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http://dx.doi.org/10.12989/anr.2022.13.4.351

An efficient C1 beam element via multi-scale material adaptable shape function  

El-Ashmawy, A.M. (Department of Aircraft Mechanics, Military Technical College)
Xu, Yuanming (School of Aeronautic Science and Engineering, Beihang University)
Publication Information
Advances in nano research / v.13, no.4, 2022 , pp. 351-368 More about this Journal
Abstract
Recently, promising structural technologies like multi-function, ultra-load bearing capacity and tailored structures have been put up for discussions. Finite Element (FE) modelling is probably the best-known option capable of treating these superior properties and multi-domain behavior structures. However, advanced materials such as Functionally Graded Material (FGM) and nanocomposites suffer from problems resulting from variable material properties, reinforcement aggregation and mesh generation. Motivated by these factors, this research proposes a unified shape function for FGM, nanocomposites, graded nanocomposites, in addition to traditional isotropic and orthotropic structural materials. It depends not only on element length but also on the beam's material properties and geometric characteristics. The systematic mathematical theory and FE formulations are based on the Timoshenko beam theory for beam structure. Furthermore, the introduced element achieves C1 degree of continuity. The model is proved to be convergent and free-off shear locking. Moreover, numerical results for static and free vibration analysis support the model accuracy and capabilities by validation with different references. The proposed technique overcomes the issue of continuous properties modelling of these promising materials without discarding older ones. Therefore, introduced benchmark improvements on the FE old concept could be extended to help the development of new software features to confront the rapid progress of structural materials.
Keywords
finite element modeling; functionally graded material; functionally graded nanocomposites beams; isotropic; nanocomposites; orthotropic; timoshenko beam element;
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