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Geometrically nonlinear analysis utilizing co-rotational framework for solid element based on modified Hellinger-Reissner principle

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Abstract

In this paper, a solution framework for solid element based on co-rotational formulation is developed for geometrically nonlinear analysis. A novel eight-node solid element embedded in the framework is developed by means of a modified Hellinger-Reissner variational principle. The stiffness matrix is derived by compatible displacement and the most desirable stress fields, as well as a penalty function. In addition, an accelerated modified Newton method is proposed to improve the efficiency of the solution of nonlinear equations. The key idea of this algorithm is that the convergence rate of modified Newton method is accelerated by Aitken method. Furthermore, the equilibrium path of structures exhibiting instability is computed by a hybrid load-controlled/arc-length algorithm. The stiffness parameter is introduced as the criterion for switching load control to arc-length method. Several numerical examples and an experiment for large displacement analysis are presented to demonstrate the efficiency and accuracy of the proposed framework.

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (Nos. 11972297, 11972300) and the Fundamental Research Funds for the Central Universities of China (Grant No. G2019KY05203).

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  1. School of Aeronautics, Northwestern Polytechnical University, 710072, Xi’an, Shaanxi, China

    Yufei Rong, Feng Sun, Qin Sun & Ke Liang

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Correspondence to Qin Sun.

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Rong, Y., Sun, F., Sun, Q. et al. Geometrically nonlinear analysis utilizing co-rotational framework for solid element based on modified Hellinger-Reissner principle. Comput Mech 71, 127–142 (2023). https://doi.org/10.1007/s00466-022-02229-z

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