Currently, the design of pressure vessels is based mainly on the simplified calculations described in the technical standards. Despite the numerous theories found in various valuable monographs and papers, the possibility of precise analytical solutions of static problems of shells including bending effects remains poor. The only alternative to such calculations is the finite element method. The presented paper focuses on the application of the Ritz method for the stress and deformation analyses of standard pressure vessels assuming orthotropic model of the material. The strain energy and the potential energy of external forces are derived for an arbitrary shell structure. Three different displacement functions are considered within the study. The results are compared to the solutions obtained with a use of the finite element method. The convergence of the results is obtained for wide range of the shell thickness. Additionally, the outcome of the study is referred to the design method of ellipsoidal and supposedly equivalent torispherical dished ends described in the technical standards, indicating significant ambiguities.

当前，压力容器的设计主要基于技术标准中描述的简化计算。尽管在各种有价值的专着和论文中找到了许多理论，但是对壳的静态问题（包括弯曲效应）进行精确分析的可能性仍然很小。此类计算的唯一替代方法是有限元方法。本文着重介绍了Ritz方法在假设材料为正交各向异性模型的标准压力容器的应力和变形分析中的应用。对于任意的壳体结构，可以导出应变能和外力势能。研究中考虑了三种不同的位移函数。将结果与使用有限元方法获得的解进行比较。对于大范围的壳厚度，获得了结果的收敛性。此外，研究结果参考了技术标准中描述的椭圆形和假定等效的球形球形端部的设计方法，这表明存在明显的歧义。