Static and dynamic buckling of deep beams with plate finite elements

Resumo

The main objective of this paper is to present results on the lateral buckling of beams using finite
elements based on Kirchhoff and Mindlin-Reissner Plate theories, merged with membrane elements in order to
include the analysis of shells. A MATLAB code was developed to calculate static and dynamic critical loads,

buckling modes, frequencies, and vibration modes of thin and thick plates subjected to conservative and non-
conservative (also called follower or circulatory) loads using a so-called geometric matrix. In case of displacement-
dependent applied forces, it is necessary to implement a matrix that will correct the loads, designated as load

matrix. In the case of conservative forces, the load matrix is symmetric, and in the case of non-conservative forces,
it is non-symmetric. In the latter case, the critical load usually will correspond to dynamic behavior designated as
flutter. Different boundary conditions and loads are considered and several cases of lateral buckling are
investigated. Theoretical values when found in the literature or in national and international rules are compared
with values determined by Finite Element Method (FEM). The lateral instability of slender beams is very important
in practice, because in some situations it may occur prior to ultimate plastic limit state in bending.