An efficient C0 continuous finite element (FE) model is developed based on a combined theory (refine higher order shear deformation theory (RHSDT) and least square error (LSE) method) for the static analysis of a soft core sandwich plate. In this (RHSDT) theory, the in-plane displacement field for the face sheets and the core is obtained by superposing a global cubically varying displacement field on a zig-zag linearly varying displacement field with a different slope in each layer. The transverse displacement assumes to have a quadratic variation within the core and it remains constant in the faces beyond the core. The proposed model satisfies the condition of transverse shear stress continuity at the layer interfaces and the zero transverse shear stress condition at the top and bottom of the sandwich plate. The nodal field variables are chosen in an efficient manner to circumvent the problem of C1 continuity requirement of the transverse displacements. In order to calculate the accurate through thickness transverse stresses variation, the Least Square Error (LSE) method has been used at the post processing stage. The proposed combined model (RHSDT and LSE) is implemented to analyze the laminated composites and sandwich plates. Many new results are also presented which should be useful for future research.
Falls das inline PDF nicht korrekt dargestellt ist, können Sie das PDF hier herunterladen.
Averill R.C. (1994): Static and dynamic response of moderately thick laminated beams with damage. - Composites Engineering Journal, vol.4, pp.381-395.
Averill R.C. and Yip Y.C. (1996): Development of simple, robust finite elements based on refined theories for thicklaminated beams. - Composite Structures, vol.59, pp.661-666.
Aitharaju V.R. and Averill R.C. (1999): C0 Zigzag kinematic displacement models for the analysis of laminatedcomposites. - Mech. of Comp. Mat. and Struct., vol.6, pp.31-56.
Aagaah M.R., Mahinfalah M. and Jazar G.N. (2003): Linear static analysis and finite element modeling for laminatedcomposite plates using third order shear deformation theory. - Composite Structures, vol.62, pp.27-39.
Akhras G. and Li W. (2007): Spline finite strip analysis of composite plates based on higher order zigzag compositeplate theory. - Composite Structures, vol.78, pp.112-118.
Aydogdu M. (2009): A new shear deformation theory for laminated composite plates. - Composite Structures, vol.89, pp.94-101.
Bhaskar K. and Varadan T.K. (1989): Refinement of higher order laminated plate theories. - AIAA J., vol.27, pp.1830-31.
Bambole A.N. and Desai Y.M. (2007): Hybrid-interface finite element for laminated composite and sandwich beams. - Finite Element in Analysis and Design, vol.43, pp.1023-36.
Cho M. and Parmerter R.R. (1992): An efficient higher order plate theory for laminated composites. - Compos. Struct., vol.20, pp.113-23.
Cho M. and Parmerter R.R. (1993): Efficient higher order composite plate theory for general lamination configurations. - AIAA J., vol.31(7), pp.1299-1306.
Carrera E. (1996): C0 Reissner-Mindlin multilayered plate element including zigzag and interlaminar stress continuity. - Int. J. for Numerical Methods in Engineering, vol.39, pp.1797-1820.
Cho Y.B. and Averill R.C. (1997): An improved theory and finite element model for laminated beams using first orderzigzag sub-laminate approximations. - Composite Structure, vol.37, pp. 281-298.
Cho Y.B. and Averill R.C. (2000): First order zigzag sub-laminate plate theory and finite element model for laminatedcomposite and sandwich panels. - Composite Structures, vol.50, pp. 1-15.
Carrera E. (2004): On the use of the Murakami’s zig-zag function in the modeling of layered plates and shells. - Compos. Struct., vol.82, pp.541-554.
Chakrabarti A. and Sheikh A.H. (2004): A new triangular element to model inter-laminar shear stress continuous platetheory. - Int. J. Num. Meth. Eng., vol.60, pp.1237-1257.
Chakrabarti A., Chalak H.D., Iqbal A. and Sheikh A.H. (2011): A new FE model based on higher order zigzag theoryfor the analysis of laminated sandwich beam with soft core. - Composite Structures, vol.93, pp.271-279.
Di Sciuva M. (1984): A refined transverse shear deformation theory for multilayered anisotropic plates. - Atti. Academia Scienze Torino, vol.118, pp.279-95.
Di Scuiva M. (1987): An improved shear deformation theory for moderately thick multilayered anisotropic shells andplates. - Journal of Applied Mechanics, vol.54, pp.589-596.
Di Scuiva M. (1992): Multilayered anisotropic plate models with continuous interlaminar stress. - Comput. Struct., vol.22(3), pp.149-67.
Di Sciuva M. (1993): A general quadrilateral multilayered plate element with continuous interlaminar stresses. - Computer Structures, vol.47, pp.91-105.
Di Sciuva M. (1995): Development of anisotropic multilayered shear deformable rectangular plate element. - Computer Structures, vol.21, pp.789-796.
Demasi L. (2005): Refined multilayered plate elements based on Murakami zig-zag functions. - Compos. Struct., vol.70, pp.308-316.
Demasi L. (2009): Mixed plate theories based on generalized unified formulation Part IV: zig-zag theories. - Compos. Struct., vol.87, pp.195-205.
Demasi L. (2009): Mixed plate theories based on generalized unified formulation. - Part V: Results. - Compos. Struct., vol.88, pp.1-16.
Frosting Y. (2003): Classical and high order computational models in the analysis of modern sandwich panels. - Composites: Part B, vol.34, pp.83-100.
Fares M.E. and Elmarghany M.K.H. (2008): A refined zigzag non-linear first order shear deformation theory ofcomposite laminated plates. - Composite Structures, vol.82, pp.71-83.
Ferreira A.J.M., Roque C.M.C., Carrera E. and Cinefra M. (2011): Analysis of thick isotropic and cross ply laminatedplates by radial basis function and a unified formulation. - Journal of Sound and Vibration, vol.330, pp.771-787.
Ferreira A.J.M., Roque C.M.C., Carrera E., Cinefra M. and Polit O. (2011): Radial basis functions collocation and aunified formulation for bending, vibration and buckling analysis of laminated plates, according to variation ofMurakami’s zigzag theory. - Eur. J. Mech., vol.30(4), pp.559-570.
Givil H.S., Rabinovitch O. and Frostig Y. (2007): High-order non-linear contact effects in the dynamic behavior ofdelaminated sandwich panel with a flexible core. - International Journal of Solids and Structures, vol.44, pp.77-99.
Goyal V.K. and Kapania R.K. (2007): A shear deformeable beam element for analysis of laminated composites. - Finite Element in Analysis and Design, vol.43, pp.463-477.
Icardi U. (2001): A three dimensional zigzag theory for analysis of thick laminated beams. - Composite Structures, vol.53, pp.123-135.
Icardi U. (2003): Applications of zigzag theories to sandwich beams. - Mechanics of Advanced Materials and Structures, vol.10, pp.77-97.
Kant T. (1982): Numerical analysis of thick plates. - Comp. Meth. Appl. Mech. Eng., vol.44(4), pp.1-18.
Kant T. and Swaminathan A. (2002): Analytical solutions for the static analysis of laminated composite and sandwichplates based on a higher order refined theory. - Composite Structures, vol.56, pp.329-344.
Kim J.S. and Cho M. (2005): Enhanced first-order shear deformation theory for laminated and sandwich plates. - Journal of Applied Mechanics, vol.72, pp.809-817.
Kim J.S. and Cho M. (2006): Enhanced modeling of laminated and sandwich plates via strain energy transformation. - Composites Science and Technology, vol.66, pp.1575-1587.
Kim J.S. and Cho M. (2007): Enhanced first-order theory based on mixed formulation and transverse normal effect. - Int. J. of Solids and Struct., vol.44(3-4), pp.1256-1276.
Kulkarni S.D. and Kapuria S. (2007): A new discrete Kirchhoff quadrilateral element based on the third order theoryfor composite plates. - Computational Mechanics, vol.39, pp.237-246.
Kapuria S. and Kulkarni S.D. (2007): An improved discrete Kirchhoff element based on third order zigzag theory forstatic analysis of composite and sandwich plates. - Int. J. Num. Meth. Eng., vol.69, pp.1948-1981.
Khandelwal R.P., Chakrabarti A. and Bhargava P. (2012): An efficient FE model and least square error method foraccurate calculation of transverse stresses in composites and sandwich laminates. - Composites: Part B. Accepted.
Lo K.H., Christensen R.M. and Wu E.M. (1977): A higher order theory of plate deformation, Part2. Laminated plates. - J. Appl. Mech. Trans. ASME, vol.44, pp.669-76.
Liou W.J. and Sun C.T. (1987): A three dimensional hybrid stress isoparametric element for analysis of laminatedcomposite plates. - Computers and Structures, vol.25(2), pp.241-249.
Lee K.H., Senthilnathan N.R., Lim S.P. and Chow S.T. (1990): An improved zigzag model for the bending of laminatedcomposite plates. - Composite Structures, vol.15, pp.137-148.
Lu X. and Liu D. (1992): An interlaminar shear stress continuity theory for both thin and thick laminates. - ASME Journal of Applied Mechanics, vol.59, pp.502-509.
Li X. and Liu D. (1995): Zigzag theory for composite laminates. - AIAA J., vol.33, No.6, pp.1163-65.
Liu D. and Li X. (1996): An overall view of laminate theories based on displacement hypothesis. - J. Compos. Mater., vol.30, pp.1539-61.
Murakami H. (1986): Laminated composite plate theory with improved in-plane responses. - Journal of Applied Mechanics, vol.53, pp.661-666.
Manjunatha B.S. and Kant T. (1992): A comparison of nine and sixteen noded quadrilateral elements based on higherorder laminate theories for estimation of transverse stresses. - J. Reinf. Plast. Compos., vol.11, pp.986-1002.
Pagano N.J. (1970): Exact solutions for rectangular bidirectional composites and sandwich plates. - Journal of Composite Materials, vol.4, pp.20-35.
Pervez T., Seibi A.C. and Al-Jahwari F.K.S. (2005): Analysis of thick orthotropic laminated composite plates based onhigher order shear deformation theory. - Composite Structures, vol.71, pp.414-422.
Pandit M.K., Sheikh A.H. and Singh B.N. (2008): An improved higher order zigzag theory for the static analysis oflaminated sandwich plate with soft-core. - Finite Element in Analysis and Design, vol.44, pp.602-10.
Pandit M.K., Sheikh A.H. and Singh B.N. (2008): Buckling of laminated sandwich plates with soft core based on animproved higher order zigzag theory. - Thin-Walled Structures, vol.46, pp.1183-1191.
Pandit M.K., Sheikh A.H. and Singh B.N. (2010): Stochastic perturbation based finite element for deflection statisticsof soft core sandwich plate with random material properties. - Int. J. Mech. Sci., vol.51, No.5, pp.14-23.
Reissner E. (1944): On the theory of bending of elastic plates. - J. Math. Physics, vol.23, pp.184-191.
Reddy J.N. (1984): A simple higher-order theory for laminated composite plates. - J. Appl. Mech. Trans. ASME, vol.51, pp.745-52.
Reddy J.N. (1987): A generalization of two dimensional theories of laminated composite plates. - Commn. Appl. Numer. Meth., vol.3, pp.173-180.
Robbins D.H. and Reddy J.N. (1993): Modeling of thick composites using a layerwise laminate theory. - Int. J. Numer. Methods Eng., vol.36, pp.655-77.
Robbins D.H. and Reddy J.N. (1996): Theories and computational models for composite laminates. - Applied Mechanics Rev., vol.49, pp.155-199.
Rao M.K., Desai Y.M. and Chitnis M.R. (2001): Free vibrations of laminated beams using mixed theory. - Composite Structures, vol.52, pp.149-160.
Ramtekkar G.S. and Desai Y.M. (2002): Natural vibrations of laminated composite beams by using mixed finite elementmodeling. - Journal of Sound and Vib., vol.257(4), pp.635-651.
Ramtekkar G.S., Desai Y.M. and Shah A.H. (2003): Application of a three dimensional mixed finite element model tothe flexure of sandwich plate. - Comput. and Struct., vol.81, pp.2383-2398.
Ramesh S.S., Wang C.M., Reddy J.N. and Ang K.K. (2009): A higher order plate element for the accurate prediction ofinterlaminar stresses in laminated composite plates. - Composite Structures, vol.91, pp.337-357.
Roque C.M.C., Cunha D., Shu C. and Ferreira A.J.M. (2011): A local radial basis functions- finite differencestechniques for the analysis of composite plates. - Eng. Ana. Boun. Elem., vol.35, pp.363-374.
Rodrigues J.D., Roque C.M.C., Ferreira A.J.M., Carrera E. and Cinefra M. (2011): Radial basis functions collocationand a unified formulation for bending, vibration and buckling analysis of laminated plates, according to variation ofMurakami’s zigzag theory. - Composite Structures, vol.93(7), pp.1613-1620.
Sheikh A.H. and Chakrabarti A. (2003): A new plate bending element based on higher order shear deformation theoryfor the analysis of composite plates. - Fin. Elem. Anal. Des., vol.39(9), pp.883-903.
Sheikh A.H. and Chakrabarti A. (2003): A new Plate bending element based on higher order shear deformation theoryfor the analysis of composite plates. - Finite Element in Analysis and Design, vol.39, pp.883-903.
Singh S.K., Chakrabarti A., Bera P. and Sony J.S.D. (2011): An efficient C0 FE model for the analysis of compositesand sandwich laminates with general layup. - Lat. Ame. J. Sol. Struc., vol.8, pp.197-212.
Srinivas S. (1973): A refined analysis of composite laminates. - J. Sound Vibration, vol.30, pp.495-507.
Toledano A. and Murakami H. (1987): A composite plate theory for arbitrary laminate configuration. - J. Appl. Mech., vol.54(1), pp.181-89.
Tu T.M., Thach L.N. and Quoc T.H. (2010): Finite element modeling for bending and vibration analysis of laminated andsandwich composite plates based on higher order theory. - Computational Material Science, vol.49, pp.390-394.
Vlachoutsis S. (1992): Shear correction factors for plates and shells. - Int. J. Num. Methods Eng., vol.33(7), pp.1537-52.
Wu Z., Chen R. and Chen W. (2005): Refined laminated plate element based on global local higher order sheardeformation theory. - Composite Structures, vol.70, pp.135-152.
Wu Z., Lo S.H., Sze K.Y. and Chen W. (2012): A higher order finite element including transverse normal strainincluding for linear elastic composite plates with general lamination configurations. - Finite Element in Analysis and Design, vol.48, pp.1346-1357.
Yang P.C., Norris C.H. and Stavsky Y. (1996): Elastic wave propagation in heterogeneous plates. - Int. J. Solids Structure, vol.2, pp.665-84.
Yip Y.C. and Averill R.C. (1996): Thick beam theory and finite element model with zigzag sub-laminateapproximations. - AIAA., vol.34, pp.1627-1632.
Zhen W., Wanji C. and Xiaohui R. (2010): An accurate higher-order theory and C0 finite element for free vibrationanalysis of laminated composite and sandwich plates. - Compos. Struct., vol.92, pp.1299-1307.
Zhen W. and Wanji C. (2010): A C0-type higher-order-theory for bending analysis of laminated composite andsandwich plates. - Compos. Struct., vol.92, pp.653-661.