Abstract Depending on the required solution, this paper presents results for the state of stress and buckling of a uniformly pressurized elastic toroidal vessel of four segments. In the first part of the paper, a closed-formed stress solution is formulated for the novel shell form, by adopting the membrane solution as the particular solution of the Reissner-Meissner general bending-theory equations, and an approximate bending solution is used to quantify discontinuity effect at the shell junctions. In the second part of the paper, linearized stability equations are formulated and simplified for the segmented toroidal vessel buckling problem. The membrane results obtained in the first part is used to predict the pre-buckling state and the stability equations are approximately solved for the segments in the middle regions of the toroidal vessel, using the Galerkin’s scheme. This leads to an expression for estimating the critical buckling pressures of pressurized isotropic toroids. Numerical results from the proposed methods are presented and compared with those from a finite element method solution.

中文翻译：

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多壳环形压力容器的解析公式与数值建模

摘要 根据所需的解决方案，本文给出了四节均匀加压弹性环形容器的应力和屈曲状态的结果。在论文的第一部分，采用膜解作为Reissner-Meissner一般弯曲理论方程的特解，为新的壳形式制定了封闭形式的应力解，并使用近似弯曲解来求解量化壳连接处的不连续效应。在论文的第二部分，为分段环形血管屈曲问题制定并简化了线性化稳定性方程。第一部分中获得的膜结果用于预测预屈曲状态，并近似求解环形血管中间区域段的稳定性方程，使用伽辽金方案。这导致了用于估计加压各向同性环面的临界屈曲压力的表达式。提出了所提出的方法的数值结果，并与有限元方法的结果进行了比较。