ON THE SO-CALLED VARIATIONAL CONSISTENCY OF PLATE MODELS, I. INDEFINITE PLATES: EVALUATION OF DISPERSIVE BEHAVIOUR
✍ Scribed by P. Muller; M. Touratier
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 571 KB
- Volume
- 188
- Category
- Article
- ISSN
- 0022-460X
No coin nor oath required. For personal study only.
✦ Synopsis
Four groups of refined shear-deformation plate theories are examined, including the so-called variationally inconsistent theories of Schmidt-Levinson and Touratier-whose ''inconsistence'' is in fact weak. After a unified presentation of these two-dimensional theories, all are deduced from the three-dimensional theory of elasticity through a suitable variational procedure which disconnects the choice of the so-called virtual motions from the choice of an approximation for the small displacement field. This procedure makes obvious in a natural way the importance of the stress boundary conditions on the faces of the plate for any two-dimensional theory. As a test of comparison, a wave dispersion evaluation of these theories is performed for the propagation of flexural waves in an indefinite plate. A detailed comparison leads to the conclusion that the inconsistent theories may offer some advantages in the domain of short waves.