Numerical Methods for FGM Composites Shells and Plates
Year 2018,
Volume: 10 Issue: 1, 5 - 12, 28.05.2018
Serçil Solmaz
Ömer Civalek
Abstract
Main formulations for free vibration analysis of functionally graded
composite shells have been given in numerical concept. Equations of motions for
conical shells are listed in differential form.
First-order shear deformation (FSDT) shell theory is used for obtaining
the equations. Then two methods have been applied for solution. These methods
are differential quadrature (DQ) and discrete singular convolution (DSC). The
discrete forms of these equations have been given.
References
- [1] Reddy, J.N., Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, New York: CRC Press; 2nd edition, 2003.
- [2] Qatu, M., Vibration of Laminated Shells and Plates, Academic Press, U.K., 2004.
- [3] Soedel, W., Vibrations of Shells and Plates, CRC Press; 3rd edition, 2004.
- [4] Leissa, A.W., Vibration of Shells, Acoustical Society of America, 1993.
- [5] Shen, H.S., Functionally Graded Materials: Nonlinear Analysis of Plates and Shells, CRC Press, 2009.
- [6] Elishakoff, I., Pentaras D., Gentilini C., Mechanics of Functionally Graded Material Structures, World Scientific Publishing Conference, 2015.
- [7] Ye, J., Laminated composite plates and shells: 3D modeling, Springer, 2003.
- [8] Timoshenko, S. and Woinowsky-Krieger, S., Theory of Plates and Shells, McGraw-Hill, New York; 2nd edition, 1959.
- [9] Liew, K.M., Zhao, X., Ferreira, A.J.M., A review of meshless methods for laminated and functionally graded plates and shells. Compos Struct, 93, 2031-2041, 2011.
- [10] Civalek, O., Finite Element Analysis of Plates and Shell, Fırat University, Elazığ, 1988 (in Turkish).
- [11] Civalek, O. Geometrically non-linear static and dynamic analysis of plates and shells resting on elastic foundation by the method of polynomial differential quadrature (PDQ) [Ph. D. thesis]. Fırat University, Elazığ, 2004 (in Turkish).
- [12] Qatu, M.S., Sullivan, R.W., Wang, W., Recent research advances on the dynamic analysis of composite shells: 2000–2009 Review Article. Compos Struct, 93, 14-31, 2010.
- [13] Ferreira A.J.M., Viola, E., Tornabene, F., Fantuzzi, N., Zenkour, A.M., Analysis of sandwich plates by generalized differential quadrature method. Math Probl Eng, Volume: 2013, 1-12. Article ID 964367, 2013.
- [14] Tornabene, F., Viola, E., Inman, D.J., 2-D differential quadrature solution for vibration analysis of functionally graded conical, cylindrical shell and annular plate structures. J Sound Vib, 328, 259-290, 2009.
- [15] Fantuzzi, N., Tornabene, F., Bacciocchi, M., Dimitri, R., Free vibration analysis of arbitrarily shaped Functionally Graded Carbon Nanotube-reinforced plates. Compos Part B: Eng, 115, 384-408, 2017
- [16] Civalek, O., Vibration analysis of laminated composite conical shells by the method of discrete singular convolution based on the shear deformation theory. Compos Part B Eng, 45(1), 1001-1009 , 2013.
- [17] Civalek, O., The determination of frequencies of laminated conical shells via the discrete singular convolution method. J Mech Mater Struct; 1(1), 163-182, 2006.
- [18] Jin, G.Y., Su, Z., Shi, S., Ye, T.G., Gao, S.Y., Three-dimensional exact solution for the free vibration of arbitrarily thick functionally graded rectangular plates with general boundary conditions. Compos Struct,108, 565-577, 2014.
- [19] Thai, H.-T., Kim, S.-E., A review of theories for the modeling and analysis of functionally graded plates and shells, Compos Struct, 128, 70-86, 2015.
- [20] Lei, Z.X., Liew, K.M., Yu, J.L., Free vibration analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method in thermal environment. Compos Struct, 106, 128-138, 2013.
- [21] Shen, H.S., Zhang C.L., Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates. Mater Des, 31, 3403–3411, 2010.
- [22] Ansari, R., Torabi, J., Faghih, M.S., Vibrational analysis of functionally graded carbon nanotube-reinforced composite spherical shells resting on elastic foundation using the variational differential quadrature method. Eur J Mech-A Solid, 60, 166–182, 2016.
- [23] Demir, Ç., Mercan, K., Civalek, O., Determination of critical buckling loads of isotropic, FGM and laminated truncated conical panel. Composites Part B: Engineering 94, 1-10, 2016.
- [24] Mercan, K., Civalek, O., DSC method for buckling analysis of boron nitride nanotube (BNNT) surrounded by an elastic matrix. Composite Structures, 143, 300-309, 2016.
- [25] Akgöz, B., Civalek, O., Buckling analysis of cantilever carbon nanotubes using the strain gradient elasticity and modified couple stress theories. Journal of Computational and Theoretical Nanoscience, 8(9), 1821-1827, 2011.
- [26] Shao, Z., Shen, Z., He, Q., Wei, G.W., A generalized higher order finite-difference time-domain method and its application in guided-wave problems, IEEE Transactions On Microwave Theory and Techniques, 51, 856-861, 2003.
- [27] Civalek, O., Nonlinear dynamic response of MDOF systems by the method of harmonic differential quadrature (HDQ), Structural Engineering and Mechanics, 25 (2), 201-217, 2007.
- [28] Bao, W., Sun, F., Wei, G.W., Numerical methods for the generalized Zakharov system, J Comput Physics, 190, 201–228, 2003.
- [29] Civalek, O., Nonlinear dynamic response of laminated plates resting on nonlinear elastic foundations by the discrete singular convolution-differential quadrature coupled approaches, Compos Part B Eng, 50, 171-179, 2013.
- [30] Civalek, O., Korkmaz, A., Demir, Ç., Discrete singular convolution approach for buckling analysis of rectangular Kirchhoff plates subjected to compressive loads on two opposite edges. Adv Eng Softw, 41, 557-560, 2010.
- [31] Civalek, O., Analysis of thick rectangular plates with symmetric cross-ply laminates based on first-order shear deformation theory. J Compos Mater, 42, 2853–2867, 2008.
- [32] Wang, X., Wang, Y., Xu, S., DSC analysis of a simply supported anisotropic rectangular plate. Compos Struct, 94, 2576-2584, 2012.
- [33] Baltacıoğlu, A.K., Civalek, Ö., Akgöz, B., Demir, F., Large deflection analysis of laminated composite plates resting on nonlinear elastic foundations by the method of discrete singular convolution. Int J Pres Ves Pip, 88, 290-300, 2011.
- [34] Civalek, O., Akgöz, B., Vibration analysis of micro-scaled sector shaped graphene surrounded by an elastic matrix. Comp Mater Sci, 77, 295-303, 2013.
- [35] Gürses, M., Civalek, O., Korkmaz, A., Ersoy, H., Free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on first-order shear deformation theory. Int J Numer Methods Eng, 79, 290-313, 2009.
- [36] Baltacıoglu, A.K., Akgöz, B., Civalek, O., Nonlinear static response of laminated composite plates by discrete singular convolution method. Compos Struct, 93, 153-161, 2010.
- [37] Gürses, M., Akgöz, B., Civalek, O., Mathematical modeling of vibration problem of nano-sized annular sector plates using the nonlocal continuum theory via eight-node discrete singular convolution transformation. Appl Math Comput, 219, 3226–3240, 2012.
- [38] Civalek, O., Mercan, K., Demir, C., Vibration analysis of FG cylindrical shells with power-law index using discrete singular convolution technique. Curved and Layer Struct, 3, 82-90, 2016.
- [39] Tong, L., Free vibration of laminated conical shells including transverse shear deformation. Int J Solids Struct, 31, 443–456, 1994.
- [40] Wang, Q., Shi, D., Liang, Q., Shi, X., A unified solution for vibration analysis of functionally graded circular, annular and sector plates with general boundary conditions. Compos Part B, 88, 264-294, 2016.
- [41] Mercan, K., Civalek, O., Buckling analysis of silicon carbide nanotubes (SiCNTs). International Journal of Engineering & Applied Sciences, 8 (2), 101-108, 2016.
- [42] Civalek, O., Çatal, H.H., Plakların diferansiyel quadrature metodu ile stabilite ve titreşim analizi. Teknik Dergi, 14 (1), 2835-2852, 2003.
- [43] Civalek, O., Diferansiyel quadrature metodu ile elastik çubukların statik dinamik ve burkulma analizi, XVI Mühendislik Teknik Kongresi, ODTU, Ankara, Kasım 2001.
- [44] Civalek, O., Numerical solutions to the free vibration problem of Mindlin sector plates using the discrete singular convolution method. International Journal of Structural Stability and Dynamics, 9 (2), 267-284, 2009.
Year 2018,
Volume: 10 Issue: 1, 5 - 12, 28.05.2018
Serçil Solmaz
Ömer Civalek
References
- [1] Reddy, J.N., Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, New York: CRC Press; 2nd edition, 2003.
- [2] Qatu, M., Vibration of Laminated Shells and Plates, Academic Press, U.K., 2004.
- [3] Soedel, W., Vibrations of Shells and Plates, CRC Press; 3rd edition, 2004.
- [4] Leissa, A.W., Vibration of Shells, Acoustical Society of America, 1993.
- [5] Shen, H.S., Functionally Graded Materials: Nonlinear Analysis of Plates and Shells, CRC Press, 2009.
- [6] Elishakoff, I., Pentaras D., Gentilini C., Mechanics of Functionally Graded Material Structures, World Scientific Publishing Conference, 2015.
- [7] Ye, J., Laminated composite plates and shells: 3D modeling, Springer, 2003.
- [8] Timoshenko, S. and Woinowsky-Krieger, S., Theory of Plates and Shells, McGraw-Hill, New York; 2nd edition, 1959.
- [9] Liew, K.M., Zhao, X., Ferreira, A.J.M., A review of meshless methods for laminated and functionally graded plates and shells. Compos Struct, 93, 2031-2041, 2011.
- [10] Civalek, O., Finite Element Analysis of Plates and Shell, Fırat University, Elazığ, 1988 (in Turkish).
- [11] Civalek, O. Geometrically non-linear static and dynamic analysis of plates and shells resting on elastic foundation by the method of polynomial differential quadrature (PDQ) [Ph. D. thesis]. Fırat University, Elazığ, 2004 (in Turkish).
- [12] Qatu, M.S., Sullivan, R.W., Wang, W., Recent research advances on the dynamic analysis of composite shells: 2000–2009 Review Article. Compos Struct, 93, 14-31, 2010.
- [13] Ferreira A.J.M., Viola, E., Tornabene, F., Fantuzzi, N., Zenkour, A.M., Analysis of sandwich plates by generalized differential quadrature method. Math Probl Eng, Volume: 2013, 1-12. Article ID 964367, 2013.
- [14] Tornabene, F., Viola, E., Inman, D.J., 2-D differential quadrature solution for vibration analysis of functionally graded conical, cylindrical shell and annular plate structures. J Sound Vib, 328, 259-290, 2009.
- [15] Fantuzzi, N., Tornabene, F., Bacciocchi, M., Dimitri, R., Free vibration analysis of arbitrarily shaped Functionally Graded Carbon Nanotube-reinforced plates. Compos Part B: Eng, 115, 384-408, 2017
- [16] Civalek, O., Vibration analysis of laminated composite conical shells by the method of discrete singular convolution based on the shear deformation theory. Compos Part B Eng, 45(1), 1001-1009 , 2013.
- [17] Civalek, O., The determination of frequencies of laminated conical shells via the discrete singular convolution method. J Mech Mater Struct; 1(1), 163-182, 2006.
- [18] Jin, G.Y., Su, Z., Shi, S., Ye, T.G., Gao, S.Y., Three-dimensional exact solution for the free vibration of arbitrarily thick functionally graded rectangular plates with general boundary conditions. Compos Struct,108, 565-577, 2014.
- [19] Thai, H.-T., Kim, S.-E., A review of theories for the modeling and analysis of functionally graded plates and shells, Compos Struct, 128, 70-86, 2015.
- [20] Lei, Z.X., Liew, K.M., Yu, J.L., Free vibration analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method in thermal environment. Compos Struct, 106, 128-138, 2013.
- [21] Shen, H.S., Zhang C.L., Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates. Mater Des, 31, 3403–3411, 2010.
- [22] Ansari, R., Torabi, J., Faghih, M.S., Vibrational analysis of functionally graded carbon nanotube-reinforced composite spherical shells resting on elastic foundation using the variational differential quadrature method. Eur J Mech-A Solid, 60, 166–182, 2016.
- [23] Demir, Ç., Mercan, K., Civalek, O., Determination of critical buckling loads of isotropic, FGM and laminated truncated conical panel. Composites Part B: Engineering 94, 1-10, 2016.
- [24] Mercan, K., Civalek, O., DSC method for buckling analysis of boron nitride nanotube (BNNT) surrounded by an elastic matrix. Composite Structures, 143, 300-309, 2016.
- [25] Akgöz, B., Civalek, O., Buckling analysis of cantilever carbon nanotubes using the strain gradient elasticity and modified couple stress theories. Journal of Computational and Theoretical Nanoscience, 8(9), 1821-1827, 2011.
- [26] Shao, Z., Shen, Z., He, Q., Wei, G.W., A generalized higher order finite-difference time-domain method and its application in guided-wave problems, IEEE Transactions On Microwave Theory and Techniques, 51, 856-861, 2003.
- [27] Civalek, O., Nonlinear dynamic response of MDOF systems by the method of harmonic differential quadrature (HDQ), Structural Engineering and Mechanics, 25 (2), 201-217, 2007.
- [28] Bao, W., Sun, F., Wei, G.W., Numerical methods for the generalized Zakharov system, J Comput Physics, 190, 201–228, 2003.
- [29] Civalek, O., Nonlinear dynamic response of laminated plates resting on nonlinear elastic foundations by the discrete singular convolution-differential quadrature coupled approaches, Compos Part B Eng, 50, 171-179, 2013.
- [30] Civalek, O., Korkmaz, A., Demir, Ç., Discrete singular convolution approach for buckling analysis of rectangular Kirchhoff plates subjected to compressive loads on two opposite edges. Adv Eng Softw, 41, 557-560, 2010.
- [31] Civalek, O., Analysis of thick rectangular plates with symmetric cross-ply laminates based on first-order shear deformation theory. J Compos Mater, 42, 2853–2867, 2008.
- [32] Wang, X., Wang, Y., Xu, S., DSC analysis of a simply supported anisotropic rectangular plate. Compos Struct, 94, 2576-2584, 2012.
- [33] Baltacıoğlu, A.K., Civalek, Ö., Akgöz, B., Demir, F., Large deflection analysis of laminated composite plates resting on nonlinear elastic foundations by the method of discrete singular convolution. Int J Pres Ves Pip, 88, 290-300, 2011.
- [34] Civalek, O., Akgöz, B., Vibration analysis of micro-scaled sector shaped graphene surrounded by an elastic matrix. Comp Mater Sci, 77, 295-303, 2013.
- [35] Gürses, M., Civalek, O., Korkmaz, A., Ersoy, H., Free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on first-order shear deformation theory. Int J Numer Methods Eng, 79, 290-313, 2009.
- [36] Baltacıoglu, A.K., Akgöz, B., Civalek, O., Nonlinear static response of laminated composite plates by discrete singular convolution method. Compos Struct, 93, 153-161, 2010.
- [37] Gürses, M., Akgöz, B., Civalek, O., Mathematical modeling of vibration problem of nano-sized annular sector plates using the nonlocal continuum theory via eight-node discrete singular convolution transformation. Appl Math Comput, 219, 3226–3240, 2012.
- [38] Civalek, O., Mercan, K., Demir, C., Vibration analysis of FG cylindrical shells with power-law index using discrete singular convolution technique. Curved and Layer Struct, 3, 82-90, 2016.
- [39] Tong, L., Free vibration of laminated conical shells including transverse shear deformation. Int J Solids Struct, 31, 443–456, 1994.
- [40] Wang, Q., Shi, D., Liang, Q., Shi, X., A unified solution for vibration analysis of functionally graded circular, annular and sector plates with general boundary conditions. Compos Part B, 88, 264-294, 2016.
- [41] Mercan, K., Civalek, O., Buckling analysis of silicon carbide nanotubes (SiCNTs). International Journal of Engineering & Applied Sciences, 8 (2), 101-108, 2016.
- [42] Civalek, O., Çatal, H.H., Plakların diferansiyel quadrature metodu ile stabilite ve titreşim analizi. Teknik Dergi, 14 (1), 2835-2852, 2003.
- [43] Civalek, O., Diferansiyel quadrature metodu ile elastik çubukların statik dinamik ve burkulma analizi, XVI Mühendislik Teknik Kongresi, ODTU, Ankara, Kasım 2001.
- [44] Civalek, O., Numerical solutions to the free vibration problem of Mindlin sector plates using the discrete singular convolution method. International Journal of Structural Stability and Dynamics, 9 (2), 267-284, 2009.