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为研究内压作用下球壳的弹塑性承载特性,以双剪统一强度理论为基础,考虑中间主应力及材料拉压异性的影响,分析了内压作用下球壳的弹性阶段、弹塑性阶段及塑性阶段,建立了适用于不同材料的极限内压统一解,探讨了半径比、拉压比对统一解的影响特性。研究结果表明:此方法使球壳的理论计算得到统一;弹、塑性极限内压均随半径比增加而增大,随拉压比增加而减小,材料的拉压强度差异对球壳的极限内压影响明显;通过算例验证了解析解的正确性,说明双剪统一强度理论可以得出更符合材料性质的极限载荷。该推导结果具有通用性,为球壳的设计及工程应用提供了一定的参考。
In order to study the elasto-plastic behavior of the spherical shell under the action of internal pressure, based on the double shear unified strength theory, considering the influence of the intermediate principal stress and the material’s tensile and compressive anisotropy, the elastic and elastoplastic phases And plasticity stage, a unified solution of ultimate internal pressure suitable for different materials is established, and the effect of radius ratio and tension-compression ratio on the unified solution is discussed. The results show that this method can make the theoretical calculation of the spherical shell uniform. The internal pressure of elasticity and plasticity increase with the increase of radius ratio and decrease with the increase of tension-compression ratio. The influence of internal pressure is obvious. The correctness of the analytical solution is verified by an example, which shows that the double shear unified strength theory can obtain the ultimate load that is more in line with the material properties. The deduced result has the versatility and provides a reference for the design and engineering application of the spherical shell.