Bending analysis of composite sandwich plates using generalized differential quadrature method based on FSDT

Document Type : Persian


1 Master student, Mechanical engineering Department, Hamadan Branch, Islamic Azad University Science and research Campus , Hamadan, Iran

2 Assistant professor, Mechanical engineering Department, Branch, Islamic Azad University, Isfahan, Iran

3 Master student Mechanical engineering Department, Isfahan University of Technology, Isfahan, Iran


Nowadays, the technology intends to use materials such as magnesium alloys due to their high strength to weight ratio in engine components. As usual, engine cylinder heads and blocks has made of various types of cast irons and aluminum alloys. However, magnesium alloys has physical and mechanical properties near to aluminum alloys and reduce the weight up to 40 percents. In this article, a new low cycle fatigue lifetime prediction model is presented for a magnesium alloy based on energy approach and to obtain this objective, the results of low cycle fatigue tests on magnesium specimens are used. The presented model has lower material constants in comparison to other criteria and also has proper accuracy; because in energy approaches, a plastic work-lifetime relation is used where the plastic work is the multiple of stress and plastic strain. According to cyclic softening behaviors of magnesium and aluminum alloys, plastic strain energy can be proper selection, because of being constant the product value of stress and plastic strain during fatigue loadings. In addition, the effect of mean stress is applied to the low cycle fatigue lifetime prediction model by using a correction factor. The results of presented models show proper conformation to experimental results


 [1] Pandit M.K., Singh B.N., Sheikh A.H., Buckling of laminated sandwich plates with soft core based on an improved higher order zigzag theory, Journal of Thin-Walled Structures, Vol. 46, 2008, pp. 1183– 1191.
 [2] Leissa A.W., Review of laminated composites plate buckling, Applied Mechanical Rev, Vol. 40, 1987.
[3] Levy M., Sur L’equilibrie Elastique d’une Plaque Rectangulaire, Compt Rend, Vol. 129, 1899, pp. 535-539.
[4] Timoshenko S.P., woinowsky – Krieger.S., Theory of plates and shells , 2d ed., McGraw Hill, New York, 1959.
[5] هنرجو ، ب،" آنالیز صفحات لایه لایه مرکب به روش differential quadrature "، دانشگاه شیراز ، 1378.
[6] Whitney J.M., Pagano.N J, Shear deformation in heteogeneous anisotropic plates, ASME Journal of Applied Mechanical, Vol. 37,1970, pp. 1031-1036.
[7] Bert C.W., Chen T.L.C., Effect of shear deformation on vibration of antisymmetric angle-ply laminated rectangular plates, International Journal of Solids Structure, Vol. 14, 1978, pp. 465-473.
[8] Reddy J.N., Chao W.C., A comparison of closed-form and finite-element solutions of thick, laminated, anisotropic rectangular plates, Nuclear Engineering and Design, Vol. 64, 1981, pp. 153-167.
[9] Kant T., Numerical analysis of thick plates, Computation and Mathematics Applied Mechanical Engineering, Vol. 31, 1982, pp.1–18.
[10] Pandya B science N., Kant T., A consistent refined theory for flexure of a symmetric laminate, Mechanics Research Communications, Vol, 14, 1987, pp.107–113.
[11] Pandya BN., Kant T., Higher order shear deformable theories for flexure of sandwich plates –finite element evaluations.InternationalJournal of Solids Structures, Vol. 24(12), 1988, pp. 1267–86.
[12] Pandya BN., Kant T., Flexure analysis of laminated composites using refined higher order C_ plate bending elements Computation and Mathematics Applied Mechanical Engineering, Vol. 66, 1988, pp. 173–98.
[13] Pandya BN., Kant T., A refined higher order generally orthotropic C_ plate bending element. Composite Structures, Vol. 28, 1988, pp. 119–133.
[14] Pandya BN., Kant T., Finite element stress analysis of laminated composites using higher order displacement model, Composite science Technology, Vol. 32, 1988, pp. 137–155.
[15] Kant T., Manjunatha BS., An unsymmetric FRC laminate C_ finite element model with 12 degrees of freedom per node. Eng Comput, Vol. 5(3), 1988, pp. 300–308.
[16] Swaminathan K., Patil S.S., Nataraja M.S, Mahabaleswara K.S., Bending of sandwich plates with anti-symmetric angle-ply face sheets – Analytical evaluation of higher order refined computational models, Composite Structures, Vol. 75, 2006, pp. 114–120.
 [17] Bellman R., Casti J., Differential quadrature and long-term integration, Journal of Mathematical Analysis and Applications, Vol. 34, 1971, pp. 235–238.
 [18] Bellman R.E., Kashef B.G., Casti J., Differential quadrature: a technique for a rapid solution of nonlinear partial differential equations, Journal Computational Physics, Vol. 10, 1972, pp. 40–52.
[19] Bert C.W., S.K. Jang., Striz A.G., Two new approximate methods for analyzing free vibration of structural components, AIAA Journal, Vol. 26, 1988, pp. 612-618.
 [20] Bert C.W., Malik M., Differential quadrature in computational mechanics: a review, Applied Mechanical Review, Vol. 49, 1996, pp. 1–27.
 [21] Chen W., Shu C., He W., Zhong, T., The application of special matrix product to differential quadrature solution of geometrically nonlinear bending of orthotropic rectangular plates, Composite Structures, Vol. 74, 2000, pp. 65–76.
 [22] Chen W., Tanaka M.A., Study on time schemes for DRBEM analysis of elastic impact wave, Computational Mechanics, Vol. 28, 2002, pp. 331–338.
 [23] Bert C.W., Jang S.K., Striz A.G., Nonlinear bending analysis of orthotropic rectangular plates by the method of differential quadrature. Computational Mechanics, Vol. 5, 1989, pp. 217–226.
 [24]. Bert C.W., Wang X., Striz, A.G., Differential quadrature for static and free vibration analyses of anisotropic plates, International Journal of Solids Structures, Vol. 30, 1993, pp.1737–1744.
 [25] Wang X., Bert C.W., A new approach in applying differential quadrature to static and free vibrational analyses of beams and plates, Journal of Sound Vibration, Vol. 162, 1993, pp. 566–572.
 [26] Wang X., Gu H., Static analysis of frame structures by the differential quadrature element method. International Journal Numer Mechanical Eng, Vol. 40, 1997, pp. 759–772.
[27] Wang X., Wang Y., Free vibration analyses of thin sector plates by the new version of differential quadrature method. Computation and Mathematics Applied Mechanical Engineering, Vol. 193, 2004, pp. 3957–3971.
 [28] Wang X., Differential quadrature for buckling analysis of laminated plates. Computers and Structures, Vol. 57, 1995, pp. 715–719.
 [29] Civan F., Sliepcevich C.M., Differential quadrature for multidimensional problems, Journal of Mathematical Analysis and Applications, Vol. 101, 1984, pp. 423– 443.
[30] Shu C., Richards B.E., Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stoaks equations, International Journal for Numerical Methods in Engineering, Vol. 15, 1992, pp.791–798.
[31] Shu, C., Wang, C.M., Treatment of mixed and non-uniform boundary conditions in GDQ vibration analysis of rectangular plate, Engineering Structures, Vol. 21, 1999, pp.125–134.
[32] Du, H., Lim, M.K., Lin, R.M., Application of generalized differential quadrature method to structural problems, International Journal for Numerical Methods in Engineering, Vol. 37, 1994, pp. 1881–1896.
[33] Wang, X., Wang, X., Shi, X., Differential quadrature buckling analyses of rectangular plates subjected to non-uniform distributed in-plane loadings. Thin-Walled Structures, Vol. 44, 2006, pp. 837–843.
[34] Hsu, M.H., Vibration analysis of annular plates using the modified generalized differential quadrature method, Journal of Applied science, Vol. 6(7), 2006, pp. 1591–1595.
[35] Tornabene, F., Viola, E., A generalized differential quadrature solution for laminated composite shells of revolution, In, Proceedings of 8th World Congress on Computational Mechanics. Venice Italy, 2008
[36] Striz, A.G., Wang, X., Bert, C.W., Harmonic differential quadrature method and applications to analysis of structural components, Acta Mechanical, Vol. 111, 1995, pp. 85–94.
[37] Liew, K.M., Teo, T.M., Han, J.B., Comparative accuracy of DQ and HDQ methods for three dimensional vibration analyses of rectangular plates, International Journal for Numerical Methods in Engineering, Vol. 45, 1999, pp. 1831–1848.
[38] Civalek, Ö., Application of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for buckling analysis of thin isotropic plates and elastic columns, Engineering Structures, Vol. 26, 2004, pp. 171–186.
[39] Malekzadeh, P., Karami,G., Polynomial and harmonic differential quadrature methods for free vibration of variable thickness thick skew plates, Engineering Structures, Vol. 27, 2005, pp. 1563–1574.
[40] Civalek, Ö, Harmonic differential quadrature-finite differences coupled approaches for geometrically nonlinear static and dynamic analysis of rectangular plates on elastic foundation, Journal of Sound Vibration, Vol. 294, 2006, pp. 966–980.
 [41] Vinson J.R., Plate and panel structures of isotropic, composite and piezoelectric materials, including sandwich construction, Springer, Netherlands, 2005.
[42] Jones R. Mechanics of composite materials, Scripta Book Company 1975.
[43] Kolakowski Z , Kowal-michalska K. Selected problems of in stabilities in composite structures. A Series of Monographs, Technical University of Lodz, 1999.
 [44] Mania R. Buckling analysis of trapezoidal composite sandwich plate subjected to in-plane compression, Composite Structures, Vol. 69. 2005, pp. 482–490.
[45] Nayak A.K, Moy S.S.J, Shenoi R.A. A higher order finite element theory for buckling and vibration analysis of initially stressed composite sandwich plates. Journal of Sound Vibration, Vol. 286, 2005, pp. 763–780.
[46] Civan, F., Sliepcevich, C.M., Differential quadrature for multidimensional problems, Journal of Mathematical Analysis and Applications, Vol. 101, 1984, pp. 423– 443.
 [47] Shu, C., Xue, H., Explicit computations of weighting coefficients in the harmonic differential quadrature. Journal of Sound Vibration, Vol. 204, 1997, pp. 549–555.
[48] Wang, X., Gan, L., Zhang,  Y., Differential quadrature analysis of the buckling of thin rectangular plates with cosine-distributed compressive loads on two opposite sides , Advances in Engineering Software, Vol. 39, 2008, pp. 497–504.
[49] Tornabene, F., Viola, E., 2-D solution for free vibrations of parabolic shells using generalized differential quadrature method, European Journal of Mechanical A/Solids, Vol. 27, 2008, pp. 1001–1025.