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Locking-free triangular plate element using polynomial incompatible approximation for analysis of cracked thick–thin plates

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Abstract

In this paper, a simple locking-free triangular plate element, referred to here as the Mindlin triangular plate element with full integration (MTPF), is presented for the analysis of cracked thick–thin plates. The element employs a new specially designed incompatible meshless approximation, independent of the nodes and triangle shape, in order to define displacements for the purpose of avoiding the use of reduced/selected integration to make the MTPF locking-free and valid for the thin plate. The current MTPF is also extended for the analysis of cracked thick–thin plates, and the virtual crack closure technique is applied in order to compute the crack tip stress intensity factors of the cracked thick–thin plates, where the formula derivation and numerical implementation are very simple and convenient for the present MTPF. Several representative numerical examples demonstrate that the MTPF is a robust and high-performance element for cracked thick–thin plates.

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Acknowledgements

The authors gratefully acknowledge the support of the national Natural Science Foundation of China (NSFC 51778473), and the Ministry of Science and Technology of China (Grant Nos. SLDRCE14-B-28 and SLDRCE14-A-09).

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Authors and Affiliations

  1. State Key Laboratory of Disaster Reduction in Civil Engineering, College of Civil Engineering, Tongji University, Shanghai, 200092, China

    Hehua Zhu, Guangchao Zhang & Yongchang Cai

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  1. Hehua Zhu
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  2. Guangchao Zhang
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  3. Yongchang Cai
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Correspondence to Guangchao Zhang.

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Zhu, H., Zhang, G. & Cai, Y. Locking-free triangular plate element using polynomial incompatible approximation for analysis of cracked thick–thin plates. Int J Fract 211, 1–12 (2018). https://doi.org/10.1007/s10704-018-0263-1

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  • DOI: https://doi.org/10.1007/s10704-018-0263-1

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