厚壁球形封头的弹性应力分析

Elastic Stress Analysis of Thick Spherical Head

厚壁球形封头在内压力作用下处于三向应力状态 ,可以按类似于拉美公式的分析方法对其三向应力作近似分析。基于这种认识 ,在厚壁球形封头上取一微元体 ,通过分析其受力、位移、变形协调及应力应变关系 ,找出了求解应力的微分方程 ,并根据边界条件得出了厚壁球形封头三向应力的计算公式 ,即径向应力为 pK3 - 1(1- R30r3 ) ,环向应力和经向应力相等 ,其值为 pK3 - 1(1+ R302r3 )。

Three stresses exist in thick spherical head under inner pressure.It can be analysed by the way similar to Lamei Formula.Based on this knowledge,a micro unit is taken from thick spherical head.By analysing the forces existing on it,displacement,deformation harmony,stress-strain relation and a differential formula are derived.According to lateral conditions,three stresses in thick spherical head are obtained,i.e.radial stress:pK 3-1(1-R 3 0r 3),circumferential and longitudinal stress are equal:pK 3-1(1+R 3 02r 3).