Classical plate buckling theory as the small-thickness limit of three-dimensional incremental elasticity
Article first published online: 19 NOV 2012
Copyright © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
Special Issue: Refined theories of plates and shells
Volume 94, Issue 1-2, pages 7–20, January 2014
How to Cite
Steigmann, D.J. and Ogden, R.W. (2014), Classical plate buckling theory as the small-thickness limit of three-dimensional incremental elasticity. Z. angew. Math. Mech., 94: 7–20. doi: 10.1002/zamm.201200160
- Issue published online: 7 JAN 2014
- Article first published online: 19 NOV 2012
- Manuscript Accepted: 20 OCT 2012
- Manuscript Received: 21 AUG 2012
- Plate buckling;
- incremental elasticity;
- elastic stability.
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.