In this article, cyclic loading results of structures, such as cylindrical and spherical vessels are investigated. The structure’s material is assumed to be isotropic and homogeneous and obey a nonlinear strain hardening law in the plastic range. Two general plasticity theories, namely the isotropic and kinematic hardening theories with the von Mises associated flow rules are used to evaluate the cyclic results of these structures under various types of mechanical and thermal loads. Prager and Armstrong-Frederick kinematic hardening models are used to simulate the transformation of the yield surface in the stress space, due to imposed loads. A new iterative method is proposed and used to analyze the structural behavior under cyclic loading conditions. The results are verified with the known data given in the literature.

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