基于三参数双τ2强度理论的厚壁圆筒极限压力分析

摘要

In order to obtain the unitive analytical solution of whole elastic-plastic analysis process for the thick-wall cylinder prepared by two materials with the same tensile and compressive strengths as well as the different tensile and compressive strengths under the effect of uniformly distributed load,the elastic-plastic stress analysis for the thick-wall cylinder was carried out with the tri-parameter and twin τ2 strength theory. Through quoting the limit stress ratio αand βin the tri-parameter twin τ2 strength theory,the uniform analysis for the materials with the same tensile and compressive strengths as well as the different tensile and compressive strengths were performed.In addition,the elastic limit pressure and elastic-plastic limit pressure as well as the relationship between the stress in the elastic and plastic zone,limit stress ratio αand βof materials and elastic-plastic radius were obtained,respectively.The results show that not only the material limit stress σt,limit stress ratio αand βhave certain influence on the ultimate bearing capacity of thick-wall cylinder,but also the limit pressure of thick-wall cylinder is associated with its inside and outside radius.%为了得到均布载荷作用下拉压同性材料与拉压异性材料厚壁圆筒弹塑性分析全过程的统一解析解，采用三参数双τ2强度理论对厚壁圆筒进行弹塑性应力分析。通过引用三参数双τ2强度理论中的极限应力比α与β对拉压同性材料和拉压异性材料进行了统一分析，分别得到了弹性极限压力、弹塑性极限压力以及弹塑性区应力与材料的极限应力比和弹塑性半径的关系式。结果表明，不仅材料的极限应力σt、极限应力比α和β对厚壁圆筒的极限承载能力有影响，而且厚壁圆筒的内、外半径亦与厚壁圆筒的极限压力有关。