Exact bending solutions of axisymmetric reissner plates in terms of classical thin plate solutions

Abstract

This paper presents exact bending solutions of circular and annular plates under rotationally symmetric loads based on the Reissner plate theory. The exact Reissner plate solutions are cast in the form of a general set of relationships linking the Reissner plate quantities to their corresponding Kirchhoff (classical thin) plate counterparts. The Reissner plate solutions may be readily deduced upon supplying the classical thin plate solutions that are well documented in the open literature. This form of displaying exact solutions is very compact and does away with the conventional need for numerous tables and charts in presenting the results of axisymmetric thick plates. Some illustrative examples in determining the Reissner plate solutions using the relationships are given. These example problems involve circular and annular plates under different loading and support conditions. In order to verify the correctness of the relationships, the results are compared with numerically obtained Reissner plate results and also with Mindlin plate results.