【摘要】 基于非线性弹性大变形理论,研究了一圆环状弹性薄膜的轴对称面外大变形.在未发生变形的参考构形下,平直圆环状薄膜的内边界连接一个圆盘,将薄膜的外边界固定在刚性的圆环上.当圆盘上作用一个竖直向下的外加载荷时,薄膜经历面外大变形后形成轴对称的形状.结合状态平衡和热力学,推导得到了描述薄膜经历面外大变形的控制方程,控制方程的求解采用了打靶法.计算结果表明,薄膜的变形场是非常不均匀的,这意味着薄膜在工作时材料的利用率较低,造成了材料的浪费.更多还原

【Abstract】 The axisymmetric large deformation of an annular elastic membrane is investigated in the frame of nonlinear elastic deformation theroy.The membrane is initially flat and attached to a disk in the inner circle and to a rigid ring in the outer circle.Then a weight is applied to the disk and the membrane deforms into an axisymmetric shape,undergoing a large out-of-plane deformation.The governing equations characterizing the large out-of plane deformation of the elastic membrane are derived by combining state equilibrium and thermodynamics.The derived governing equations are solved by using the shooting method.The results obtained show that the deformation field in the membrane is very inhomogeneous.This indicates that the membrane doesn’t function efficiently,which leads to a material waste.更多还原