【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,并采用适当的线性化处理,得到了包含动力刚度项的线性动力学方程.针对矩形板编制了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.更多还原

【Abstract】 Dynamic stiffening effect may appear on elastic bodies undergoing the high-speed and large overall motion 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 element elastic displacement is expressed as the second order small quantities of element 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 linear dynamic equations including dynamic stiffening. A dynamic stiffening finite element analysis program for rectangular plates is developed. The validity of the theory and algorithm presented in the paper are verified by the numerical simulation example.更多还原