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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.
As the elastic body with high-speed and large-scale movement, the dynamic stiffening phenomenon will occur due to the coupling of motion and deformation, and the traditional kinetic theory can hardly account for this effect.In this paper, the finite element method for the first time introduced the unit coupling function (matrix) , The elastic displacement of the element is expressed as a second order small form of displacement of the element.Using the geometric nonlinear strain-displacement relation, the unit coupling shape function is determined under the condition of small deformation.On the basis of this, Kane equation.Using modal coordinate compression, and using the appropriate linearization process, a linear dynamic equation containing the power stiffness terms is obtained.Analytical program of rigid force finite element method is developed for the rectangular plate.The simulation example proves that the theory and algorithm Correctness