Note on mathematical development of plate theories

Abstract

In this article, the history of mathematical development for plate analysis is reviewed with emphasis on providing the plate’s governing differential equations in rectangular coordinates. Attention is mainly devoted to theories based on the Kirchhoff, Reissner, Mindlin, and Levinson theories for isotropic plates with uniform thickness. Therefore, it is expected that this review paper should be useful for scientists and researchers in assisting them to understand and classify relevant existing plate’s theories quickly. Mathematics Subject Classification: 35Q74, 74K20