非线性薄膜的轴对称大变形

Large Axisymmetric Deformations of Nonlinear Membranes

本文基于有限弹性理论导出一组描述非线性薄膜轴对称大变形问题的简化基本方程.在各种边界条件下它可以用打靶法求解.作为一个算例,本文数值计算了球形薄膜膨胀失稳的临界载荷,它与文献中的精确解相吻合.

In this paper,the problem of lager axisymmetrie deformations ofnonlinear membranes is reformulated on the basis of the general theory offinite elasticity.The fundamental equations are simplified to a set of threefirst order ordinary differential equations equations with explicit derivatives.Under various boundary conditions they can be solved by using theshooting methods.As a numerical example,tensile instability of sphericalrubberlike membranes with a Mooney-Rivlin's moder stree-strain relationis resolved by using the equations derived in this paper,the results areclose to exact solution in literature[3].