پیوندهای مفید
اخبار و اعلانات
آمار
| تعداد نشریات | 162 |
| تعداد شمارهها | 6,622 |
| تعداد مقالات | 71,533 |
| تعداد مشاهده مقاله | 126,862,228 |
| تعداد دریافت فایل اصل مقاله | 99,905,046 |
Static response of laminated plate using new parabolic higher order shear deformation theory: A finite element approach | ||
| Journal of Computational Applied Mechanics | ||
| دوره 56، شماره 1، فروردین 2025، صفحه 101-126 اصل مقاله (801.59 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22059/jcamech.2024.377272.1111 | ||
| نویسندگان | ||
| Sumit Khare1؛ Rahul Kumar2؛ Harish K Sharma3؛ Ram Bilas Prasad4؛ Kanif Markad* 5؛ Suraj Singh2؛ Ashutosh K. Tiwari2؛ Sourabh Ven6 | ||
| 1Department of Mechanical Engineering, SVNIT, Surat (GJ), India | ||
| 2Department of Mechanical Engineering, IET, DDU, Gorakhpur, India | ||
| 3Department of Mechanical Engineering, GLA University, Mathura, India | ||
| 4Department of Mechanical Engineering, MMMUT, Gorakhpur, U.P, India | ||
| 5Department of Mechanical Engineering, DVVP College of Engineering, Ahmednagar, India | ||
| 6Department of Civil, Computer Science and Aeronautical Technologies Engineering, Roma Tre University, Via Vito Volterra 62, Rome, 00146, Italy | ||
| چکیده | ||
| This study presents a new exponential higher-order shear deformation theory (NEHSDT) to examine the flexural analysis of multi-layered laminated composite plates. The novel parabolic shear deformation function is developed to analyze the bending response of laminated plates. A new shear deformation theory eliminates the need for shear correction factors. The present theory gives an exact parabolic distribution of transverse shear stress over the thickness and fulfills the traction-free boundary conditions on the outer surfaces of multi-layered laminated plates. The governing equations are solved using the finite element method. In this finite element method, a nine-nodded isoperimetric element with seven degrees of freedom per node is formed especially for this purpose. Illustrative examples are presented to demonstrate the predictive capability of the proposed finite element method. The presented numerical results are compared with the existing results to illustrate the correctness and robustness of the finite element method. The proposed analysis is accurate, converges rapidly, and is valid for thin and thick laminated plates based on comparisons with earlier higher-order shear deformation theories. In addition, the present results may be taken as the benchmark for further studies. | ||
| کلیدواژهها | ||
| HSDT؛ FEM؛ Laminated Plate؛ Stress distribution؛ Deflection | ||
| مراجع | ||
|
[1] J. M. Whitney, 1987, Structural Analysis of Laminated Anisotropic Plates, CRC Press, [2] R. Kumar, A. Lal, B. N. Singh, J. Singh, Numerical simulation of the thermomechanical buckling analysis of bidirectional porous functionally graded plate using collocation meshfree method, Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, Vol. 236, No. 4, pp. 787-807, 2022. [3] S. Khare, N. D. Mittal, Axisymmetric bending and free vibration of symmetrically laminated circular and annular plates having elastic edge constraints, Ain Shams Engineering Journal, Vol. 10, No. 2, pp. 343-352, 2019. [4] S. Khare, N. D. Mittal, Free vibration of thick laminated circular and annular plates using three-dimensional finite element analysis, Alexandria Engineering Journal, Vol. 57, No. 3, pp. 1217-1228, 2018. [5] A. K. Noor, W. S. Burton, Assessment of shear deformation theories for multilayered composite plates, 1989. [6] J. Reddy, D. Robbins Jr, Theories and computational models for composite laminates, 1994. [7] D. Li, Layerwise theories of laminated composite structures and their applications: a review, Archives of Computational Methods in Engineering, Vol. 28, pp. 577-600, 2021. [8] A. Gupta, A. Ghosh, Isogeometric static and dynamic analysis of laminated and sandwich composite plates using nonpolynomial shear deformation theory, Composites Part B: Engineering, Vol. 176, pp. 107295, 2019. [9] E. Reissner, The effect of transverse shear deformation on the bending of elastic plates, 1945. [10] R. Mindlin, Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates, 1951. [11] A. S. Sayyad, Y. M. Ghugal, On the free vibration analysis of laminated composite and sandwich plates: A review of recent literature with some numerical results, Composite structures, Vol. 129, pp. 177-201, 2015. [12] Z. Wu, R. Chen, W. Chen, Refined laminated composite plate element based on global–local higher-order shear deformation theory, Composite structures, Vol. 70, No. 2, pp. 135-152, 2005. [13] M. Aydogdu, Comparison of various shear deformation theories for bending, buckling, and vibration of rectangular symmetric cross-ply plate with simply supported edges, Journal of Composite materials, Vol. 40, No. 23, pp. 2143-2155, 2006. [14] A. Idlbi, M. Karama, M. Touratier, Comparison of various laminated plate theories, Composite Structures, Vol. 37, No. 2, pp. 173-184, 1997. [15] M. Levy, Memoire sur la theorie des plaques elastiques planes, Journal de mathématiques pures et appliquées, Vol. 3, pp. 219-306, 1877. [16] J. Monge, J. Mantari, Best non-polynomial shear deformation theories for cross-ply single skin and sandwich shells, Engineering Structures, Vol. 203, pp. 109678, 2020. [17] B. R. Thakur, S. Verma, B. Singh, D. Maiti, Dynamic analysis of folded laminated composite plate using nonpolynomial shear deformation theory, Aerospace Science and Technology, Vol. 106, pp. 106083, 2020. [18] N. Grover, D. Maiti, B. Singh, A new inverse hyperbolic shear deformation theory for static and buckling analysis of laminated composite and sandwich plates, Composite Structures, Vol. 95, pp. 667-675, 2013. [19] T. N. Nguyen, C. H. Thai, H. Nguyen-Xuan, On the general framework of high order shear deformation theories for laminated composite plate structures: A novel unified approach, International Journal of Mechanical Sciences, Vol. 110, pp. 242-255, 2016. [20] A. M. Zenkour, Generalized shear deformation theory for bending analysis of functionally graded plates, Applied Mathematical Modelling, Vol. 30, No. 1, pp. 67-84, 2006. [21] J. Mantari, A. Oktem, C. G. Soares, A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates, International Journal of Solids and Structures, Vol. 49, No. 1, pp. 43-53, 2012. [22] N. Grover, B. Singh, D. Maiti, New nonpolynomial shear-deformation theories for structural behavior of laminated-composite and sandwich plates, AIAA journal, Vol. 51, No. 8, pp. 1861-1871, 2013. [23] K. Soldatos, A transverse shear deformation theory for homogeneous monoclinic plates, Acta Mechanica, Vol. 94, No. 3, pp. 195-220, 1992. [24] N. El Meiche, A. Tounsi, N. Ziane, I. Mechab, A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate, International Journal of Mechanical Sciences, Vol. 53, No. 4, pp. 237-247, 2011. [25] S. Akavci, A. Tanrikulu, Buckling and free vibration analyses of laminated composite plates by using two new hyperbolic shear-deformation theories, Mechanics of Composite Materials, Vol. 44, pp. 145-154, 2008. [26] R. Kumar, A. Lal, B. Singh, J. Singh, Meshfree approach on buckling and free vibration analysis of porous FGM plate with proposed IHHSDT resting on the foundation, Curved and Layered Structures, Vol. 6, No. 1, pp. 192-211, 2019. [27] R. Kumar, M. Bajaj, J. Singh, K. K. Shukla, New HSDT for free vibration analysis of elastically supported porous bidirectional functionally graded sandwich plate using collocation method, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 236, No. 16, pp. 9109-9123, 2022. [28] M. Karama, K. Afaq, S. Mistou, Mechanical behaviour of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity, International Journal of solids and structures, Vol. 40, No. 6, pp. 1525-1546, 2003. [29] M. Aydogdu, A new shear deformation theory for laminated composite plates, Composite structures, Vol. 89, No. 1, pp. 94-101, 2009. [30] J. Mantari, A. Oktem, C. G. Soares, Static and dynamic analysis of laminated composite and sandwich plates and shells by using a new higher-order shear deformation theory, Composite structures, Vol. 94, No. 1, pp. 37-49, 2011. [31] S. Sarangan, B. Singh, Higher-order closed-form solution for the analysis of laminated composite and sandwich plates based on new shear deformation theories, Composite Structures, Vol. 138, pp. 391-403, 2016. [32] J. N. Reddy, A simple higher-order theory for laminated composite plates, 1984. [33] R. Shimpi, H. Patel, A two variable refined plate theory for orthotropic plate analysis, International Journal of Solids and Structures, Vol. 43, No. 22-23, pp. 6783-6799, 2006. [34] S.-E. Kim, H.-T. Thai, J. Lee, Buckling analysis of plates using the two variable refined plate theory, Thin-Walled Structures, Vol. 47, No. 4, pp. 455-462, 2009. [35] J. Mantari, A simple polynomial quasi-3D HSDT with four unknowns to study FGPs. Reddy’s HSDT assessment, Composite Structures, Vol. 137, pp. 114-120, 2016. [36] J. Reddy, A review of refined theories of laminated composite plates, The shock and vibration digest, Vol. 22, No. 7, pp. 3-17, 1990. [37] V. Vasil'Ev, Theory of thin plates, Rossijskaya Akademiya Nauk Izvestiya Mekhanika Tverdogo Tela, Vol. 3, pp. 26-47, 1992. [38] E. Carrera, Theories and finite elements for multilayered, anisotropic, composite plates and shells, Archives of computational methods in engineering, Vol. 9, pp. 87-140, 2002. [39] C. Pryor Jr, R. Barker, A finite-element analysis including transverse shear effects for applications to laminated plates, AIAA journal, Vol. 9, No. 5, pp. 912-917, 1971. [40] C. W. Bert, M. Malik, Differential quadrature method in computational mechanics: a review, 1996. [41] S. C. Panda, R. Natarajan, Finite element analysis of laminated composite plates, International journal for numerical methods in engineering, Vol. 14, No. 1, pp. 69-79, 1979. [42] G. Ramtekkar, Y. Desai, A. Shah, Application of a three-dimensional mixed finite element model to the flexure of sandwich plate, Computers & structures, Vol. 81, No. 22-23, pp. 2183-2198, 2003. [43] O. C. Zienkiewicz, R. L. Taylor, 2000, The finite element method: solid mechanics, Butterworth-heinemann, [44] I. Fried, A. Johnson, A. Tessler, Minimal-degree thin triangular plate and shell bending finite elements of order two and four, Computer methods in applied mechanics and engineering, Vol. 56, No. 3, pp. 283-307, 1986. [45] E. N. Dvorkin, On nonlinear finite element analysis of shell structures, Thesis, Massachusetts Institute of Technology, 1984. [46] S. Verma, B. R. Thakur, B. Singh, D. Maiti, Geometrically nonlinear flexural analysis of multilayered composite plate using polynomial and non-polynomial shear deformation theories, Aerospace Science and Technology, Vol. 112, pp. 106635, 2021. [47] M. Motezaker, R. Kolahchi, D. K. Rajak, S. Mahmoud, Influences of fiber reinforced polymer layer on the dynamic deflection of concrete pipes containing nanoparticle subjected to earthquake load, Polymer Composites, Vol. 42, No. 8, pp. 4073-4081, 2021. [48] R. Kolahchi, B. Keshtegar, N.-T. Trung, Optimization of dynamic properties for laminated multiphase nanocomposite sandwich conical shell in thermal and magnetic conditions, Journal of Sandwich Structures & Materials, Vol. 24, No. 1, pp. 643-662, 2022. [49] M. H. Hajmohammad, A. Farrokhian, R. Kolahchi, Dynamic analysis in beam element of wave-piercing Catamarans undergoing slamming load based on mathematical modelling, Ocean Engineering, Vol. 234, pp. 109269, 2021. [50] M. Al-Furjan, M. H. Hajmohammad, X. Shen, D. K. Rajak, R. Kolahchi, Evaluation of tensile strength and elastic modulus of 7075-T6 aluminum alloy by adding SiC reinforcing particles using vortex casting method, Journal of Alloys and Compounds, Vol. 886, pp. 161261, 2021. [51] M. Al-Furjan, M. Xu, A. Farrokhian, G. S. Jafari, X. Shen, R. Kolahchi, On wave propagation in piezoelectric-auxetic honeycomb-2D-FGM micro-sandwich beams based on modified couple stress and refined zigzag theories, Waves in Random and Complex Media, pp. 1-25, 2022. [52] R. Kumar, B. Singh, J. Singh, Geometrically nonlinear analysis for flexure response of FGM plate under patch load, Mechanics Based Design of Structures and Machines, Vol. 51, No. 11, pp. 6532-6556, 2023. [53] M. Al‐Furjan, Y. Yang, A. Farrokhian, X. Shen, R. Kolahchi, D. K. Rajak, Dynamic instability of nanocomposite piezoelectric‐leptadenia pyrotechnica rheological elastomer‐porous functionally graded materials micro viscoelastic beams at various strain gradient higher‐order theories, Polymer Composites, Vol. 43, No. 1, pp. 282-298, 2022. [54] M. Al-Furjan, C. Yin, X. Shen, R. Kolahchi, M. S. Zarei, M. Hajmohammad, Energy absorption and vibration of smart auxetic FG porous curved conical panels resting on the frictional viscoelastic torsional substrate, Mechanical Systems and Signal Processing, Vol. 178, pp. 109269, 2022. [55] M. Al-Furjan, L. Shan, X. Shen, R. Kolahchi, D. K. Rajak, Combination of FEM-DQM for nonlinear mechanics of porous GPL-reinforced sandwich nanoplates based on various theories, Thin-Walled Structures, Vol. 178, pp. 109495, 2022. [56] R. Kumar, B. Singh, J. Singh, J. Singh, Meshfree approach for flexure analysis of bidirectional porous FG plate subjected to I, L, and T types of transverse loading, Aerospace Science and Technology, Vol. 129, pp. 107824, 2022. [57] C. Chu, L. Shan, M. Al-Furjan, M. Zarei, M. Hajmohammad, R. Kolahchi, Experimental study for the effect of hole notched in fracture mechanics of GLARE and GFRP composites subjected to quasi-static loading, Theoretical and Applied Fracture Mechanics, Vol. 122, pp. 103624, 2022. [58] M. Al-Furjan, R. Kolahchi, L. Shan, M. Hajmohammad, A. Farrokhian, X. Shen, Slamming impact induced hydrodynamic response in wave-piercing catamaran beam elements with controller, Ocean Engineering, Vol. 266, pp. 112908, 2022. [59] C. Chu, M. Al-Furjan, R. Kolahchi, A. Farrokhian, A nonlinear Chebyshev-based collocation technique to frequency analysis of thermally pre/post-buckled third-order circular sandwich plates, Communications in Nonlinear Science and Numerical Simulation, Vol. 118, pp. 107056, 2023. [60] M. Al-Furjan, Z. Qi, L. Shan, A. Farrokhian, X. Shen, R. Kolahchi, Nano supercapacitors with practical application in aerospace technology: Vibration and wave propagation analysis, Aerospace Science and Technology, Vol. 133, pp. 108082, 2023. [61] P. Wan, M. Al-Furjan, R. Kolahchi, L. Shan, Application of DQHFEM for free and forced vibration, energy absorption, and post-buckling analysis of a hybrid nanocomposite viscoelastic rhombic plate assuming CNTs’ waviness and agglomeration, Mechanical Systems and Signal Processing, Vol. 189, pp. 110064, 2023. [62] M. Al-Furjan, S. Fan, L. Shan, A. Farrokhian, X. Shen, R. Kolahchi, Wave propagation analysis of micro air vehicle wings with honeycomb core covered by porous FGM and nanocomposite magnetostrictive layers, Waves in Random and Complex Media, pp. 1-30, 2023. [63] C. Chu, M. Al-Furjan, R. Kolahchi, Energy harvesting and dynamic response of SMA nano conical panels with nanocomposite piezoelectric patch under moving load, Engineering Structures, Vol. 292, pp. 116538, 2023. [64] P. Wan, M. Al-Furjan, R. Kolahchi, Nonlinear flutter response and reliability of supersonic smart hybrid nanocomposite rupture trapezoidal plates subjected to yawed flow using DQHFEM, Aerospace Science and Technology, Vol. 145, pp. 108862, 2024. [65] S. Serdoun, S. Hamza Cherif, Free vibration analysis of composite and sandwich plates by alternative hierarchical finite element method based on Reddy’s C1 HSDT, Journal of Sandwich Structures & Materials, Vol. 18, No. 4, pp. 501-528, 2016. [66] J. N. Reddy, 2003, Mechanics of laminated composite plates and shells: theory and analysis, CRC press, [67] S. Ambartsumian, K obshchei teorii anizotropnykh obolochek PMM vol. 22, no. 2, 1958, pp. 226-237, Journal of Applied Mathematics and Mechanics, Vol. 22, No. 2, pp. 305-319, 1958. [68] E. Reissner, On tranverse bending of plates, including the effect of transverse shear deformation, 1974. [69] R. P. Shimpi, Zeroth-order shear deformation theory for plates, AIAA journal, Vol. 37, No. 4, pp. 524-526, 1999. [70] H. Guenfoud, H. Ziou, M. Himeur, M. Guenfoud, Analyses of a composite functionally graded material beam with a new transverse shear deformation function, Journal of Applied Engineering Science & Technology, Vol. 2, No. 2, pp. 105-113, 2016. [71] A. A. Daikh, A. M. Zenkour, Effect of porosity on the bending analysis of various functionally graded sandwich plates, Materials Research Express, Vol. 6, No. 6, pp. 065703, 2019. [72] R. Kumar, A. Lal, B. Singh, J. Singh, New transverse shear deformation theory for bending analysis of FGM plate under patch load, Composite Structures, Vol. 208, pp. 91-100, 2019. [73] H. Arya, R. Shimpi, N. Naik, A zigzag model for laminated composite beams, Composite structures, Vol. 56, No. 1, pp. 21-24, 2002. [74] A. Zenkour, Analytical solution for bending of cross-ply laminated plates under thermo-mechanical loading, Composite Structures, Vol. 65, No. 3-4, pp. 367-379, 2004. [75] V.-H. Nguyen, T.-K. Nguyen, H.-T. Thai, T. P. Vo, A new inverse trigonometric shear deformation theory for isotropic and functionally graded sandwich plates, Composites Part B: Engineering, Vol. 66, pp. 233-246, 2014. [76] C. H. Thai, S. Kulasegaram, L. V. Tran, H. Nguyen-Xuan, Generalized shear deformation theory for functionally graded isotropic and sandwich plates based on isogeometric approach, Computers & Structures, Vol. 141, pp. 94-112, 2014. [77] C. H. Thai, A. Ferreira, S. P. A. Bordas, T. Rabczuk, H. Nguyen-Xuan, Isogeometric analysis of laminated composite and sandwich plates using a new inverse trigonometric shear deformation theory, European Journal of Mechanics-A/Solids, Vol. 43, pp. 89-108, 2014. [78] S. Suganyadevi, B. Singh, Assessment of composite and sandwich laminates using a new shear deformation theory, AIAA Journal, Vol. 54, No. 2, pp. 789-792, 2016. [79] C. Xiao, G. Zhang, Y. Yu, Y. Mo, R. Mohammadi, Nonlinear vibration analysis of the nanobeams subjected to magneto-electro-thermal loading based on a novel HSDT, Waves in Random and Complex Media, pp. 1-20, 2022. [80] H. Ait Atmane, A. Tounsi, I. Mechab, E. A. Adda Bedia, Free vibration analysis of functionally graded plates resting on Winkler–Pasternak elastic foundations using a new shear deformation theory, International Journal of Mechanics and Materials in Design, Vol. 6, pp. 113-121, 2010. [81] S. Akavci, An efficient shear deformation theory for free vibration of functionally graded thick rectangular plates on elastic foundation, Composite Structures, Vol. 108, pp. 667-676, 2014. [82] M. Karama, K. Afaq, S. Mistou, A new theory for laminated composite plates, Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, Vol. 223, No. 2, pp. 53-62, 2009. [83] Y. Zhu, P. Shi, Y. Kang, B. Cheng, Isogeometric analysis of functionally graded plates with a logarithmic higher order shear deformation theory, Thin-Walled Structures, Vol. 144, pp. 106234, 2019. [84] F. Pathan, S. Singh, S. Natarajan, G. Watts, An analytical solution for the static bending of smart laminated composite and functionally graded plates with and without porosity, Archive of Applied Mechanics, Vol. 92, No. 3, pp. 903-931, 2022. [85] C. Kumar, R. Kumar, H. K. Sharma, S. Khare, Simulation and Modelling for Bending Analysis of Elastically Supported Laminated Plates Under Concentrated Load: A Meshless Approach, International Journal of Steel Structures, Vol. 23, No. 4, pp. 1091-1104, 2023. [86] M. K. Solanki, R. Kumar, J. Singh, Flexure analysis of laminated plates using multiquadratic RBF based meshfree method, International Journal of Computational Methods, Vol. 15, No. 06, pp. 1850049, 2018. [87] O. Zienkiewicz, J. Zhu, Superconvergence and the superconvergent patch recovery, Finite elements in analysis and design, Vol. 19, No. 1-2, pp. 11-23, 1995. [88] J. E. Akin, 2005, Finite element analysis with error estimators: An introduction to the FEM and adaptive error analysis for engineering students, Elsevier, [89] F. Tornabene, N. Fantuzzi, M. Bacciocchi, J. Reddy, A posteriori stress and strain recovery procedure for the static analysis of laminated shells resting on nonlinear elastic foundation, Composites Part B: Engineering, Vol. 126, pp. 162-191, 2017. [90] L. V. Tran, S.-E. Kim, Static and free vibration analyses of multilayered plates by a higher-order shear and normal deformation theory and isogeometric analysis, Thin-Walled Structures, Vol. 130, pp. 622-640, 2018. [91] J. Reddy, C. Liu, A higher-order shear deformation theory of laminated elastic shells, International journal of engineering science, Vol. 23, No. 3, pp. 319-330, 1985. | ||
|
آمار تعداد مشاهده مقاله: 144 تعداد دریافت فایل اصل مقاله: 113 |
||
سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب