建立每节梁临界状态下弯曲和扭转变形微分方程,根据杆件变形的边界条件以及杆件之间的变形协调关系,得出了一端固定一端悬臂的弯曲梁在非保向力作用下平面外失稳的特征方程。
Afterward the numerical method was used to decompose the inherited integration , so the matrix form of constitution equations was derived . then through utilizing the lagrange equation directly , the paper gets the finite element formula . to test the model , the paper calculate the osteoblast ' s dynamic response under near static load and sinusoidal load at a simple tension beam and a four point bending beam 针对单向拉伸和四点弯曲两种离体培养成骨细胞的装置，再根据实际情况，将培养基看成是一种多孔材料，而将成骨细胞看成是粘弹性体，利用自编的有限元分析程序分别计算了受拟静态载荷和受交变载荷下细胞的动力响应，结果很好地反映了细胞的粘弹性性质。
At first , ploygon aggregate structure of concrete is randomly generated in two - dimensional plane with monte carlo method on the meso - level . then , the growth process of a crack of concrete 3 - point bending beam specimen is analyzed by fem , according to the criterion of maximum circumferential tensile stress . and the path of crack to spread in mortar , aggregate and interfaces of them is gained by the ultimate fracture criteria in construction standard that the width of crack should not be more than 0 . 2mm 首先，在细观层次上，根据蒙特卡罗随机抽样原理，在二维平面上建立了混凝土多边形随机骨料结构模型，然后采用有限元计算方法，根据最大周向正应力准则，对三点弯曲梁构件进行了开裂过程的模拟，并以建筑规范中构件裂缝小于0 . 2mm的要求为最终破坏标准，得出了裂纹在基质、骨料及界面的扩展路径。
In the beginning of this thesis , types and characteristics of intelligent material elements have been introduced . and the basic equations of piezoelectric material have been given . then according to hamilton principle , both the static and dynamic finite element equations for the intelligent structure are formulated with isoparametric element of bending plate or bending beam 在本论文的开始，简要介绍了智能材料元件的种类和性质，并给出了压电材料的本构方程，然后根据hamilton原理，采用任意等参四边形板梁弯曲单元，导出了智能梁的静态、动态有限元方程；对于复杂几何形状或边界条件的一般结构，根据三维有限元模型，导出三维动态有限元方程。
The mathematic model of the ultra - thin spherical mirror is to be treated as elastic thin shell . then the predigested model , i . e . , bended beam , used in qualitative analysis was proposed , and its deflection and stress formulas under the freely supported condition were set up . based on an off - axis aspherical primary mirror , the relationship of aspherical surface error ( rms ) in tangential plane with bended beam ’ s radius r , position s of concentrated load p and geometry length l of arc was analyzed 根据这一设想,本文建立了超薄镜的数学模型?薄壳,并提出了强制力作用下超薄镜的简化模型?曲梁,推导了曲梁在简支情况下受力变形的挠度公式,并结合一个实例,计算出曲梁变形后与所需非球面的面形残差( rms )在子午方向与曲梁弧长l 、曲梁半径r及集中力位置s的关系及满足面形精度的r和s范围,分析了弧矢方向的rms ,得出了同时满足子午和弧矢方向面形要求的l 、 r和p 。
The result shows that the potential difference between the upper side and bottom side of the cantilever sample present the biphasic pulse when it is under step load , the result also shows the potential between the upper side and bottom side of the four point bending beam adds with the frequency of load , but the phase difference changes opposite from the potential 结果表明流动电位差在跃阶载荷作用下存在双脉冲现象，而在受交变载荷时其值随载荷频率的增加而增加并趋于平缓，其相位差则与电位差的变化刚好相反，这与gross和salzstein等的结果一致。
