摘要
作高速大范围运动的弹性体，由于运动和变形的耦合将产生动力刚化现象，传统的动力学理论难以计及这种影响。本文在有限元方法中首次引入了单元耦合形函数（阵），以此将单元弹性位移表示为单元结点位移的二阶小量形式。利用几何非线性的应变－位移关系式，在小变形假设条件下确定了单元耦合形函数。在此基础上，根据Ｋａｎｅ方程，运用模态坐标压缩，并通过适当的线性化处理，得到了一致线性化的动力学方程。编制了计及动力刚化的空间桁架结构有限元分析程序。
Elastic bodies undergoing high speed and large overall motion can produce the phenomenon of dynamic stiffening due to the coupling between rigid motion and elastic deflection. Traditional dynamic analysis can hardly involve these terms. A new kind of element coupling shape function matrices is used in finite element method, so that the element elastic displacements are expressed as the second order small quantities of element node displacements. The element coupling shape function matrices are derived by means of geometrically nonlinear strain displacement relation under small deformation assumption. The Kane’s equations and the modal coordinate reduction are used to establish the consistent linearization dynamic equations. A finite element analysis program for spatial truss structures with dynamic stiffening is developed. The validity of the theories and algorithms presented in this paper is verified by a numerical simulation example.
出处
《振动工程学报》
EI
CSCD
1998年第1期18-23,共6页
Journal of Vibration Engineering
基金
国家自然科学基金
国家教委博士点专项基金
关键词
结构动力学
空间桁架
非线性变形
大范围运动
structural dynamics
space trusses
element coupling shape function
Kane’s equation
