On the dynamical behaviour of plates in unilateral contact with an elastic foundation: a finite element approach.

Luigi Ascione; Domenico Bruno; Renato S. Olivito

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1984)

  • Volume: 76, Issue: 2, page 93-106
  • ISSN: 1120-6330

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Ascione, Luigi, Bruno, Domenico, and Olivito, Renato S.. "On the dynamical behaviour of plates in unilateral contact with an elastic foundation: a finite element approach.." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 76.2 (1984): 93-106. <http://eudml.org/doc/287227>.

@article{Ascione1984,
author = {Ascione, Luigi, Bruno, Domenico, Olivito, Renato S.},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {dynamical problem; elastic plate; unilateral contact; Winkler subgrade; Mindlin's theory; effects of the shear stresses; rotatory inertia; existence; time integration; nonlinear motion equations; Newmark's method; interpolation functions; mesh parameter; time stepsize},
language = {eng},
month = {2},
number = {2},
pages = {93-106},
publisher = {Accademia Nazionale dei Lincei},
title = {On the dynamical behaviour of plates in unilateral contact with an elastic foundation: a finite element approach.},
url = {http://eudml.org/doc/287227},
volume = {76},
year = {1984},
}

TY - JOUR
AU - Ascione, Luigi
AU - Bruno, Domenico
AU - Olivito, Renato S.
TI - On the dynamical behaviour of plates in unilateral contact with an elastic foundation: a finite element approach.
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1984/2//
PB - Accademia Nazionale dei Lincei
VL - 76
IS - 2
SP - 93
EP - 106
LA - eng
KW - dynamical problem; elastic plate; unilateral contact; Winkler subgrade; Mindlin's theory; effects of the shear stresses; rotatory inertia; existence; time integration; nonlinear motion equations; Newmark's method; interpolation functions; mesh parameter; time stepsize
UR - http://eudml.org/doc/287227
ER -

References

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  1. FICHERA, G. (1972) - Boundary Value Problems of Elasticity with Unilateral Costraints, in «Encyclopedia of Physics», Vol. VIa/2, Mechanics of Solid II, 391-423, Springer-Verlag. 
  2. DUVAUT, G. and LIONS, J.L. (1972) - Les Inéquations en Mécanique et en Phisique, Dunod, Paris. Zbl0298.73001
  3. GLOWINSKI, R., LIONS, J.L. and TREMOLIÈRES, R. (1976) - Analyse Numérique des Inéquations Variationnelles, Dunod, Paris. Zbl0358.65091
  4. BREZZI, F., HAGER, W.W. and RAVIART, P.A. (1977-78) - Error Estimates for the Finite Element Solution of Variational Inequalities, Part. I and II, «Numer. Math.», 28, 431-443, 31, 1-16. Zbl0369.65030
  5. ODEN, J.T. (1981) - Mixed Finite Element Approximations via Interior and Exterior Penalties for Contact Problems in Elasticity, Int. Symp. on Hybrid and Mixed Finite Element Methods, Georgia Institute of Technology, Atlanta, Georgia, April 8-10. 
  6. WEITSMANN, Y. (1970) - On Foundation that Reacts in Compression Only, «J. Appl. Mech.» 37, 1019-1030. 
  7. TOSCANO, R. and MACERI, A. (1980) - On the Problem of the Elastic Plate on One-side Foundation, «Meccanica», 15 (2), 95-106. Zbl0482.73036
  8. PONAGIOTOPOULOS, P.D. and TALASLIDIS, D. (1980) - A linear Analysis Approach to the Solution of Certain Classes of Viariational Inequality Problems in Structurals Analysis, «Int. J. Sol. Struc.», 16, 991-1005. 
  9. VILLAGGIO, P. (1983) - A Free Boundary Value Problem in Plate Theory, «J. Appl. Mech.» to appear. Zbl0545.73097
  10. ASCIONE, L., GRIMALDI, A. and MACERI, F. (1983) - Modelling and Analysis of Beam on Tensionless Foundations, «Int. J. Modelling and Simulation», 3 (2). 
  11. GLADWELL, Gf.M.L. and IYER, K.R.P. (1974) - Unbonded Contact Between a Circular Plate and an Elastic Half-Space, «J. of Elasticity», 4 (2), 115-130. Zbl0286.73016
  12. ASCIONE, L. and GRIMALDI, A. (1983) - Unilateral Contact Between a Plate and an Elastic Foundation, «Meccanica» to appear. 
  13. ASCIONE, L., OLIVITO, R.S. and SPADEA, G. (1983) - The Unbonded Conctact Problem of a Rectangular Plate Resting on an Elastic Foundation, «Acc. Naz. dei Lincei», 6, Vol. LXXIV, giugno. Zbl0565.73100
  14. PETERSON, H. (1978) - Application of the Finite Element Method in the Analysis of Contact Problems, in «Finite Elements in Nonlinear Mechanics» (Eds. Bergan et al.), TABIR Publishers, 845, 862, Trondheim. 
  15. FREDRIKSSON, B., RYDHOLM, G. and SJÖBLOM, P. (1978) - Variational Inequalities in Structural Mechanics with Emphasis on Contact Problems, in «Finite Elements in Nonlinear Mechanics» (Eds. Bergan et al.), TABIR Publishers, 863-884, Trondheim. Zbl0409.73080
  16. HUGHES, T.J.R., TAYLOR, R.L. and KANOKNUKULCHAI, W. (1977) - A Finite Element Method for Large Displacement Contact and Impact Problems, in «Formulation and Computational Algorithms in Finite Element Analysis» (Eds. Bathe et al.), MIT Press, 468-495, Massachusetts. 
  17. REDDY, J.N. (1983) - An Introduction to the Finite Element Method, McGraw-Hill, New York. 
  18. TALASLIDIS, D. and PANAGIOTOPOULOS, P.D. (1982) - A Linear Finite Element Approach to the Solution of the Variational Inequalities Arising in Contact Problems of Structural Dynamics, «Int. J. Num. Meth. Engng.», vol. 0.00. Zbl0489.73078
  19. MINDLIN, R.D. (1951) - Influence of Rotatory Inertia and Shear on Flexural Motions of Isotropic Elastic Plates, «J. Appl. Mech.», 18, 31-88. Zbl0044.40101
  20. BATHE, K.J. and WILSON, E.L. (1976) - Numerical Methods in Finite Element Analysis, Prentice-Hall, Inc., Englewood Cliffs, New Jersey. 
  21. GRIMALDI, A. and REDDY, J.N. (1982) - On Delamination in Plates: A Unilateral Contact Approach, Virginia Polytechnic Institute and State University, Rep. VPI-E 83.23 Blacksburg, Virginia. 
  22. ASCIONE, L. and OLIVITO, R.S. (1983) - Unbonded Contact of a Rectangular Plate on an Elastic Half-Space, Università della Calabria, Rep. n. 50, April. 

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