不同拉压模量厚壁球壳弹塑性分析

对具有不同拉压模量的厚壁球壳，采用双剪统一强度理论推导了其扩张问题的应力及位移的统一解. 分析了不同模量、不同模型控制参数对厚壁球壳扩张时的扩张压力和应力场的影响.结果表明：厚壁球壳弹性极限压力、应力场、位移场等均随着模量控制参数、模型参数的变化而变化，在$alpha<1$的情况下(即$E^ + < E^ - $)，可以明显提高球壳的弹性极限压力$p_e $; 厚壁球壳塑性极限压力与材料的拉压模量无关，与模型参数$eta$有关，且随$eta$的增加，先增大后减小. 因此若采用经典的弹性理论和单一的模型参数对厚壁球壳进行设计计算，会带来较大的误差.

ELASTO-PLASTIC ANALYSIS OF THICK SPHERIC SHELL WITH DIFFERENT ELASTIC MODULI FOR TENSILE AND COMPRESSIVE DEFORMATIONS

Based on the twin shear unified strength theory and formaterials with different elastic moduli in tension and compression, thispaper derives unified solutions for the stress and displacementfields in a thick spherical shell in expansion. The influences of severalfactors are analyzed, including different elastic moduli in tension andcompression, different parameters in models and the development of plasticzone. The results show that the elastic ultimate expansion pressure, stressand displacement fields depend on the elastic moduli, and the modelparameters. If $alpha $is less than 1, the elastic limit pressure ($p_e$) can be increasedsignificantly. The plastic ultimate pressure $(p_r)$ is not related withelastic moduli, it depends on parameter $(eta)$ in models, and increasesfirst and then decreases with the increasing $eta $. Large errors may beresulted if the classical elastic theory and the single model are adopted and thestrain-softening properties are neglected.