DOI QR코드

DOI QR Code

Analytical solutions for skewed thick plates subjected to transverse loading

  • Chun, Pang-Jo (Department of Civil and Environmental Engineering, Ehime University) ;
  • Fu, Gongkang (Department of Civil and Environmental Engineering, Wayne State University) ;
  • Lim, Yun Mook (Department of Civil and Environmental Engineering, Yonsei University)
  • 투고 : 2010.10.10
  • 심사 : 2011.01.08
  • 발행 : 2011.06.10

초록

This paper presents analytical solutions for skewed thick plates under transverse loading that have previously been unreported in the literature. The thick plate solution is obtained in a framework of an oblique coordinate system. The governing equation is first derived in the oblique coordinate system, and the solution is obtained using deflection and rotation as partial derivatives of a potential function developed in this research. The solution technique is applied to three illustrative application examples, and the results are compared with numerical solutions in the literature and those derived from the commercial finite element analysis package ANSYS 11. These results are in excellent agreement. The present solution may also be used to model skewed structures such as skewed bridges, to facilitate efficient routine design or evaluation analyses, and to form special elements for finite element analysis. At the same time, the analytical solution developed in this research could be used to develop methods to address post-buckling and dynamic problems.

키워드

참고문헌

  1. Argyris, J.H. (1965), "Continua and discontinua", Proceedings of Conference on Matrix Methods in Structural Mechanics, Wright-Pat-terson Air Force Base, Ohio.
  2. Butalia, T.S., Kant, T. and Dixit, V.D. (1990), "Performance of heterosis element for bending of skew rhombic plates", Comput. Struct., 34(1), 23-49. https://doi.org/10.1016/0045-7949(90)90298-G
  3. Carstensen, C., Xie, X., Yu, G. and Zhou, T. (2010), "A priori and a posteriori analysis for a locking-free low order quadrilateral hybrid finite element for Reissner-Mindlin plates", Comput. Meth. Appl. Mech. Eng., 200(9-12), 1161-1175.
  4. Cheung, Y.K. and Tham, L.G. (1998), Finite Strip Method, CRC Press, Boca Raton.
  5. Civalek, O. (2009), "A four-node discrete singular convolution for geometric transformation and its application to numerical solution of vibration problem of arbitrary straight-sided quadrilateral plates", Appl. Math. Model., 33(1), 300-314. https://doi.org/10.1016/j.apm.2007.11.003
  6. Dawe, D.J. (1966), "Parallelogrammic elements in the solution of rhombic cantilever plate problems", J. Strain Anal. Eng. Des., 1(3), 223-230. https://doi.org/10.1243/03093247V013223
  7. De Veubeke, B.F. and Sander, G. (1967), "An equilibrium model for plate bending", Int. J. Solids Struct., 4(4), 447-468.
  8. Gangarao, H.V.S. and Chaudhary, V.K. (1998), "Analysis of skew and triangular plates in bending", Comput. Struct., 28(2), 223-235.
  9. Garcea, G., Madeo, A., Zagari, G. and Casciaro, R. (2009), "Asymptotic post-buckling FEM analysis using corotational formulation", Int. J. Solids Struct., 46(2), 377-397. https://doi.org/10.1016/j.ijsolstr.2008.08.038
  10. Gurses, M., Civalek, O., Korkmaz, A.K. and Ersoy, H. (2009), "Free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on first-order shear deformation theory", Int. J. Numer. Meth. Eng., 79(3), 290-313. https://doi.org/10.1002/nme.2553
  11. Hangai, Y. (1995), Fundamental Theory of Plates, Shokokusha, Tokyo. (in Japanese)
  12. Hencky, H. (1947), "Dber die Berficksichtigung der Schubverzerrungen in ebenen Platten", Ingenieur-Archiv, 16, 72-76 https://doi.org/10.1007/BF00534518
  13. Jirousek, J. (1987), "Hybrid-Trefftz plate bending elements with p-method capabilities", Int. J. Numer. Meth. Eng., 24, 1367-1393. https://doi.org/10.1002/nme.1620240712
  14. Liao, H.W. and Huang, H.Y. (2008), "Buckling and postbuckling analyses of a skew plate", J. Mech., 24(4), 347-355. https://doi.org/10.1017/S1727719100002471
  15. Liew, K.M. and Han, J.B. (1997), "Bending analysis of simply supported shear deformable skew plates", J. Eng. Mech., 123(3), 214-221. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:3(214)
  16. Liew, K.M., Huang, Y.Q. and Reddy, J.N. (2003), "Vibration analysis of symmetrically laminated plates based on FSDT using the moving least squares differential quadrature method", Comput. Meth. Appl. Mech. Eng., 192(19), 2203-2222. https://doi.org/10.1016/S0045-7825(03)00238-X
  17. Liu, G.R., Nguyen-Thoi, T. and Lam, K.Y. (2008), "An edge-based smoothed finite element method (ES-FEM) for static and dynamic problems of solid mechanics", J. Sound Vib., 320, 1100-1130.
  18. Malekzadeh, P. and Karami, G. (2005), "Polynomial and harmonic differential quadrature methods for free vibration of variable thickness thick skew plates", Eng. Struct., 27(10), 1563-1574. https://doi.org/10.1016/j.engstruct.2005.03.017
  19. Malekzadeh, P. (2008), "Differential quadrature large amplitude free vibration analysis of laminated skew plates based on FSDT", Compos. Struct., 83(2), 189-200. https://doi.org/10.1016/j.compstruct.2007.04.007
  20. Mindlin, R.D. (1951), "Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates", J. Appl. Mech., 18(1), 31-38.
  21. Ming, P.G. and Song, L.F. (1987), "A new element used in the non-orthogonal boundary plate bending theory - an arbitrary quadrilateral element", Int. J. Numer. Meth. Eng., 24, 1031-1042. https://doi.org/10.1002/nme.1620240602
  22. Mizusawa, T. and Kondo, Y. (2001), "Application of the spline element method to analyze vibration of skew Mindlin plates with varying thickness in one direction", J. Sound Vib., 241(3), 485-501. https://doi.org/10.1006/jsvi.2000.3303
  23. Mizusawa, T., Wada, H. and Nagino, H. (2007), "Free vibration analysis of skew Mindlin plates by the BFspline Ritz method", JSCE J. Appl. Mech., 10, 109-119. (in Japanese) https://doi.org/10.2208/journalam.10.109
  24. Monforton, G.R. and Schmit, L.A. (1968), "Finite element analysis of skew plates in bending (Skew parallelogram plates bending analyzed by finite element method, discussing stiffness and mass matrices application)", AIAA J., 6, 1150-1152. https://doi.org/10.2514/3.4688
  25. Morley, L.S.D. (1962), "Bending of a simply supported rhombic plate under uniform normal loading", The Quarterly Journal of Mechanics and Applied Mathematics, 15(4), 413-426. https://doi.org/10.1093/qjmam/15.4.413
  26. Morley, L.S.D. (1963), Skew Plates and Structures, Pergamon Press, New York.
  27. Muhammad, T. and Singh, A.V. (2004), "A p-type solution for the bending of rectangular, circular, elliptic and skew plates", Int. J. Solids Struct., 41(15), 3977-3997. https://doi.org/10.1016/j.ijsolstr.2004.02.047
  28. Nguyen-Xuan, H., Rabczuk, T., Bordas, S. and Debongnie, J.F. (2008), "A smoothed finite element method for plate analysis", Comput. Meth. Appl. Mech. Eng., 197(13-16), 1184-1203. https://doi.org/10.1016/j.cma.2007.10.008
  29. Nguyen-Xuan, H., Liu, G.R., Thai-Hoang, C. and Nguyen-Thoi, T. (2010), "An edge-based smoothed finite element method (ES-FEM) with stabilized discrete shear gap technique for analysis of Reissner-Mindlin plates", Comput. Meth. Appl. Mech. Eng., 199(9-12), 471-489. https://doi.org/10.1016/j.cma.2009.09.001
  30. Ramadoss, P. and Nagamani, K. (2009), "Behavior of high-strength fiber reinforced concrete plates under inplane and transverse loads", Struct. Eng. Mech., 31(4), 371-382. https://doi.org/10.12989/sem.2009.31.4.371
  31. Ramesh, S.S., Wang, C.M., Reddy, J.N. and Ang, K.K. (2008), "Computation of stress resultants in plate bending problems using higher-order triangular elements", Eng. Struct., 30, 2687-2706. https://doi.org/10.1016/j.engstruct.2008.03.003
  32. Ramesh, S.S., Wang, C.M., Reddy, J.N. and Ang, K.K. (2009), "A higher-order plate element for accurate prediction of interlaminar stresses in laminated composite plates", Compos. Struct., 91(3), 337-357. https://doi.org/10.1016/j.compstruct.2009.06.001
  33. Razaqpur, A.G., Nofal, M. and Vasilescu, A. (2003), "An improved quadrilateral finite element for analysis of thin plates", Finite Elem. Analy. Des., 40(1), 1-23. https://doi.org/10.1016/S0168-874X(02)00165-8
  34. Reddy, J.N. (2007), Theory and Analysis of Elastic Plates and Shells, CRC Press, Taylor & Francis.
  35. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", J. Appl. Mech., 12, A69-A77.
  36. Sengupta, D. (1991), "Stress analysis of flat plates with shear using explicit stiffness matrix", Int. J. Numer. Meth. Eng., 32, 1389-1409. https://doi.org/10.1002/nme.1620320703
  37. Sengupta, D. (1995), "Performance study of a simple finite element in the analysis of skew rhombic plates", Comput. Struct., 54(6), 1173-1182. https://doi.org/10.1016/0045-7949(94)00405-R
  38. Szilard, R. (2004), Theories and Applications of Plate Analysis, John Wiley & Sons, Inc., Hoboken, New Jersey.
  39. Tham, L.G., Li, W.Y., Cheung, Y.K. and Chen, M.J. (1986), "Bending of skew plates by spline-finite-strip method", Comput. Struct., 22(1), 31-38. https://doi.org/10.1016/0045-7949(86)90082-9
  40. Timoshenko, S.P. and Woinowsky-Krieger, S. (1959), Theory of Plates and Shells (2nd edition), Engineering Societies Monographs, McGraw-Hill, New York.
  41. Wang, G. and Hsu, C.T.T. (1994), "Static and dynamic analysis of arbitrary quadrilateral flexural plates by B3-spline functions", Int. J. Solids Struct., 31(5), 657-667. https://doi.org/10.1016/0020-7683(94)90144-9

피인용 문헌

  1. Analytical Behavior Prediction for Skewed Thick Plates on Elastic Foundation vol.2011, 2011, https://doi.org/10.1155/2011/509724
  2. First-Ply Failure Behavior of Laminated Composite Skew Plates of Various Edge Conditions vol.57, pp.5, 2011, https://doi.org/10.1007/s11029-021-09989-4