轴对称胀形双曲金属薄壳非线性静力分析

对承受内压、非等厚轴对称双曲薄壳,基于大塑性变形几何关系,通过严格的数学推导,建立了用微分代数方程组描述的数学模型。避免了Gleyzal等建立的变形几何关系采用Taylor展开,导致求解大应变问题精度较低的不足。采用可变步长和变阶的Klopfenstein-Shampine数值微分方法进行计算,可方便地获得该类结构应力、应变和位移等参量的变化规律。通过对比该数学模型和基于Gleyzal几何关系数学模型的数值计算结果与试验结果,验证了模型能较好地描述胀形双曲金属薄壳的大应变特性。

NONLINEAR STATIC ANALYSIS OF AXISYMMETRIC BULGED HYPERBOLIC THIN-METAL SHELLS

Based on large deformation geometrical relations, a mathematical model described with differential algebraic equations is presented for axisymmetric hyperbolic thin-metal shells with variable thickness under internal pressure, which remedies the low precision in solving finite strain problems based on Gleyzal’s geometrical relations expanded with Taylor’s formula. Numerical solutions are carried out using Klopfenstein-Shampine numerical differentiation formulae with varying step size and order. The distributions of stresses, strains, and displacements of metal shells at specific moments can be obtained. Numerical solutions by the proposed model and the Gleyzal’s model were compared with experiments. The results show that the proposed model can give more objective results in the finite strain analysis of bulged hyperbolic thin-metal shells.