Common Mathematical Structure of Various Beam and Plate Theories and Its Use to Finding Solutions

J. N. Reddy
Distinguished Professor and Holder of the Oscar S. Wyatt Chair
Texas A & M University
Department of Mechanical Engineering
College Station, TX   77843-3123
e-mail:  jnreddy@shakti.tamu.edu

Date:  Friday, November 1, 2002
Time:  2:00 p.m.
Place:  W183 Nebraska Hall


Equations governing shear deformation plate theories are typically more complicated than those of the classical theory. However, they share a common mathematical structure. The mathematical structure can be exploited to exact relationships between solutions of the classical (beam) plate theory and shear deformation (beam) plate theories. Thus, 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, and possibly allow the development of so-called locking-free finite elements of the shear deformation theories. The relationships for beams and plates have been developed by the author and his colleagues over the last several years. 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. Numerical results will be presented to illustrate the usefulness of the developed relationships.