Abstract
The Analog Equation Method is applied to large deflection analysis of thin elastic plates. The von-Kármán plate theory is adopted. The deflection and the stress function of the non-linear problem are established by solving two linear uncoupled plate bending problems under the same boundary conditions subjected to “appropriate” (equivalent) fictitious loads. Numerical examples are presented which illustrate the efficiency and the accuracy of the proposed method.
Similar content being viewed by others
References
Atluri, S. N.; Pipkins, D. S. 1991: Large deformation analysis of plates and shells. In: Beskos, D. (ed.): Boundary element analysis of plates and shells, pp. 141–166. Berlin, Springer-Verlag
Chia, C. Y. 1980: Analysis of Plates. New York: McGraw-Hill
Elzein, A.; Syngellakis, S. 1989: High-order elements for the BEM stability analysis of imperfect plates. In: Brebbia, C. A., Connor, J. J. (eds.): Advances in Boundary Elements 3: 269–284. Berlin, Springer-Verlag
Isaacson, E.; Keller, M. B. 1966: Analysis of numerical methods. New York, John Wiley and Sons
Kamiya, N. 1988: Structural non-linear analysis by boundary element methods. In: Brebbia, C. A. (ed.): Boundary Element X, 3: 17–27. Berlin, Springer-Verlag
Kamiya, N.; Sawaki, Y. 1982a: An integral equation approach to finite deflection of elastic plates. Int. J. Non-linear Mechanics 17: 187–194
Kamiya, N.; Sawaki, Y. 1982b: Integral formulation for non-linear bending of plates. ZAMM 62: 651–655
Kamiya, N.; Sawaki, Y.; Nakamura, Y.; Fukui, A. 1982: An approximate finite deflection of a heated elastic plate by the boundary element method. Appl. Math. Model. 6: 23–27
Kamiya, N.; Sawaki, Y.; Nakamura, Y. 1984: Postbuckling analysis by the boundary element method. Engineering Analysis 1: 40–44
Katsikadelis, J. T. 1990: A boundary element solution to the vibration problem of plates. J. Sound Vibr. 141: 313–322
Katsikadelis, J. T. 1994: The analog equation method — A powerful BEM-based solution technique for solving linear and non-linear engineering problems. To appear in the proceedings of Int. Conference BEM-16, Southampton, July 13–15, 1994
Katsikadelis, J. T.; Armenakas, A. E. 1989: A new boundary equation solution to the plate problem. ASME J. Appl. Mech. 56: 364–374
Katsikadelis, J. T.; Nerantzaki, M. S. 1988: Large deflections of thin plates by the boundary element method. In: Brebbia, C. A. (ed.): Boundary Elements X, 3: 435–456. Berlin, Springer-Verlag
Nerantzaki, M. S. 1992: Non-linear analysis of plates by the boundary element method. Ph.D. Dissertation, National Technical University, Athens
Nerantzaki, M. S.; Katsikadelis, J. T. 1988: A Green's function method for large deflection analysis of plates. Acta Mech. 25: 211–225
O'Donoghue, P. E.; Atluri, S. N. 1987: Field/boundary element approach to the large deflection of thin flat plates. Comp. and Struc. 27(3): 427–435
Sawaki, Y.; Tachinchi, K.; Kamiya, N. 1989: Finite deflection analysis of plates by dual reciprocity boundary elements. In: Brebbia, C. A.; Connor, J. T. (eds.): Advances in Boundary Elements 3: 269–284. Berlin, Springer-Verlag
Sladek, J.; Sladek, V. 1983: The BIE analysis of the Berger equation. Ing. Archiv. 53: 385–397
Tanaka, M. 1982: Integral equation approach to small and large displacements of thin elastic plates. In: Brebbia, C. A. (ed.): Boundary element methods in engineering, pp. 526–539. Berlin, Springer-Verlag
{btTanaka, M.} 1984: Large deflection analysis of thin elastic plastes. In: Banerjee, D. K.; Mukherjee, S. (eds.): Developments in Boundary Element Methods 3: 115–136, Elsevier Applied Science Publications
Author information
Authors and Affiliations
Additional information
Communicated by D. E. Beskos, 18 October 1993
Rights and permissions
About this article
Cite this article
Katsikadelis, J.T., Nerantzaki, M.S. Non-linear analysis of plates by the Analog Equation Method. Computational Mechanics 14, 154–164 (1994). https://doi.org/10.1007/BF00350282
Issue Date:
DOI: https://doi.org/10.1007/BF00350282