Application of Trefftz theory in thin-plate buckling with in-plane pre-buckling deformations

Abstract

The paper presents the application of Trefftz initial stress theory in determining the elastic buckling load of rectangular thin plates under in-plane stress resultants, with allowance for in-plane pre-buckling deformations. Exact buckling solutions for simply supported plates are obtained and compared with earlier results furnished by Ziegler (1983, Ing.-Arch. 53, 61 [1]). Although somewhat different, due to the use of different theories, both sets of results show that the buckling loads may be reduced when pre-buckling deformations are accounted for. This observation is contrary to that for column buckling where it has been shown that the allowance for pre-buckling shortening results in a higher buckling load. This reduction in plate-buckling load is significant especially for plates with large thickness-to-span ratios and subject to a combination of tensile and compressive in-plane stress resultants that increase pre-buckling deformations. © 1992.