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将冻结壁等效为弹性模量、黏聚力呈抛物线分布的功能梯度材料(FGM)厚壁圆筒,基于统一强度理论,考虑中间主应力的影响,推导得到冻结壁的弹性极限荷载、弹塑性应力场及塑性极限荷载的解析解。将所得结果与均质冻结壁进行比较,并分析强度理论参数对各个解析解的影响。研究结果表明:考虑冻结壁的FGM特性,应力分布较均质冻结壁有一定的变化,环向应力由线性分布变为抛物线型分布;环向应力的最大值不再出现在冻结壁的内壁或外壁,而是出现在冻结壁厚度的中部;与均质冻结壁相比,FGM冻结壁的弹性极限荷载较大,但塑性极限荷载却较小;FGM冻结壁的弹性极限荷载、塑性极限荷载、径向应力及环向应力均随强度理论参数的增大而增大。所得结果可为冻结壁的设计提供一定的理论参考。
The frozen wall is equivalent to a FGM thick wall cylinder with elastic modulus and cohesion distribution. Based on the unified strength theory, considering the influence of middle principal stress, the elastic ultimate load of the frozen wall is deduced. Analytical Solution of Plastic Stress Field and Plastic Ultimate Load. The results obtained are compared with those of homogeneous frozen walls, and the influence of theoretical parameters of strength on the analytical solutions is analyzed. The results show that considering the FGM characteristics of the frozen wall, the stress distribution changes somewhat compared with the homogeneous frozen wall, and the circumferential stress changes from a linear distribution to a parabolic distribution. The maximum value of the circumferential stress no longer appears on the inner wall of the frozen wall or Compared with the homogeneous frozen wall, the FGM frozen wall has larger ultimate load but lower plastic limit load. The ultimate ultimate load, plastic ultimate load, The radial stress and hoop stress increase with the increase of theoretical parameters of strength. The results can provide some theoretical reference for the design of frozen wall.