The R-function method used to solve nonlinear bending problems for orthotropic shallow shells on an elastic foundation

The paper proposes a method to solve geometrically nonlinear bending problems for thin orthotropic shallow shells and plates interacting with a Winkler–Pasternak foundation under transverse loading. This method is based on Ritz’s variational method and the R-function method. The developed algorithm...

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Bibliographic Details
Published in:International applied mechanics 2010-11, Vol.46 (6), p.660-668
Main Authors: Kurpa, L. V., Lyubitskaya, E. I., Morachkovskaya, I. O.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Bending
Classical Mechanics
Foundations
Load distribution (forces)
Nonlinearity
Orthotropic shells
Physics
Physics and Astronomy
Shallow shells
Shells
Variational methods
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Summary:The paper proposes a method to solve geometrically nonlinear bending problems for thin orthotropic shallow shells and plates interacting with a Winkler–Pasternak foundation under transverse loading. This method is based on Ritz’s variational method and the R-function method. The developed algorithm and software are used to solve a number of test problems and to study complex-shaped shells. The effect of the shape of shells, the boundary conditions, the stiffness of the foundation, and the load distribution on the behavior of isotropic and orthotropic shells undergoing geometrically nonlinear bending is studied
ISSN:1063-7095
1573-8582
DOI:10.1007/s10778-010-0353-x