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Total Lagrangian particle method for the large-deformation analyses of solids and curved shells

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Abstract

A high-accuracy smoothed-particle hydrodynamics (SPH) method for a large-deformation solid is developed from two aspects: improving the completeness of the approximation function and deducing the governing equation in the undeformed configuration. On the basis of Combescure’s researches and our previous studies, the SPH shell theory based on the Mindlin–Ressiner plate is detailed, which has overcome the unbridgeable drawbacks of solid modeling of thin structures and pushed forward the engineering applications of solving large-deformation and other nonlinear issues. Afterward, several treatments of SPH solid and shell are carried out, including the hourglass mode, boundary conditions and irregular structures; moreover, the corresponding validations are also conducted to reveal the feasibility and effectiveness of the proposed treatments. Finally, the accuracy of the present SPH program is verified further through two benchmarks of a curved shell.

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Authors and Affiliations

  1. College of Shipbuilding Engineering, Harbin Engineering University, Harbin, 150001, Heilongjiang, China

    Aman Zhang, Furen Ming & Xueyan Cao

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  1. Aman Zhang
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  2. Furen Ming
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  3. Xueyan Cao
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Correspondence to Aman Zhang.

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Zhang, A., Ming, F. & Cao, X. Total Lagrangian particle method for the large-deformation analyses of solids and curved shells. Acta Mech 225, 253–275 (2014). https://doi.org/10.1007/s00707-013-0938-7

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  • DOI: https://doi.org/10.1007/s00707-013-0938-7

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