Structural Engineering and Mechanics

  • 제10권4호
  • /
  • Pages.337-357
  • /
  • 2000
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Analytical solutions using a higher order refined theory for the stability analysis of laminated composite and sandwich plates

  • Kant, T. (Department of civil Engineering, Indian Institute of Technology Bombay) ;
  • Swaminathan, K. (Department of civil Engineering, Indian Institute of Technology Bombay)
  • 발행 : 2000.10.25
⟨ 이전 논문 다음 논문 ⟩

초록

Analytical formulations and solutions for the first time, to the stability analysis of a simply supported composite and sandwich plates based on a higher order refined theory, developed by the first author and already reported in the literature are presented. The theoretical model presented herein incorporates laminate deformations which account for the effects of transverse shear deformation, transverse normal strain/stress and a nonlinear variation of inplane displacements with respect to the thickness coordinate - thus modelling the warping of transverse cross sections more accurately and eliminating the need for shear correction coefficients. The equations of equilibrium are obtained using the Principle of Minimum Potential Energy (PMPE). The comparison of the results using this higher order refined theory with the available elasticity solutions and the results computed independently using the first order and the other higher order theories developed by other investigators and available in the literature shows that this refined theory predicts the critical buckling load more accurately than all other theories considered in this paper. New results for sandwich laminates are also presented which may serve as a benchmark for future investigations.

키워드

참고문헌

  1. Hildebrand, F.B., Reissner, E. and Thomas, G.B. (1949), "Note on the foundations of the theory of small displacements of orthotropic shells," NACA TN-1833.
  2. Kant, T. (1982), "Numerical analysis of thick plates", Computer Methods in Applied Mechanics and Engineering, 31, 1-18. https://doi.org/10.1016/0045-7825(82)90043-3
  3. Kant, T. and Manjunatha, B.S. (1988), "An unsymmetric FRC laminate $C^0$ finite element model with 12 degrees of freedom per node", Engineering Computation, 5(3), 300-308. https://doi.org/10.1108/eb023749
  4. Kant, T and Patil, H.S. (1991), "Buckling loads of sandwich columns with a higher order theory", Journal of Reinforced Plastics and Composites, 10, 102-129. https://doi.org/10.1177/073168449101000107
  5. Kant, T and Manjunatha, B. S. (1994), "On accurate estimation of transeverse stresses in multilayer laminates", Computers and Structures, 50(3), 351-365. https://doi.org/10.1016/0045-7949(94)90005-1
  6. Kant, T., Owen, D.R.J. and Zienkiewicz, O.C. (1982), "A refined higher order $C^0$ plate bending element", Computers and Structures, 15, 177-183. https://doi.org/10.1016/0045-7949(82)90065-7
  7. Levinson, M. (1980), "An accurate simple theory of the statics and dynamics of elastic plates", Mechanics Research Communications, 7, 343. https://doi.org/10.1016/0093-6413(80)90049-X
  8. Librescu, L. (1975), Elastostatics and Kinematics of Anisotropic and Heterogeneous Shell-Type Structures, Noordhoff, The Netherlands.
  9. Lo, K.H., Christensen, R.M. and Wu, E.M. (1977a), "A higher order theory of plate deformation. Part 1: Homogeneous plates", ASME Journal of Applied Mechanics, 44(4), 663-668. https://doi.org/10.1115/1.3424154
  10. Lo, K.H., Christensen, R.M. and Wu, E.M. (1977b), "A higher order theory of plate deformation. Part 2: Laminated plates", ASME Journal of Applied Mechanics, 44(4), 669-676. https://doi.org/10.1115/1.3424155
  11. Manjunatha, B.S. and Kant, T. (1992), "A comparison of 9 and 16 node quadrilateral elements based on higher order laminate theories for estimation of transeverse stresses", Journal of Reinforced Plastics and Composites, 11(9), 968-1002. https://doi.org/10.1177/073168449201100902
  12. Mindlin, R.D. (1951), "Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates", ASME Journal of Applied Mechanics, 18, 31-38.
  13. Murthy, M.V.V. (1981), "An improved transverse shear deformation theory for laminated anisotropic plates", NASA Technical Paper, No. 1903.
  14. Nelson, R.B. and Lorch, D.R. (1974), "A refined theory for laminated orthotropic plates", ASME Journal of Applied Mechanics, 41, 177-183. https://doi.org/10.1115/1.3423219
  15. Noor, A.K. and Burton, W.S. (1989) "Assesment of shear deformation theories for multilayered composite plates", Applied Mechanics Reviews, 42, 1-13. https://doi.org/10.1115/1.3152418
  16. Noor, A.K. (1975), "Stability of multilayered composite plates", Fibre Science and Technulugy, 8(2), 81-89. https://doi.org/10.1016/0015-0568(75)90005-6
  17. Pandya, B.N. and Kant, T. (1987), "A consistent refined theory for flexure of a symmetric laminate", Mechanics Research Communications, 14, 107-113. https://doi.org/10.1016/0093-6413(87)90026-7
  18. Pandya, B.N. and Kant, T. (1988a), "Higher order shear deformable theories for flexure of sandwich plates finite element evaluations", International Journal of Solids and Structures, 24(12), 1267-1286. https://doi.org/10.1016/0020-7683(88)90090-X
  19. Pandya, B.N. and Kant, T. (1988b), "Flexure analysis of laminated composites using refined higher order $C^0$ plate bending elements", Cumputer Methods in Applied Mechanics and Engineering, 66, 173-198. https://doi.org/10.1016/0045-7825(88)90075-8
  20. Pandya, B.N. and Kant, T. (1988c), "A refined higher order generally orthotropic $C^0$ plate bending element", Computers and Structures, 28, 119-133. https://doi.org/10.1016/0045-7949(88)90031-4
  21. Pandya, B.N. and Kant, T. (1988d), "Finite element stress analysis of laminated composite plates using higher order displacement model", Composite Science and Technology, 32, 137-155. https://doi.org/10.1016/0266-3538(88)90003-6
  22. Qatu, M.S. and Leissa, A.W. (1993), "Buckling or transverse deflection of unsymmetrically laminated plates subjected to in-plane loads", AIAA Journal, 31(1), 189-194. https://doi.org/10.2514/3.11336
  23. Reddy, J.N. (1984a), "A simple higher order theory for laminated composite plates", ASME Journal of Applied Mechanics, 51, 745-752. https://doi.org/10.1115/1.3167719
  24. Reddy, J.N. (1984b), Energy and Variational Methods in Applied Mechanics, John Wiley and Sons, New York, USA.
  25. Reddy, J.N. (1996), Mechanics of Laminated Composite Plates, Theory and Analysis, CRC Press, Inc., Boca Raton, Florida, USA.
  26. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", ASME Journal of Applied Mechanics, 12(2), 69-77.
  27. Reissner, E. and Stavsky, Y. (1961), "Bending and stretching of certain types of heterogeneous aerotropic elastic plates", ASME Journal of Applied Mechanics, 28, 402. https://doi.org/10.1115/1.3641719
  28. Senthilnathan, N.R., Lim, K.H., Lee, K.H. and Chow, S.T. (1987), "Buckling of shear deformable plates", AIAA Journal, 25(9), 1268-1271. https://doi.org/10.2514/3.48742
  29. Szilard, R. (1974), Theory and Analysis of Plates (Classical and Numerical Methods), Prentice-Hall Inc, Engle Wood Cliffs, New Jersy.
  30. Timoshenko, S. P. and Woinowsky-Krieger, S. (1959), Theory of Plates and Shells, McGraw -Hill, New York.
  31. Whitney, J.M. and Pagano, N.J. (1970), "Shear deformation in heterogeneous anisotropic plates", ASMEJournal of Applied Mechanics, 37, 1031-1036. https://doi.org/10.1115/1.3408654

피인용 문헌

  1. Free vibration analysis of nanocomposite sandwich plates reinforced with CNT aggregates 2017, https://doi.org/10.1002/zamm.201600209
  2. A solid-shell layerwise finite element for non-linear geometric and material analysis vol.92, pp.6, 2010, https://doi.org/10.1016/j.compstruct.2009.10.032
  3. Dynamic response of composite sandwich plates subjected to initial stresses vol.37, pp.8, 2006, https://doi.org/10.1016/j.compositesa.2005.05.034
  4. A novel two-dimensional finite element to study the instability phenomena of sandwich plates vol.283, 2015, https://doi.org/10.1016/j.cma.2014.08.006
  5. Assumed Strain Finite Elements for Buckling and Vibration Analysis of Initially Stressed Damped Composite Sandwich Plates vol.7, pp.4, 2005, https://doi.org/10.1177/1099636205050084
  6. Analytical solutions using a higher order refined computational model with 12 degrees of freedom for the free vibration analysis of antisymmetric angle-ply plates vol.82, pp.2, 2008, https://doi.org/10.1016/j.compstruct.2007.01.001
  7. Thermomechanical buckling of laminated composite and sandwich plates using global–local higher order theory vol.49, pp.6, 2007, https://doi.org/10.1016/j.ijmecsci.2006.10.006
  8. Postbuckling and postbuckled vibration analysis of sandwich plates under non-uniform mechanical edge loadings vol.115-116, 2016, https://doi.org/10.1016/j.ijmecsci.2016.06.025
  9. Effects of higher-order global–local shear deformations on bending, vibration and buckling of multilayered plates vol.82, pp.2, 2008, https://doi.org/10.1016/j.compstruct.2007.01.017
  10. A higher order finite element theory for buckling and vibration analysis of initially stressed composite sandwich plates vol.286, pp.4-5, 2005, https://doi.org/10.1016/j.jsv.2004.10.055
  11. Assessment of inverse trigonometric zigzag theory for stability analysis of laminated composite and sandwich plates vol.101-102, 2015, https://doi.org/10.1016/j.ijmecsci.2015.07.023
  12. A generalized high-order global–local plate theory for nonlinear bending and buckling analyses of imperfect sandwich plates subjected to thermo-mechanical loads vol.92, pp.1, 2010, https://doi.org/10.1016/j.compstruct.2009.07.007
  13. Buckling and postbuckling response of sandwich panels under non-uniform mechanical edge loadings vol.60, 2014, https://doi.org/10.1016/j.compositesb.2013.12.072
  14. Buckling of soft-core sandwich plates with angle-ply face sheets by means of a C0 finite element formulation vol.84, pp.8, 2014, https://doi.org/10.1007/s00419-014-0876-4
  15. Analytical solutions using a higher-order refined theory for the static analysis of antisymmetric angle-ply composite and sandwich plates vol.64, pp.3-4, 2004, https://doi.org/10.1016/j.compstruct.2003.09.042
  16. Higher Order Refined Computational Models for the Free Vibration Analysis of Antisymmetric Angle Ply Plates vol.27, pp.5, 2008, https://doi.org/10.1177/0731684407084125
  17. On the accuracy of recent global–local theories for bending and vibration of laminated plates vol.95, 2013, https://doi.org/10.1016/j.compstruct.2012.06.018
  18. Thermomechanical Buckling of Laminated Composite Plates Using Mixed, Higher-Order Analytical Formulation vol.69, pp.6, 2002, https://doi.org/10.1115/1.1490372
  19. Bending of sandwich plates with anti-symmetric angle-ply face sheets – Analytical evaluation of higher order refined computational models vol.75, pp.1-4, 2006, https://doi.org/10.1016/j.compstruct.2006.04.007
  20. On the elastic stability of simply supported anisotropic sandwich panels vol.80, pp.4, 2007, https://doi.org/10.1016/j.compstruct.2006.07.008
  21. Isogeometric finite element analysis of composite sandwich plates using a higher order shear deformation theory vol.55, 2013, https://doi.org/10.1016/j.compositesb.2013.06.044
  22. A New, Efficient 8-Node Serendipity Element with Explicit and Assumed Strains Formulations vol.6, pp.4, 2005, https://doi.org/10.1080/155022891009486
  23. Buckling of laminated sandwich plates with soft core based on an improved higher order zigzag theory vol.46, pp.11, 2008, https://doi.org/10.1016/j.tws.2008.03.002
  24. Buckling of Sandwich Plates with Random Material Properties Using Improved Plate Model vol.47, pp.2, 2009, https://doi.org/10.2514/1.39180
  25. Parametric vibration response of foam-filled sandwich plates under periodic loads vol.48, pp.5, 2012, https://doi.org/10.1007/s11029-012-9297-z
  26. Buckling Analysis of Angle-ply Composite and Sandwich Plates by Combination of Geometric Stiffness Matrix vol.39, pp.6, 2007, https://doi.org/10.1007/s00466-006-0073-6
  27. Static and dynamic analysis of soft core sandwich panels with through-thickness deformation vol.92, pp.2, 2010, https://doi.org/10.1016/j.compstruct.2009.07.015
  28. Buckling analysis of a laminated composite plate with delaminations using the enhanced assumed strain solid shell element vol.26, pp.10, 2012, https://doi.org/10.1007/s12206-012-0829-1
  29. Biaxial wrinkling analysis of composite-faced sandwich plates with soft core using improved high-order theory vol.43, 2014, https://doi.org/10.1016/j.euromechsol.2013.08.002
  30. Higher order refined computational models for the stability analysis of FGM plates – Analytical solutions vol.47, 2014, https://doi.org/10.1016/j.euromechsol.2014.06.003
  31. Buckling analysis of laminated plates by wavelets vol.89, pp.7-8, 2011, https://doi.org/10.1016/j.compstruc.2011.01.007
  32. Stability Analysis of Laminated Soft Core Sandwich Plates Using Higher Order Zig-Zag Plate Theory vol.22, pp.11, 2015, https://doi.org/10.1080/15376494.2013.874061
  33. Stability of sandwich plates by mixed, higher-order analytical formulation vol.40, pp.17, 2003, https://doi.org/10.1016/S0020-7683(03)00283-X
  34. A Novel Higher-Order Shear and Normal Deformable Plate Theory for the Static, Free Vibration and Buckling Analysis of Functionally Graded Plates vol.2017, 2017, https://doi.org/10.1155/2017/6879508
  35. Linear and nonlinear parametric instability behavior of cylindrical sandwich panels subjected to various mechanical edge loadings vol.23, pp.1, 2016, https://doi.org/10.1080/15376494.2014.918222
  36. A high-order theory for the analysis of circular cylindrical composite sandwich shells with transversely compliant core subjected to external loads vol.94, pp.7, 2012, https://doi.org/10.1016/j.compstruct.2012.02.002
  37. Post-buckling of cross-ply laminated rectangular plates containing short random fibers vol.68, pp.3, 2005, https://doi.org/10.1016/j.compstruct.2004.03.018
  38. Higher order refined computational model with 12 degrees of freedom for the stress analysis of antisymmetric angle-ply plates – analytical solutions vol.80, pp.4, 2007, https://doi.org/10.1016/j.compstruct.2006.07.006
  39. An improved in-plane displacement model for the stability analysis of laminated composites with general lamination configurations vol.93, pp.6, 2011, https://doi.org/10.1016/j.compstruct.2011.01.006
  40. Buckling Analysis of Soft-Core Composite Sandwich Plates Using 3D Finite Element Method vol.105-107, pp.1662-7482, 2011, https://doi.org/10.4028/www.scientific.net/AMM.105-107.1768
  41. Exact solution for Free Vibration and Buckling of sandwich S-FGM Plates on Pasternak Elastic Foundation with Various Boundary Conditions pp.1793-6764, 2019, https://doi.org/10.1142/S0219455419500287
  42. Interfacial Strain Energy Continuity Assumption-Based Analysis of an Orthotropic-Skin Sandwich Plate Using a Refined Layer-by-Layer Theory vol.54, pp.3, 2018, https://doi.org/10.1007/s11029-018-9739-3
  43. Analytical solution for bending analysis of soft-core composite sandwich plates using improved high-order theory vol.44, pp.1, 2012, https://doi.org/10.12989/sem.2012.44.1.015
  44. Free vibration and parametric instability of viscoelastic sandwich plates with functionally graded material constraining layer vol.230, pp.8, 2000, https://doi.org/10.1007/s00707-019-02433-8
  45. Thermal buckling analysis of magneto-electro-elastic porous FG beam in thermal environment vol.8, pp.1, 2000, https://doi.org/10.12989/anr.2020.8.1.083
  46. Thermal flexural analysis of anti-symmetric cross-ply laminated plates using a four variable refined theory vol.25, pp.4, 2000, https://doi.org/10.12989/sss.2020.25.4.409