A 16-node locking-free Mindlin plate resting on two-parameter elastic foundation – static and eigenvalue analysis

• Autorzy: Buczkowski R. , Taczała M. , Kleiber M.
• Języki publikacji: EN

Abstrakty

EN

The Pasternak elastic foundation model is employed to study the statics and natural frequencies of thick plates in the framework of the finite element method. A new 16-node Mindlin plate element of the Lagrange family and a 32-node zero-thickness interface element representing the response of the foundation are used in the analysis. The plate element avoids ill-conditioned behaviour due to its small thickness. In the case of the eigenvalue analysis, the equation of motion is derived by applying the Hamilton principle involving the variation of the kinetic and potential energy of the plate and foundation. Regarding the plate, the firstorder shear deformation theory is used. By employing the Lobatto numerical integration in which the integration points coincide with the element nodes, we obtain the diagonal form of the mass matrix of the plate. In practice, diagonal mass matrices are often employed due to their very attractive timeintegration schemes in explicit dynamic methods in which the inversion of the effective stiffness matrix as a linear combination of the damping and mass matrices is required. The numerical results of our analysis are verified using thin element based on the classical Kirchhoff theory and 16-node thick plate elements.

Słowa kluczowe

EN

Mindlin plate; two-parameter elastic foundation; Lobatto integration; bending analysis; eigenvalue analysis

PL

płyta Mindlina; podstawa elastyczna dwuparametrowa; integracja Lobatto; analiza gięcia; analiza wartości własnych

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Methods in Engineering and Science
• Rocznik: 2015
• Tom: Vol. 22, no. 2
• Strony: 99--114
• Opis fizyczny: Bibliogr. 26 poz., rys., tab.

Twórcy

autor

Buczkowski R.

• Maritime University of Szczecin Division of Computer Methods Pobożnego 11, 70-507 Szczecin, Poland

autor

Taczała M.

• West Pomeranian University of Technology Piastów 41, 71-065 Szczecin, Poland

autor

Kleiber M.

• Institute of Fundamental Technological Research Polish Academy of Sciences Pawińskiego 5B, 02-106 Warszawa, Poland

Bibliografia

• [1] M.H. Omurtag, A. Özütok, A.Y. Aköz. Free vibration analysis of Kirchhoff plates resting on elastic foundation by mixed finite element fomulation based on Gâteaux differential. Int. J. for Numer. Methods in Eng., 40: 295–317, 1997.
• [2] D. Zhou, Y.K. Cheung, S.H. Lo, F.T.K. Au. Three-dimensional vibration analysis of rectangular thick plates on Pasternak foundation. Int. J. for Numer. Methods in Eng., 59: 1313–1334, 2004.
• [3] M. Çelik, A. Saygun. A method for the analysis of plates on a two-parameter foundation. Int. J. of Solids and Struct., 36: 2891–2915, 1999.
• [4] M. Çelik, M. Omurtag. Determination of the Vlasov foundation parameters – quadratic variation of elasticity modulus – using FE analysis. Structural Engineering and Mechanics, 19(6): 619–637, 2005.
• [5] K. Ozgan, A.T. Daloglu. Alternative plate elements for the analysis of thick plates on elastic foundation. Structural Engineering and Mechanics, 26(1): 69–86, 2007.
• [6] K. Ozgan, A.T. Daloglu. Effect of transverse shear strains on plates resting on elastic foundation using modified Vlasov model. Thin-Walled Structures, 46: 1236–1250, 2008.
• [7] R. Buczkowski, W. Torbacki. Finite element modelling of thick plates on two-parameter elastic foundation. International Journal for Numerical and Analytical Methods in Geomechanics, 25(14): 1409–1427, 2001.
• [8] R. Buczkowski, W. Torbacki. Finite element analysis of plates on layered tensionless foundation. Archives of Civil Engineering, 56(3): 255–274, 2010.
• [9] Z. Celep. Rectangular plates resting on tensionless elastic foundation. J. of Eng. Mech. ASCE, 114(12): 2083– 2092, 1988.
• [10] Z. Celep, K. Güler. Axisymmetric forced vibrations of an elastic free circular plate on tensionless two parameter foundation. Journal of Sound and Vibration, 301: 495–509, 2007.
• [11] R.C. Mishra, S.K. Chakrabarti. Rectangular plates resting on tensionless elastic foundation: some new results. Journal of Engineering Mechanics ASCE, 122(4): 385–387, 1996.
• [12] N. Eratll, A.Y. Aköz. The mixed finite element formulation for the thick plates on elastic foundations. Comput. and Struct., 65(4): 515–529, 1997.
• [13] Y. Ozçelikörs, M.H. Omurtag, H. Demir. Analysis of orthotropic plate-foundation interaction by mixed finite element formulation using Gâteaux differential. Comput. and Struct., 62(1): 93–106, 1997.
• [14] H.-S. Shen. Nonlinear bending of Reissner-Mindlin plates with free edges under transverse and in-plane loads and resting on elastic foundations. Int. J. of Mech. Sci., 41: 845–864, 1999.
• [15] Y.T. Feng, D.R.J. Owen. Iterative solution of coupled FE/BE discretizations for plate-foundation interaction problems. Int. J. for Numer. Methods in Eng., 39: 1889–1901, 1996.
• [16] L. Sadecka. A finite/infinite element analysis of thick plate on a layered foundation. Comput. and Struct., 76: 603–610, 2000.
• [17] Ö. Civalek, M.H. Acar. Discrete singular convolution method for the analysis of Mindlin plates on elastic foundations. International Journal of Pressure Vessels and Piping, 84: 527–535, 2007.
• [18] Ö. Civalek, H. Ersoy. Free vibration and bending analysis of circular Mindlin plates using singular convolution method. Commun. Numer. Meth. Engrg., 25: 907–92, 2009.
• [19] H. Akhavan, Sh. Hosseini Hashemi, H. Rokni Damavandi Taher, A. Alibeigloo, Sh.Vahabi. Exact solutions for rectangular Mindlin plates under in-plane loads resting on Pasternak elastic foundation. Part I: Buckling analysis. Computational Materials Science, 44: 968–978, 2009.
• [20] H. Akhavan, Sh. Hosseini Hashemi, H. Rokni Damavandi Taher, A. Alibeigloo, Sh. Vahabi. Exact solutions for rectangular Mindlin plates under in-plane loads resting on Pasternak elastic foundation. Part II: Frequency analysis. Computational Materials Science, 44: 951–961, 2009.
• [21] A.M. Zenkour. Bending of orthotropic plates resting on Pasternak’s foundations using mixed shear deformation theory. Acta Mechanica Sinica, 27(6): 956–962, 2011.
• [22] A.M. Zenkour, M.N.M. Allam, M.O. Shaker, A.F. Radwan. On simple and mixed first-order theories for plates resting on elastic foundations. Acta Mech., 220: 33–46, 2011.
• [23] A.M. Zenkour, M.N.M. Allam, M. Sobhy. Bending of a fiber-reinforced viscoelastic composite plate resting on elastic foundations. Arch. Appl. Mech., 81: 77–96, 2011.
• [24] V.G. Vallabhan, A.T. Daloglu. Consistent FEM-Vlasov model for plates on layered soil. Journal of Structural Engineering ASCE, 125 (1): 108–113, 1999.
• [25] Y.I. Özdemir. Development of a higher order finite element on a Winkler foundation. Finite Elements in Analysis and Design, 48: 1400–1408, 2012.
• [26] H.-Ch. Huang. Static and dynamic analyses of plates and shells, Springer, Berlin, 1989.