Benchmark symplectic solutions for bending of corner-supported rectangular thin plates

Abstract

This work presents the first ever analytical solutions for bending of a rectangular, thin plate supported only at its four corners. This breakthrough analysis employs a new symplectic elasticity approach that extends beyond the limitation of the classical plate bending methods such as Timoshenko's method, Navier method, Levy method and the polynomial approximation analysis of Lee and Ballesteros (Int J Mech Sci 1960;2:206). The classical methods are, in fact, special cases of this symplectic approach in the real eigenvalue regime for wavenumber with at least one pair of opposite sides of plates simply supported. For plate problems that do not fall into this category, the classical methods fail to yield any analytical solutions, but the symplectic approach does because in these cases the plate bending problems enter the complex eigenvalue regime for wavenumber. Another distinctive feature of this new approach is its necessity to pose an eigenvalue problem even for plate bending. In short, this innovative a...