Abstract
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.
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