Static Bending Analysis of Auxetic Plate by FEM and a New Third-Order Shear Deformation Plate Theory
Main Article Content
Abstract
In this paper, a finite element method (FEM) and a new third-order shear deformation plate theory are proposed to investigate a static bending model of auxetic plates with negative Poisson’s ratio. The three – layer sandwich plate is consisted of auxetic honeycombs core layer with negative Poisson’s ratio integrated, isotropic homogeneous materials at the top and bottom of surfaces. A displacement-based finite element formulation associated with a novel third-order shear deformation plate theory without any requirement of shear correction factors is thus developed. The results show the effects of geometrical parameters, boundary conditions, uniform transverse pressure on the static bending of auxetic plates with negative Poisson’s ratio. Numerical examples are solved, then compared with the published literatures to validate the feasibility and accuracy of proposed analysis method.
Keywords:
Static bending; new third-order shear deformation plate theory; auxetic material.
References
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[11] K. Di, X.B. Mao, Free lexural vibration of honeycomb sandwich plate with negative Poisson’s ratio simple supported on opposite edges, Acta Materiae Compositae Sinica 33 (2016) 910–920. https://doi.org/10.13801/j.cnki.fhclxb.20151010.001
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[2] S. Mohammad, R. Naveen, A. Kim, A. Andrew, Auxetic materials for sports applications, Procedia Engineering 72 (2014) 453–458. https://doi.org/10. 1016/j.proeng.2014.06.079.
[3] M. Shariyat, M.M. Alipour, Analytical Bending and Stress Analysis of Variable Thickness FGM Auxetic Conical/Cylindrical Shells with General Tractions, Latin American Journal of Solids and Structures 14 (2017) 805-843. http://dx.doi.org/10. 1590/1679-78253413.
[4] M.M. Alipour, M. Shariyat, Analytical zigzag formulation with 3D elasticity corrections for bending and stress analysis of circular/annular composite sandwich plates with auxetic cores, Composite Structures 132 (2015) 175-197. https:// doi.org/10.1016/j.compstruct.2015.05.003.
[5] Y. Hou, Y.H. Tai, C. Lira, F. Scarpa, J.R. Yates, B. Gu, The Bending and Failure of Sandwich Structures with Auxetic Gradient Cellular Cores, Composites Part A: Applied Science and Manufacturing 49(2013) 119-131. https://doi.org/ 10.1016/j.compositesa.2013.02.007.
[6] N.D. Duc, P.H. Cong, Nonlinear dynamic response and vibration of sandwich composite plates with negative Poisson’s ratio in auxetic honeycombs, Journal of Sandwich Structures and Materials 20(6) (2018) 692-717. https://doi.org/10.1177/10996362 16674729.
[7] P.H. Cong, P.T. Long, N.V. Nhat, N.D. Duc, Geometrically nonlinear dynamic response of eccentrically stiffened circular cylindrical shells with negative Poisson’s ratio in auxetic honeycombs core layer, International journal of Mechanical Sciences 152 (2019) 443-453. https:// doi.org/10.1016/j.ijmecsci.2018.12.052.
[8] P.H. Cong, N.D. Khanh, N.D. Khoa, N.D. Duc, New approach to investigate nonlinear dynamic response of sandwich auxetic double curves shallow shells using TSDT, Compos. Struct. 185 (2018) 455-465. https://doi.org/10.1016/j. compstruct.2017.11.047.
[9] N.D. Duc, K.S. Eock, P.H. Cong, N.T. Anh, N.D. Khoa, Dynamic response and vibration of composite double curved shallow shells with negative Poisson’s ratio in auxetic honeycombs core layer on elastic foundations subjected to blast and damping loads, International Journal of Mechanical of Sciences 133 (2017) 504-512. https: //doi.org/10.1016/j.ijmecsci.2017.09.009.
[10] N.D. Duc, K.S. Eock, N.D. Tuan, P. Tran, N.D. Khoa, New approach to study nonlinear dynamic response and vibration of sandwich composite cylindrical panels with auxetic honeycomb core layer, Aerosp. Sci. Technol. 70 (2017) 396-404. https://doi.org/10.1016/j.ast.2017.08.023.
[11] K. Di, X.B. Mao, Free lexural vibration of honeycomb sandwich plate with negative Poisson’s ratio simple supported on opposite edges, Acta Materiae Compositae Sinica 33 (2016) 910–920. https://doi.org/10.13801/j.cnki.fhclxb.20151010.001
[12] G. Shi, A new simple third-order shear deformation theory of plates. Int. J. Solids Struct. 44 (2007) 4399-4417. https://doi.org/10.1016/j.ijsolstr.2006. 11.031.
[13] H.T. Hu, B.H. Lin, Buckling optimization of symmetrically laminated plates with various geometries and end conditions, Composite Science and Technology 55 (1995) 277-285. https://doi. org/10.1016/0266-3538(95)00105-0.
[14] A.J.M Ferreira, Matlab coddes for finite element analysis. Solids and Structures. Solid Mechanics and ít applications, Springer, pages: 165-166.