轴对称变厚度圆板反对称弯曲的传递矩阵法

A transfer matrix method for antisymmetric bending of circular plates with axisymmetric variable thickness

提出了轴对称变厚度圆板反对称弯曲的传递矩阵法。首先,沿环向把圆板离散成一系列圆板和环板单元,圆板和环板单元均按等厚度板处理。由常微分方程求解方法,给出圆板和环板单元的挠度、径向转角、径向弯矩和径向剪力的解析解。其次,基于这一解析解,导出环板单元挠度、径向转角、径向弯矩和径向剪力的传递矩阵和变厚度圆板的总体传递矩阵。这一方法的明显优点是:无论划分多少个单元,总体传递矩阵的阶数始终保持5阶,计算简便,节省内存。最后,通过与有限单元法比较,证实了该传递矩阵方法的有效性。对于指数型变厚度圆板,讨论了指数对圆板最大挠度、最大径向弯矩和最小径向弯矩的影响。

A transfer matrix method was proposed for the antisymmetric bending of circular plates with axisymmetric variable thickness.First,the circular plate is discreted into a series of circular and annular plate elements along the circumferential direction and the circular and annular plate elements are all treated as plates with uniform thickness.According to the solution method of ordinary differential equations,the analytical solution for the deflection,radial rotation angle,radial bending moment,and radial shear force of circular and annular plates with uniform thickness are given.Based on the analytical solution,the tranfer matrix for the deflection,radial rotation angle,radial bending moment,and radial shear force of the annular plate element and the global transfer matrix for the circular plate with variable thickness are then derived.An obvious advantage of this method is that,no matter how many elements the circular plate is discreted into,the order of the global transfer matrix is always maintained as five,which is simple in computation and memory-saving.Finally,the validity of the method is verified through comparison with the finite element method.For circular plates with exponentially variable thickness,the effects of exponent on the maximum deflection,maximum radial bending moment,and minimum bending moment of circular plates are discussed.