可塌陷气管的弹性薄壳模型分析

A Thin Shell Modeling for Collapsible Tracheae

建立气管的一个弹性薄壳数学模型.气管的软骨部分为薄圆柱壳的弹性小变形薄膜和弯曲变形状态,而肌肉部分为大应变薄膜应力状态.软骨为Hooke弹性材料而肌肉采用二参数指数型本构关系.由拟合气管p-V关系的实验数据和计算结果得到了肌肉的材料参数.在均匀分布外压力载荷和平面应变变形条件下,求得了软骨和肌肉的耦合变形解析解,图示了软骨内力和位移,以及气管在外压逐渐增大时的肌肉塌陷变形过程.

An elastic thin shell model was developed for the analysis of collapsible tracheae. The cartilage part of tracheae is modeled by a thin cylindrical shell in membrane and bending states of infinitesimal deformation. The muscle part of tracheae is in membrane state of finite deformation. The cartilage is of Hooke elastic material and the muscle has a constitutive equation of exponential type with two parameters. The parameters were obtained by fitting the experimental data to the computational results of the pressure-volume relation of tracheae. Under the conditions of uniform pressure and plane strain deformation, the resultant forces and deformations of cartilages for the coupling deformation model of cartilage and muscle were obtained and shown.