A Novel Approach to Solve Nonlinear Boundary Problems of Multilayered Thin-Walled Shell Theory


(*) Corresponding author


Authors' affiliations


DOI's assignment:
the author of the article can submit here a request for assignment of a DOI number to this resource!
Cost of the service: euros 10,00 (for a DOI)

Abstract


The paper presents a novel approach to solve nonlinear boundary problems for partial differential equations and its application nonlinear boundary problems of multilayered thin-walled shell theory. The approach based on Kolmogorov’s superposition allows reduction to a series of single-dimensional boundary value problems for delayed differential equations. The last ones are solved numerically with employment of Newton-Raphson method.
Copyright © 2019 Praise Worthy Prize - All rights reserved.

Keywords


Numerical Method for Nonlinear Boundary Problem; Kolmogorov’s Superposition; Delayed Differential Equations; Multilayered Cylindrical Shell; Newton-Raphson Method

Full Text:

PDF


References


N. I. Obodan, O. G. Lebedyev, V. A. Gromov, Nonlinear Behaviour and Stability of Thin-walled Shells (Springer, 2013). (in press)

P. Wriggers, Nonlinear Finite Elements Method (Springer, 2008).

K. M. Liew, X. Zhao, A. J. M. Ferreira, A review of meshless methods for laminated and functionally graded plates and shells, Composite Structures, vol. 93, n. 8, July 2011, pp. 2031-2041.

S. S. Haykin, Neural Networks and Learning Machines (Prentice Hall, 2009).

G. J. Lord, A. R. Champneys, G. W. Hunt, Computation of homoclinic orbits in partial differential equations: An application to cylindrical shell buckling, SIAM J Sci Comp, vol. 21, n 2, 1999, pp. 591-619.

L. V. Kantorovich, V. I. Krylov, Approximate Methods of Higher Analysis (Interscience, 1958).

A. D. Kerr, An extension of the Kantorovich methods, Q Appl Math, vol. 26, 1968, pp. 21–29.

M. M. Aghdam, M. Mohammadi, V. Erfanian, Bending analysis of thin annular sector plates using extended Kantorovich method, Thin-Walled Structures, vol. 45, n 12, December 2007, pp. 983–990.

N. I. Obodan, V. A. Gromov, Nonlinear behavior and buckling of cylindrical shells subjected to localized external pressure, J of Engrg Math, vol. 78, n 1, February 2013, pp. 239-248.

I. I. Vorovich Nonlinear Theory of Shallow Shells (Springer, 1999).

D. A. Sprecher, On the structure of continuous functions of several variables, Trans Am Math Society, vol. 115, n 3, 1965, pp. 340-355.

D. A. Sprecher, A numerical implementation of Kolmogorov’s superpositions, Neural Networks, vol. 9, n 5, July 1996, pp. 765-772.

J. Braun, M. Griebel, On a constructive proof of Kolmogorov’s superposition theorem, Constructive approximation, vol. 30, n 3, December 2009, pp. 653-675.

A. Bellen, M. Zennaro Numerical Methods for Delay Differential Equations (Oxford University Press, 2003).


Refbacks

  • There are currently no refbacks.


Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2024 Praise Worthy Prize