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A Higher-Order Plate Element Formulation for Dynamic Analysis of Hyperelastic Silicone Plate

Published online by Cambridge University Press:  16 July 2019

Qiping Xu ,
Jinyang Liu  and
Lizheng Qu
Qiping Xu
Affiliation:
Department of Engineering Mechanics School of Naval architecture, Ocean and Civil Engineering Shanghai Jiao Tong UniversityShanghai, China
Jinyang Liu*
Affiliation:
Department of Engineering Mechanics School of Naval architecture, Ocean and Civil Engineering Shanghai Jiao Tong UniversityShanghai, China
Lizheng Qu
Affiliation:
Department of Engineering Mechanics School of Naval architecture, Ocean and Civil Engineering Shanghai Jiao Tong UniversityShanghai, China
*
*Corresponding author ([email protected])
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Abstract

Most of previous work for modeling and analyzing various traditional linear elastic materials concentrated on numerical simulations based on lower-order absolute nodal coordinate formulation (ANCF) plate element, in which linear interpolation in transverse direction is utilized and stiffening effect caused by volumetric locking occurs. Relatively little attention is paid to modeling hyperelastic incompressible materials with nonlinear effect and large deformation. In view of this, a higher-order plate element formulation with quadratic interpolation in transverse direction for static and dynamic analysis of incompressible hyperelastic silicone material plate is developed in this investigation. The use of higher-order plate element can not only alleviate volumetric locking, but also improve accuracy in simulating large bending deformation as compared to improved lower-order plate element with selective reduced integration method and originally proposed lower-order plate element. Subsequently, experimental investigation that captures free-falling motion of silicone cantilever plate and corresponding simulations are implemented, the results obtained using higher-order plate element are in excellent accordance with experimental data, whereas the results gained applying other two types of plate elements are distinguished from experimental data. Finally, it is concluded that the developed higher-order plate element formulation achieves approving precision and has superiority in simulating large deformation motion of hyperelastic silicone plate.

Keywords

Dynamic analysisLarge deformationHigher-order plate elementVolumetric locking
Type
Research Article
Information
Journal of Mechanics , Volume 35 , Issue 6 , December 2019 , pp. 795 - 808
Copyright
© The Society of Theoretical and Applied Mechanics 2019 

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References

REFERENCES

Shabana, A. A., “An absolute nodal coordinates formulation for the large rotation and deformation analysis of flexible bodies,” Technical Report MBS96-1-UIC, University of Illinois at Chicago, Chicago, IL (1996).Google Scholar
Shabana, A. A., “Definition of the slopes and the finite element absolute nodal coordinate formulation,” Multibody System Dynamics, 1, pp. 339–348 (1997).CrossRefGoogle Scholar
Shabana, A. A., Computational Continuum Mechanics, Cambridge University Press, Cambridge (2008).CrossRefGoogle Scholar
Dufva, K. and Shabana, A. A., “Analysis of Thin Plate Structures Using the Absolute Nodal Coordinate Formulation,” “Proceedings of the Institution of Mechanical Engineers” Part K: J. Multi-body System Dynamics, 219, pp. 345–355 (2005).Google Scholar
Mikkola, A. M. and Matikainen, M. K., “Development of elastic forces for a large deformation plate element based on the absolute nodal coordinate formulation,” Journal of Computational and Nonlinear Dynamics, 1, pp. 103–108 (2006).CrossRefGoogle Scholar
Abbas, L. K., Rui, X. and Hammoudi, Z. S., “Plate/shell Element of variable thickness based on the absolute nodal coordinate formulation, Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body System Dynamics. 224, pp. 127–141 (2010).Google Scholar
Matikainen, M. K., Valkeapää, A. I., Mikkola, A. M. and Schwab, A. L., “A study of moderately thick quadrilateral plate elements based on the absolute nodal coordinate formulation,” Multibody System Dynamics, 31, pp. 309–338 (2014).CrossRefGoogle Scholar
Henrik, E., Matikainen, M. K., Hurskainen, V. V. and Mikkola, A. M., “Analysis of high-order quadrilateral plate elements based on the absolute nodal coordinate formulation for three-dimensional elasticity,” Advances in Mechanical Engineering, 9, pp. 1–12 (2017).Google Scholar
Jung, S., Park, T. and Chung, W., “Dynamic analysis of rubber-like material using absolute nodal coordinate formulation based on the nonlinear constitutive law,” Nonlinear Dynamics, 63, pp. 149–157 (2011).CrossRefGoogle Scholar
Orzechowski, G. and Fraczek, J., “Nearly incompressible nonlinear material models in the large deformation analysis of beams using ANCF,” Nonlinear Dynamics, 82, pp 451–464 (2015).CrossRefGoogle Scholar
Elguedj, T., Bazilevs, Y., Calo, V. M. and Hughes, T. J., “B-bar and F-bar projection methods for nearly incompressible linear and non-linear elasticity and plasticity using higher-order NURBS elements,” Computer Methods in Applied Mechanics & Engineering, 197, pp. 2732–2762 (2008).CrossRefGoogle Scholar
Gerstmayr, J., Matikainen, M. K. and Mikkola, A. M., “A geometrically exact beam element based on the absolute nodal coordinate formulation,” Multibody System Dynamics, 20, pp. 359–384 (2008).CrossRefGoogle Scholar
Xu, Q. P. and Liu, J. Y., “An improved dynamic model for a silicone material beam with large deformation,” Acta Mechanica Sinica, 34, pp. 744–753 (2018).CrossRefGoogle Scholar
Olshevskiy, A., Dmitrochenko, O. and Kim, C. W., “Three-Dimensional Solid Brick Element Using Slopes in the Absolute Nodal Coordinate Formulation,” Journal of Computational and Nonlinear Dynamics, 9, pp. 1–10 (2013).Google Scholar
Olshevskiy, A., Dmitrochenko, O. and Kim, C. W., “A triangular plate element 2343 using second-order absolute-nodal-coordinate slopes: numerical computation of shape functions,” Nonlinear Dynamics, 74, pp. 769–781 (2013).CrossRefGoogle Scholar
Luo, K., Liu, C., Tian, Q. and Hu, H. Y., “Nonlinear static and dynamic analysis of hyper-elastic thin shells via the absolute nodal coordinate formulation,” Nonlinear Dynamics, 85, pp. 949–971 (2016).CrossRefGoogle Scholar
Olshevskiy, A., Dmitrochenko, Noh, H. J., Yang, H. I. and Kim, C. W., “Experimental Validation of Benchmark Simulations for Plate and Solid Finite Elements Employing the ANCF,” The 4th Joint International Conference on Multibody System Dynamics, Montréal, Canada (2016).Google Scholar
Bonet, J. and Wood, R. D., Nonlinear Continuum Mechanics for Finite Element Analysis, Cambridge University Press, Cambridge (1997).Google Scholar
Yeoh, O. H., “Characterization of elastic properties of carbon black filled rubber vulcanizates,” Rubber Chemistry and technology, 66, pp.754–771 (1990).CrossRefGoogle Scholar
Selvadurai, A. P. S., “Deflections of a rubber membrane,” Journal of the Mechanics and Physics of Solids, 6, pp. 1093–1119 (2006).CrossRefGoogle Scholar
Bathe, K.J., Finite Element Procedures, Prentice Hall, New Jersey (1996).Google Scholar
Olshevskiy, A., Dmitrochenko, O. and Kim, C. W., “Three-dimensional solid brick element using slopes in the abso lute nodal coordinate formulation,” Journal of Computational and Nonlinear Dynamics, 9, 021001 (2014).CrossRefGoogle Scholar