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Analytical DSA for Explicit Dynamics of Elastic-plastic Shells

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Abstract

The paper presents an analytical constitutive design sensitivity analysis (DSA) algorithm for explicit dynamics of elastic-plastic finite rotation shells. Two explicit dynamical algorithms for finite rotation shells are presented, and the DSA is developed for the one formulated in terms of the rotation vector and its time derivatives, \(\{ \mathbf{\psi}, \mathbf{\dot{\psi}}, \mathbf{\ddot{\psi}}\}\). The hypo-elastic constitutive model based on the Green–McInnis–Naghdi stress rate is used to derive an incremental algorithm in terms of ‘back-rotated’ objects. The associative deviatoric Huber–Mises plasticity modified by plane stress conditions is implemented in the form suitable for finite rotation/small elastic strain increments. The analytical DSA is developed for the above-specified problem, with the design derivatives calculated w.r.t. material parameters. Design- differentiation of the dynamic algorithm and the scheme of handling the history data and the predicted values in differentiation, which is crucial in computing correct derivatives, are described. Besides, we show how to avoid Newton loops in the DSA algorithm, when such a loop is present in the constitutive algorithm. Numerical examples show that, despite a great complexity of the solution algorithm for the finite-rotation elastic-plastic shells, it is feasible to compute analytical design derivatives of very good accuracy.

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Authors and Affiliations

  1. Polish Academy of Sciences, IFTR, Swietokrzyska 21, 00-049, Warsaw, Poland

    K. Wisniewski, P. Kowalczyk & E. Turska

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  1. K. Wisniewski
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  2. P. Kowalczyk
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  3. E. Turska
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Correspondence to K. Wisniewski.

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Wisniewski, K., Kowalczyk, P. & Turska, E. Analytical DSA for Explicit Dynamics of Elastic-plastic Shells. Comput Mech 39, 761–785 (2007). https://doi.org/10.1007/s00466-006-0068-3

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  • DOI: https://doi.org/10.1007/s00466-006-0068-3

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