On the Bifurcation of the Thermo-Elastic Deformation of an Asymmetric Plate (Preprint)
Abstract
The deformation of a thin flat elastic plate typically exhibits classic elastic bifurcation behavior when subjected to a through-thickness-graded thermal, or other inelastic, strain. For small strain there is a unique solution to the governing equations, while for larger strain multiple equilibrium solutions exist. Physically, the plate will initially deform to a particular shape or mode and when a critical strain is reached the mode of deformation will snap to a secondary form. This problem has been examined numerous times in the literature. However, in the special case of square symmetry, in both plate shape and materials properties, additional equilibrium deformation modes become available which are not predicted by the existing calculations. In this paper, analytic solutions are presented for these additional bifurcation modes, and the stability of these solutions was evaluated numerically. It is shown that for certain plate materials and geometry the special-case modes occur at a significantly lower strain than predicted by existing analyses. The predictions are verified by comparison with a finite element simulation.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 2007
- Accession Number
- ADA469285
Entities
People
- George Jefferson
- Triplicane A. Parthasarathy
Organizations
- Universal Energy Systems