Classical plate buckling theory as the small-thickness limit of three-dimensional incremental elasticity

@inproceedings{Steigmann2013ClassicalPB,
  title={Classical plate buckling theory as the small-thickness limit of three-dimensional incremental elasticity},
  author={David J. Steigmann and Ray W. Ogden},
  year={2013}
}
Classical plate buckling theory is obtained systematically as the small-thickness limit of the three-dimensional linear theory of incremental elasticity with null incremental data. Various a priori assumptions associated with classical treatments of plate buckling, including the Kirchhoff–Love hypothesis, are here derived rather than imposed, and the conditions under which they emerge are stated precisely. 

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References

Publications referenced by this paper.
Showing 1-10 of 16 references

Non-linear elastic deformations of multi-phase fluid systems

2005 International Conference on MEMS,NANO and Smart Systems • 2005
View 5 Excerpts
Highly Influenced

On uniqueness and stability in the theory of finite elastic strain

R. Hill
J. Mech. Phys. Solids • 1957
View 4 Excerpts
Highly Influenced

Koiter’s Elastic Stability of Solids and Structures

A.M.A. van der Heijden, W.T
2009
View 6 Excerpts
Highly Influenced

Two-dimensional models for the combined bending and stretching of plates and shells based on three-dimensional linear elasticity

D. J. Steigmann
Int. J. Eng. Sci • 2008
View 3 Excerpts
Highly Influenced

The Buckling of Plates and Shells

H. L. Cox
1963
View 4 Excerpts
Highly Influenced

Applications of Polyconvexity and Strong Ellipticity to Nonlinear Elasticity and Elastic Plate Theory, in: CISM Course on Applications of Poly-, Quasi-, and Rank-One

D. J. Steigmann
Convexity in Applied Mechanics, • 2010
View 1 Excerpt

Linear theory for the bending and extension of a thin, residually stressed, fiber-reinforced lamina

D. J. Steigmann
Int. J. Eng. Sci • 2009
View 1 Excerpt

Theory of linearly elastic residually stressed plates

R. Paroni
Math. Mech. Solids • 2006
View 1 Excerpt

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