Buckling of Rectangular Mindlin Plates on Non-Homogeneous Elastic Foundations

摘要

This paper is concerned with the buckling behaviour of rectangular Mindlin plates resting on non-homogenous elastic foundations that consist of multi-segment Winkler-type elastic foundations. A rectangular plate is assumed to be simply supported on two parallel edges and the two remaining edges may have any combination of free, simply supported or clamped conditions. The plate is first divided into subdomains along the interfaces of the multi-segment foundations. For each segment, the governing differential equations for buckling of a Mindlin plate on a Winkler-type elastic foundation are solved by employing the Levy solution approach associated with the state space technique [1-2]. The domain decomposition method is used to cater for the continuity and equilibrium conditions at the interfaces of the subdomains. An eigenvalue equation for buckling of a rectangular Mindlin plate on a non-homogenous elastic foundation is derived through an appropriate application of the plate boundary and interface conditions.Rectangular plates subjected to uni- and bi-axial in-plane loads are considered. First-known exact solutions for buckling of rectangular Mindlin plates on a non-homogenous elastic foundation are obtained. The buckling of square Mindlin plates partially resting on an elastic foundation is studied in details. The influence of the foundation stiffness parameter, the foundation length ratio and the plate thickness ratio on the buckling factors of square Mindlin plates is discussed. The effect of the non-homogenous elastic foundations on the buckling mode shapes of the plates is also examined. The exact buckling solutions presented in this paper may be used as benchmarks for researchers to check their numerical methods for such a plate buckling problem.