Skip to main content Accessibility help
×
Home

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

  • Qiping Xu (a1), Jinyang Liu (a1) and Lizheng Qu (a1)

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.

Copyright

Corresponding author

*Corresponding author (liujy@sjtu.edu.cn)

References

Hide All
1.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).
2.Shabana, A. A., “Definition of the slopes and the finite element absolute nodal coordinate formulation,” Multibody System Dynamics, 1, pp. 339348 (1997).
3.Shabana, A. A., Computational Continuum Mechanics, Cambridge University Press, Cambridge (2008).
4.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. 345355 (2005).
5.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. 103108 (2006).
6.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. 127141 (2010).
7.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. 309338 (2014).
8.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. 112 (2017).
9.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. 149157 (2011).
10.Orzechowski, G. and Fraczek, J., “Nearly incompressible nonlinear material models in the large deformation analysis of beams using ANCF,” Nonlinear Dynamics, 82, pp 451464 (2015).
11.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. 27322762 (2008).
12.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. 359384 (2008).
13.Xu, Q. P. and Liu, J. Y., “An improved dynamic model for a silicone material beam with large deformation,” Acta Mechanica Sinica, 34, pp. 744753 (2018).
14.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. 110 (2013).
15.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. 769781 (2013).
16.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. 949971 (2016).
17.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).
18.Bonet, J. and Wood, R. D., Nonlinear Continuum Mechanics for Finite Element Analysis, Cambridge University Press, Cambridge (1997).
19.Yeoh, O. H., “Characterization of elastic properties of carbon black filled rubber vulcanizates,” Rubber Chemistry and technology, 66, pp.754771 (1990).
20.Selvadurai, A. P. S., “Deflections of a rubber membrane,” Journal of the Mechanics and Physics of Solids, 6, pp. 10931119 (2006).
21.Bathe, K.J., Finite Element Procedures, Prentice Hall, New Jersey (1996).
22.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).

Keywords

Related content

Powered by UNSILO

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

  • Qiping Xu (a1), Jinyang Liu (a1) and Lizheng Qu (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.