摘要
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．
A new kind of element coupling shape function matrices is used in the finite element method to express the element elastic displacement as the second order small quantities of element node displacement.The element coupling shape function matrices are derived by means of the geometrically nonlinear strain displacement relation under small deformation assumption.The Kane's equations and the modal coodinate reduction method are used to establish the linear dynamic equations including dynamic stiffness.A dynamic stiffening finite element analysis program for rectangular plates is developed.The validity of the theories and algorithms presented in the paper is verified by the numerical simulation sample.
出处
《天津大学学报》
EI
CAS
CSCD
1998年第5期563-568,共6页
Journal of Tianjin University(Science and Technology)
基金
国家自然科学基金
关键词
动力刚化
有限元法
矩形板
非线性动力学
dynamic stiffness,finite element method,element coupling shape function,Kane's equation,rectangular plate
