【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。仿真算例的计算结果验证了理论和算法的正确性更多还原

【Abstract】 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.更多还原