Bending solutions of Levinson beams and plates in terms of the classical theories

Using the mathematical similarity of the governing equations of the classic al beam and plate theories and the Levinson beam and plate theories, and th e basis of load equivalence, exact relationships between the bending soluti ons of the two theories for beams and plates are derived. These relationshi ps enable the conversion of the well-known classical (Euler-Bernoulli) beam and (Kirchhoff) plate solutions to their shear deformable counterparts usi ng the Levinson beam and plate theories. Examples are given to illustrate t he use of these relationships. (C) 2001 Elsevier Science Ltd. All rights re served.