Bending Analysis of Composite Sandwich Plates with Laminated Face Sheets: New Finite Element Formulation
الموضوعات :
1 - Laboratoire de Génie Energétique et Matériaux, LGEM. Université de Biskra, B.P. 145, R.P. 07000
2 - Laboratoire de Génie Energétique et Matériaux, LGEM. Université de Biskra, B.P. 145, R.P. 07000
الکلمات المفتاحية: Finite Element, Bending, Sandwich plates, Layer-wise,
ملخص المقالة :
The bending behavior of composites sandwich plates with multi-layered laminated face sheets has been investigated, using a new four-nodded rectangular finite element formulation based on a layer-wise theory. Both, first order and higher-order shear deformation; theories are used in order to model the face sheets and the core, respectively. Unlike any other layer-wise theory, the number of degrees of freedom in this present model is independent of the number of layers. The compatibility conditions as well as the displacement continuity at the interface ‘face sheets–core’ are satisfied. In the proposed model, the three translation components are common for the all sandwich layers, and are located at the mid-plane of the sandwich plate. The obtained results show that the developed model is able to give accurate transverse shear stresses directly from the constitutive equations. Moreover, a parametric study was also conducted to investigate the effect of certain characteristic parameters (core thickness to total thickness ratio, side-to-thickness ratio, boundary conditions, plate aspect ratio, core-to-face sheet anisotropy ratio, core shear modulus to the flexural modulus ratio and degree of orthotropy of the face sheet) on the transverse displacement variation. The numerical results obtained by our model are compared favorably with those obtained via analytical solution and numerical/experimental, results obtained by other models. The results obtained from this investigation will be useful for a more comprehensive understanding of the behavior of sandwich laminates.
[1] Khandelwal R., Chakrabarti A., Bhargava P., 2013, An efficient FE model based on combined theory for the analysis of soft core sandwich plate, Computational Mechanics 51(5): 673-697.
[2] Kant T., Swaminathan K., 2000, Estimation of transverse/interlaminar stresses in laminated composites – a selective review and survey of current developments, Composite Structures 49(1): 65-75.
[3] Kirchhoff G., 1850, Über das gleichgewicht und die bewegung einer elastischen scheibe, Journal für die Reine und Angewandte Mathematik 40: 51-88.
[4] Librescu L., 1975, Elastostatics and Kinetics of Anisotropic and Heterogeneous Shell-Type Structures, Noordhoff, Leyden, Netherlands.
[5] Ounis H., Tati A., Benchabane A., 2014, Thermal buckling behavior of laminated composite plates: a finite-element study, Frontiers of Mechanical Engineering 9(1): 41-49.
[6] Stavsky Y., 1965, On the theory of symmetrically heterogeneous plates having the same thickness variation of the elastic moduli, Topics in Applied Mechanics 105-166.
[7] Reissner E., 1975, On transverse bending of plates, including the effect of transverse shear deformation, International Journal of Solids and Structures 11(5): 569-573.
[8] Whitney J., Pagano N., 1970, Shear deformation in heterogeneous anisotropic plates, Journal of Applied Mechanics 37 (4) : 1031-1036.
[9] Mindlin R., 1951, Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates, Journal of Applied Mechanics 18 :31-38.
[10] Yang P.C., Norris C.H., Stavsky Y., 1966, Elastic wave propagation in heterogeneous plates, International Journal of Solids and Structures 2(4): 665-684.
[11] Lo K., Christensen R., Wu E., 1977, A high-order theory of plate deformation-part 2: laminated plates, Journal of Applied Mechanics 44(4) : 669-676.
[12] Manjunatha B., Kant T., 1993, On evaluation of transverse stresses in layered symmetric composite and sandwich laminates under flexure, Engineering Computations 10(6): 499-518.
[13] Nayak A., Moy S.J., Shenoi R., 2003, Quadrilateral finite elements for multilayer sandwich plates, The Journal of Strain Analysis for Engineering Design 38(5): 377-392.
[14] Reddy J.N., 1984, A simple higher-order theory for laminated composite plates, Journal of Applied Mechanics 51(4): 745-752.
[15] Rezaiee-Pajand M., Shahabian F., Tavakoli F., 2012, A new higher-order triangular plate bending element for the analysis of laminated composite and sandwich plates, Structural Engineering and Mechanics 43(2): 253-271.
[16] Tu T.M., Thach L.N., Quoc T.H., 2010, Finite element modeling for bending and vibration analysis of laminated and sandwich composite plates based on higher-order theory, Computational Materials Science 49(4) S390-S394.
[17] Chakrabarti A., Sheikh A.H., 2005, Analysis of laminated sandwich plates based on interlaminar shear stress continuous plate theory, Journal of Engineering Mechanics 131(4): 377-384.
[18] Pandit M.K., Sheikh A.H., Singh B.N., 2008, An improved higher order zigzag theory for the static analysis of laminated sandwich plate with soft core, Finite Elements in Analysis and Design 44(9): 602-610.
[19] Carrera E., 2003, Historical review of zig-zag theories for multilayered plates and shells, Applied Mechanics Reviews 56: 287-308.
[20] Cho M., Parmerter R., 1993, Efficient higher order composite plate theory for general lamination configurations, AIAA Journal 31(7): 1299-1306.
[21] Di Sciuva M., 1986, Bending vibration and buckling of simply supported thick multilayered orthotropic plates: an evaluation of a new displacement model, Journal of Sound and Vibration 105(3): 425-442.
[22] Chalak H.D., 2012 , An improved C0 FE model for the analysis of laminated sandwich plate with soft core, Finite Elements in Analysis and Design 56: 20-31.
[23] Kapuria S., Nath J., 2013, On the accuracy of recent global–local theories for bending and vibration of laminated plates, Composite Structures 95: 163-172.
[24] Li X., Liu D., 1997, Generalized laminate theories based on double superposition hypothesis, International Journal for Numerical Methods in Engineering 40(7) : 1197-1212.
[25] Wu Z., Chen R., Chen W., 2005, Refined laminated composite plate element based on global–local higher-order shear deformation theory, Composite Structures 70(2) : 135-152.
[26] Zhen W., Wanji C., 2010, A C0-type higher-order theory for bending analysis of laminated composite and sandwich plates, Composite Structures 92(3): 653-661.
[27] Shariyat M., 2010, A generalized global–local high-order theory for bending and vibration analyses of sandwich plates subjected to thermo-mechanical loads, International Journal of Mechanical Sciences 52(3): 495-514.
[28] Lee L. Fan Y., 1996, Bending and vibration analysis of composite sandwich plates, Computers and Structures 60(1): 103-112.
[29] Linke M., Wohlers W., Reimerdes H.G., 2007, Finite element for the static and stability analysis of sandwich plates, Journal of Sandwich Structures and Materials 9(2): 123-142.
[30] Mantari J., Oktem A., Guedes Soares C., 2012, A new trigonometric layerwise shear deformation theory for the finite element analysis of laminated composite and sandwich plates, Computers and Structures 94: 45-53.
[31] Oskooei S., Hansen J., 2000, Higher-order finite element for sandwich plates, AIAA Journal 38(3): 525-533.
[32] Plagianakos T.S., Saravanos D.A., 2009, Higher-order layerwise laminate theory for the prediction of interlaminar shear stresses in thick composite and sandwich composite plates, Composite Structures 87(1): 23-35.
[33] Ramesh S.S., 2009, A higher-order plate element for accurate prediction of interlaminar stresses in laminated composite plates, Composite Structures 91(3): 337-357.
[34] Reddy J.N., 1987, A generalization of two-dimensional theories of laminated composite plates, Communications in Applied Numerical Methods 3(3): 173-180.
[35] Wu C. P., Lin C. C., 1993, Analysis of sandwich plates using a mixed finite element, Composite Structures 25(1): 397-405.
[36] Maturi D.A., 2014, Analysis of sandwich plates with a new layerwise formulation, Composites Part B: Engineering 56: 484-489.
[37] Phung-Van P., 2014, Static and free vibration analyses of composite and sandwich plates by an edge-based smoothed discrete shear gap method (ES-DSG3) using triangular elements based on layerwise theory, Composites Part B: Engineering 60: 227-238.
[38] Reddy J.N., 1993, An evaluation of equivalent-single-layer and layerwise theories of composite laminates, Composite Structures 25(1-4): 21-35.
[39] Carrera E., 2002, Theories and finite elements for multilayered, anisotropic, composite plates and shells, Archives of Computational Methods in Engineering 9(2): 87-140.
[40] Ha K., 1990, Finite element analysis of sandwich plates: an overview, Computers and Structures 37(4): 397-403.
[41] Khandan R., 2012, The development of laminated composite plate theories: a review, Journal of Materials Science 47 (16): 5901-5910.
[42] Noor A.K., Burton W.S., Bert C.W., 1996, Computational models for sandwich panels and shells, Applied Mechanics Reviews 49: 155-199.
[43] Zhang Y., Yang C., 2009, Recent developments in finite element analysis for laminated composite plates, Composite Structures 88(1): 147-157.
[44] Ramtekkar G., Desai Y., Shah A., 2002, Mixed finite-element model for thick composite laminated plates, Mechanics of Advanced Materials and Structures 9(2): 133-156.
[45] Ramtekkar G., Desai Y., Shah A., 2003, Application of a three-dimensional mixed finite element model to the flexure of sandwich plate, Computers and Structures 81(22): 2183-2198.
[46] Pagano N., 1970, Exact solutions for rectangular bidirectional composites and sandwich plates, Journal of Composite Materials 4(1): 20-34.
[47] Kanematsu H.H., Hirano Y., Iyama H., 1988, Bending and vibration of CFRP-faced rectangular sandwich plates, Composite Structures 10(2): 145-163.
[48] Zienkiewicz O.C., Taylor R.L., 2000, The Finite Element Method: Solid Mechanics, Butterworth-heinemann.
[49] Singh S.K., 2011, An efficient C0 FE model for the analysis of composites and sandwich laminates with general layup, Latin American Journal of Solids and Structures 8(2): 197-212.
[50] Meunier M., Shenoi R., 1999, Free vibration analysis of composite sandwich plates, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 213(7): 715-727.