Abstract
To address the issue of incompatible nodal parameters between finite elements of different dimensions, this paper introduces a new interpolation formula, named “trial-correction” displacement interpolation, utilizing trilinear and cubic interpolations. This interpolation method is applied to construct an 8-node hexahedral solid element (Solid-H8-TC) with rotational degrees of freedom, featuring 6 nodal parameters including 3 translational and 3 rotational displacements. The element successfully passed the patch test and demonstrated convergence. Subsequent numerical examples show that the Solid-H8-TC element achieves a numerical accuracy of over 99% as the mesh is refined. Furthermore, the Solid-H8-TC element can be directly combined with shell elements, effectively resolving the compatibility issues of nodal parameters between finite elements of different dimensions. Lastly, the trial-correction displacement interpolation method employed in this study exhibits excellent scalability and provides a new theoretical basis for finite element analysis of plane, beam, and shell structures.
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant No. U20A6004), the National Key R &D Program of China (Grant No. 2022YFB4701001), the Guangzhou Science and Technology Plan Project (Grant No. 202201010277). The authors greatly acknowledge the financial support.
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Huang, G., Li, H., Lu, Y. et al. Hexahedral Solid Element with Rotational Degrees of Freedom Based on a Novel Trail-Correction Displacement Interpolation Scheme. Iran J Sci Technol Trans Mech Eng (2024). https://doi.org/10.1007/s40997-024-00763-0
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DOI: https://doi.org/10.1007/s40997-024-00763-0