Finite Element Analysis of Functionally Graded Skew Plates in Thermal Environment based on the New Third-order Shear Deformation Theory

Document Type: Research Paper

Author

1 Department of Civil Engineering, Ho Chi Minh City University of Architecture, 196 Pasteur Street, District 3, Ho Chi Minh City, Viet Nam

2 Department of Civil Engineering, Ho Chi Minh City University of Technology and Education, 01 Vo Van Ngan Street, Thu Duc District, Ho Chi Minh City, Viet Nam

Abstract

Functionally graded materials are commonly used in thermal environment to change the properties of constituent materials. The new numerical procedure of functionally graded skew plates in thermal environment is presented in this study based on the C0-form of the novel third-order shear deformation theory. Without the shear correction factor, this theory is also taking the desirable properties and advantages of the third-order shear deformation theory. We assume that the uniform distribution of temperature is embedded across the thickness of this structure. Both the rule of mixture and the micromechanics approaches are considered to describe the variation of material compositions across the thickness. Numerical solutions and comparison with other available solutions suggest that this procedure based on novel third-order shear deformation theory is accuracy and efficiency.

Keywords

[1] N. Wattanasakulpong, G.B. Prusty, and D.W. Kelly, Free and forced vibration analysis using improved third-order shear deformation theory for functionally graded plates under high temperature loading, Journal of Sandwich Structures & Materials, 15, 2013, 583-606.

[2] N. Wattanasakulpong, B. Gangadhara Prusty, and D.W. Kelly, Thermal buckling and elastic vibration of third-order shear deformable functionally graded beams, International Journal of Mechanical Sciences, 53, 2011, 734-743.

[3] X.-L. Huang and H.-S. Shen, Nonlinear vibration and dynamic response of functionally graded plates in thermal environments, International Journal of Solids and Structures, 41, 2004, 2403-2427.

[4] J. Yang and H.S. Shen, Nonlinear bending analysis of shear deformable functionally graded plates subjected to thermo-mechanical loads under various boundary conditions, Composites Part B: Engineering, 34, 2003, 103-115.

[5] D.K. Jha, T. Kant, and R.K. Singh, A critical review of recent research on functionally graded plates, Composite Structures, 96, 2013, 833-849.

[6] H.-T. Thai and S.-E. Kim, A review of theories for the modeling and analysis of functionally graded plates and shells, Composite Structures, 128, 2015, 70-86.

[7] G. Shi, A new simple third-order shear deformation theory of plates, International Journal of Solids and Structures, 44, 2007, 4399-4417.

[8] T.Q. Bui, T.V. Do, L.H.T. Ton, D.H. Doan, S. Tanaka, D.T. Pham, et al., On the high temperature mechanical behaviors analysis of heated functionally graded plates using FEM and a new third-order shear deformation plate theory, Composites Part B: Engineering, 92, 2016, 218-241.

[9] T. Van Do, D.K. Nguyen, N.D. Duc, D.H. Doan, and T.Q. Bui, Analysis of bi-directional functionally graded plates by FEM and a new third-order shear deformation plate theory, Thin-Walled Structures, 119, 2017, 687-699.

[10] T.T. Tran, N.H. Nguyen, T.V. Do, P.V. Minh, and N.D. Duc, Bending and thermal buckling of unsymmetric functionally graded sandwich beams in high-temperature environment based on a new third-order shear deformation theory, Journal of Sandwich Structures & Materials, 2019, https://doi.org/10.1177/1099636219849268.

[11] H.L. Ton-That, H. Nguyen-Van, and T. Chau-Dinh, An Improved Four-Node Element for Analysis of Composite Plate/Shell Structures Based on Twice Interpolation Strategy, International Journal of Computational Methods, 2019, https://doi.org/10.1142/S0219876219500208.

[12] L.T. That-Hoang, H. Nguyen-Van, T. Chau-Dinh, and C. Huynh-Van, Enhancement to four-node quadrilateral plate elements by using cell-based smoothed strains and higher-order shear deformation theory for nonlinear analysis of composite structures, Journal of Sandwich Structures & Materials, 2019, https://doi.org/10.1177/1099636218797982.

[13] H.L. Ton That, H. Nguyen-Van, and T. Chau-Dinh, Nonlinear Bending Analysis of Functionally Graded Plates Using SQ4T Elements based on Twice Interpolation Strategy, Journal of Applied and Computational Mechanics, 6, 2020, 125-136.

[14] L.V. Tran, A.J.M. Ferreira, and H. Nguyen-Xuan, Isogeometric analysis of functionally graded plates using higher-order shear deformation theory, Composites Part B: Engineering, 51, 2013, 368-383.

[15] S. Yin, T. Yu, T.Q. Bui, X. Zheng, and G. Yi, Rotation-free isogeometric analysis of functionally graded thin plates considering in-plane material inhomogeneity, Thin-Walled Structures, 119, 2017, 385-395.

[16] H. Nguyen-Xuan, L.V. Tran, T. Nguyen-Thoi, and H.C. Vu-Do, Analysis of functionally graded plates using an edge-based smoothed finite element method, Composite Structures, 93, 2011, 3019-3039.

[17] M.D. Demirbas, Thermal stress analysis of functionally graded plates with temperature-dependent material properties using theory of elasticity, Composites Part B: Engineering, 131, 2017, 100-124.

[18] H. Nourmohammadi and B. Behjat, Geometrically nonlinear analysis of functionally graded piezoelectric plate using mesh-free RPIM, Engineering Analysis with Boundary Elements, 99, 2019, 131-141.

[19] G. Taj and A. Chakrabarti, Static and Dynamic Analysis of Functionally Graded Skew Plates, Journal of Engineering Mechanics, 139, 2013, 848-857.

[20] M.N.A. Gulshan Taj, A. Chakrabarti, and V. Prakash, Vibration Characteristics of Functionally Graded Material Skew Plate in Thermal Environment, International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering, 8, 2014, 142-153.

[21] M. Janghorban and A. Zare, Thermal effect on free vibration analysis of functionally graded arbitrary straight-sided plates with different cutouts, Latin American Journal of Solids and Structures, 8, 2011, 245-257.

[22] H. Parandvar and M. Farid, Large amplitude vibration of FGM plates in thermal environment subjected to simultaneously static pressure and harmonic force using multimodal FEM, Composite Structures, 141, 2016, 163-171.

[23] T. Mori and K. Tanaka, Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metallurgica, 21, 1973, 571-574.

[24] A.J.M. Ferreira, R.C. Batra, C.M.C. Roque, L.F. Qian, and P.A.L.S. Martins, Static analysis of functionally graded plates using third-order shear deformation theory and a meshless method, Composite Structures, 69, 2005, 449-457.

[25] M. Chehel Amirani, S.M.R. Khalili, and N. Nemati, Free vibration analysis of sandwich beam with FG core using the element free Galerkin method, Composite Structures, 90, 2009, 373-379.

[26] N. Valizadeh, S. Natarajan, O.A. Gonzalez-Estrada, T. Rabczuk, T.Q. Bui, and S.P.A. Bordas, NURBS-based finite element analysis of functionally graded plates: Static bending, vibration, buckling and flutter, Composite Structures, 99, 2013, 309-326.

[27] N. Naderi Beni, Free vibration analysis of annular sector sandwich plates with FG-CNT reinforced composite face-sheets based on the Carrera’s Unified Formulation, Composite Structures, 214, 2019, 269-292.

[28] J.L. Mantari, I.A. Ramos, E. Carrera, and M. Petrolo, Static analysis of functionally graded plates using new non-polynomial displacement fields via Carrera Unified Formulation, Composites Part B: Engineering, 89, 2016, 127-142.

[29] N. Naderi Beni and M. Botshekanan Dehkordi, An extension of Carrera unified formulation in polar coordinate for analysis of circular sandwich plate with FGM core using GDQ method, Composite Structures, 185, 2018, 421-434.

[30] I.A. Ramos, J.L. Mantari, and A.M. Zenkour, Laminated composite plates subject to thermal load using trigonometrical theory based on Carrera Unified Formulation, Composite Structures, 143, 2016, 324-335.

[31] A.J.M. Ferreira, E. Carrera, M. Cinefra, E. Viola, F. Tornabene, N. Fantuzzi, et al., Analysis of thick isotropic and cross-ply laminated plates by generalized differential quadrature method and a Unified Formulation, Composites Part B: Engineering, 58, 2014, 544-552.

[32] A. Alesadi, M. Galehdari, and S. Shojaee, Free vibration and buckling analysis of cross-ply laminated composite plates using Carrera's unified formulation based on Isogeometric approach, Computers & Structures, 183, 2017, 38-47.

[33] M. Bayat, I.M. Alarifi, A.A. Khalili, T.M.A.A. El-Bagory, H.M. Nguyen, and A. Asadi, Thermo-mechanical contact problems and elastic behaviour of single and double sides functionally graded brake disks with temperature-dependent material properties, Scientific Reports, 9, 2019, 15317.

[34] M. Ghamkhar, M.N. Naeem, M. Imran, M. Kamran, and C. Soutis, Vibration frequency analysis of three-layered cylinder shaped shell with effect of FGM central layer thickness, Scientific Reports, 9, 2019, 1566.

[35] H. Nguyen-Van, H.L. Ton-That, T. Chau-Dinh, and N.D. Dao, Nonlinear Static Bending Analysis of Functionally Graded Plates Using MISQ24 Elements with Drilling Rotations, in Proceedings of the International Conference on Advances in Computational Mechanics 2017, Singapore, 2018, 461-475.