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Elastoplastic analysis of shells without any local iterative calculations by block Newton method

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Abstract

In this article, a pseudo-stress for local residual and an algebraically derived consistent tangent are applied to elastic–plastic boundary value problems of shells. The authors define a coupled problem of the weak form of the equilibrium equation for the overall structure and the constrained equations for stress state, which include the yield condition and the plane stress condition, at every material point. Since the pseudo-stress for the residuals of yield criterion and plane stress state is incorporated into the linearized weak form of the equilibrium equation, the proposed scheme does not have any local iterative calculations and enables us to decrease the residuals in the coupled boundary value problems simultaneously. Some numerical examples using shell elements demonstrate the validity and effectiveness of the procedures in complex situation with material and geometrical nonlinearities.

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Acknowledgements

This work was supported by JSPS KAKENHI Grant Numbers JP16H03914, JP20H04198, JP22K14147.

Funding

This work was supported by JSPS KAKENHI Grant Numbers JP16H03914, JP20H04198, JP22K14147.

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Authors and Affiliations

  1. Graduate School of Advanced Science and Engineering, Hiroshima University, 1-4-1, Kagamiyama, Higashi-Hiroshima, Hiroshima, 739-8527, Japan

    Takeki Yamamoto

  2. Graduate School of Environment and Information Science, Yokohama National University, Tokiwadai 79-7, Hodogaya-ku, Yokohama, Kanagawa, 240-8501, Japan

    Takahiro Yamada & Kazumi Matsui

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  1. Takeki Yamamoto
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  2. Takahiro Yamada
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  3. Kazumi Matsui
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Correspondence to Takeki Yamamoto.

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Yamamoto, T., Yamada, T. & Matsui, K. Elastoplastic analysis of shells without any local iterative calculations by block Newton method. Comput Mech 72, 967–989 (2023). https://doi.org/10.1007/s00466-023-02322-x

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