The problem of bending of a rectangular plate with clamped edges has attracted attention of authors for many years but exact solutions have never been obtained. The difficulty arises from the fact that there is no simple procedure for selecting a proper deflection function that will satisfy both the differential equation of bending and the specified boundary conditions. The only exception occurs when two opposite edges of a rectangular plate are simply supported. In such a case, a simple solution either in the form of a single series as proposed by Levy, or in the form of a double series as proposed by Navier (9) can be easily derived. However, these types of solutions cannot be applied to a plate with two adjacent edges clamped. Because of this difficulty, different approximate methods have been proposed by many authors since 1903. A rather complete list of references of the early works can be found in the discussion of Stiles paper by D. Young (2).
Proceedings of the Iowa Academy of Science
©1955 Iowa Academy of Science, Inc.
Li, J. P.
"Bending of a Rectangular Plate with Even and Odd Order of Boundary Conditions,"
Proceedings of the Iowa Academy of Science, 62(1), 384-392.
Available at: https://scholarworks.uni.edu/pias/vol62/iss1/42