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

^{(*)}

*Corresponding author*

**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 © 2013 Praise Worthy Prize - All rights reserved.*#### Keywords

#### 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)

http://dx.doi.org/10.1007/978-94-007-6365-4

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

http://dx.doi.org/10.1007/978-3-540-71001-1_10

2041.(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

http://dx.doi.org/10.1016/j.compstruct.2011.02.018

619.(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

http://dx.doi.org/10.1137/s1064827597321647

2041.-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

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

619.-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

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

http://dx.doi.org/10.1126/science.134.3487.1358

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.

http://dx.doi.org/10.1016/j.tws.2007.07.012

248.(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

http://dx.doi.org/10.1007/s10665-012-9553-1

248.-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

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

http://dx.doi.org/10.1007/b98970

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

http://dx.doi.org/10.1090/s0002-9947-1965-0210852-x

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

http://dx.doi.org/10.1016/0893-6080(95)00081-x

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

http://dx.doi.org/10.1007/s00365-009-9054-2

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

http://dx.doi.org/10.1093/acprof:oso/9780198506546.001.0001

### Refbacks

- There are currently no refbacks.

Please send any question about this web site to info@praiseworthyprize.com**Copyright © 2005-2023 Praise Worthy Prize**