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Generalized modal element method: part II—application to eight-node asymmetric and symmetric solid-shell elements in linear analysis

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Abstract

In this paper, two eight-node asymmetric solid-shell elements are firstly presented to illustrate the use of traditional finite element technique in GMEM for constructing new finite element formulations. In these two elements, the analytical method is utilized to derive the displacement functions of the basic in-plane modes, which makes the resulted elements free of mesh distortions for these modes. For out-of-plane modes, the Mindlin plate elements CQUAD4 and QTS4 are integrated to calculate the corresponding modal displacement vectors and modal force vectors of solid-shell elements. As a result, the displacement functions of the plate-bending element range up to three orders of magnitude. On the other hand, since the asymmetric elements cannot be applied to frequency analysis, two symmetric solid-shell elements are proposed by using a modal transformation method, in which the in-plane modes are derived from the previous proposed symmetric solid element S-MEM8S and the out-of-plane modes are constructed by plate elements CQUAD4 and QTS4, respectively. Various benchmarks including linear static and frequency analysis are presented to demonstrate the accuracy and efficiency of the presented elements.

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (Nos. 51375386 and 11602286).

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  1. Northwestern Polytechnical University, Xi’an, 710072, China

    P. Q. He, Q. Sun & K. Liang

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  1. P. Q. He
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Correspondence to Q. Sun.

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He, P.Q., Sun, Q. & Liang, K. Generalized modal element method: part II—application to eight-node asymmetric and symmetric solid-shell elements in linear analysis. Comput Mech 63, 783–804 (2019). https://doi.org/10.1007/s00466-018-1622-5

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