空间桁架结构动力刚化有限元分析

FINITE ELEMENT ANALYSIS FOR SPATIAL TRUSS STRUCTURES WITH DYNAMIC STIFFENING

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成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。编制了空间桁架结构动力刚化有限元分析程序,仿真算例证明了理论和算法的正确性。

Elastic bodies, undergoing high-speed and large overall motion, may introduce dynamic stiffening due to coupling between rigid motion and elastic deflection. Traditional dynamics can hardly consider these terms. A new kind of element coupling shape function matrices is used in finite element method, so that element elastic displacements is expressed as the second order small quantities of node displacement. 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 method 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 the paper are verified by a numerical simulation example.