**Prof. J. N. Reddy**

Texas A & M University

**"Anaysis of Shear Deformation in Plate Structures"**

**Abstract:**

The seminar will consist of two distinct topics. The first one is concerned with relationships between the solutions of shear deformation plate theories and the classical plate theory. The second one deals with a multiple model approach for the local-global analysis of laminated composite structures.
Equations governing shear deformation plate theories are typically more complicated than those of the classical theory. Hence, it is desirable to have exact relationships between solutions of the classical plate theory and shear deformation plate theories so that whenever solutions using the classical theory are available, the corresponding solutions of shear deformation theories can be readily obtained. Such relationships not only furnish benchmark solutions of shear deformation theories but also provide insight into the significance of shear deformation on the response. The lecture will present the basic ideas behind the development of the relationships for bending (deflections, forces, and moments), frequencies of natural vibration, and buckling loads.
A hierarchical, 2-D, displacement-based, global-local finite element model is developed to permit an accurate, efficient analysis of localized 3-D effects in laminated composite plates. The model is developed using hierarchical, multiple assumed displacement fields at two different levels: (1) at the element level, and (2) at the mesh level. By superimposing a hierarchy of assumed displacement fields within the same finite element domain, a new variable kinematic finite element (VKFE) is developed. The displacement field hierarchy contains both a conventional 2-D plate expansion and a full layerwise expansion. Since the resulting model is hierarchic, these different element types can easily be connected together in the same computational domain to permit simultaneous multiple model analysis. The resulting model is used to analyze a number of laminated composite plate problems that contain localized subregions where significant 3-D stress fields exist (e.g., free edge effects).

#### Friday, March 2, 2001

3:00 PM in 127 Jabara Hall

Please join us for refreshments before the lecture at 2:30p.m. in room 353 Jabara Hall.

[ Spring 2001]