Analytical buckling solutions for Levy-type plates with edge and interior point-support(s)

Abstract

Abstract Rectangular Levy-type plates restrained using point-supports have wide engineering applications. However, the analytical solutions for the buckling behaviour of such plates are not well developed. This paper presents the derivation and application of analytical solutions for the buckling analysis of Levy-type rectangular plates with arbitrarily positioned single or multiple point-supports, which may be located on free edges or within the interior domain. Two general approaches, the impulse function approach (IFA) and the flexibility function approach (FFA), are developed to obtain the critical buckling coefficients (Kcr) and buckled shapes of point-supported rectangular plates. In the IFA, the shear or moment distribution is expressed using a Fourier expansion of the impulse function whereas in the FFA a flexibility function, with zero values of the deflection at the point-support locations and sufficiently large values over the rest of the plate, representing the fictitious elastic distribution, is used to modify the plate support conditions. These approaches are employed in both one-dimensional (1D), and two-dimensional (2D) forms. The developed methods can be adopted to analyse any rectangular Levy-type plate subjected to uniaxial or biaxial loads restrained by arbitrarily positioned point-supports. The IFA and FFA results are validated with finite element method solutions obtained using Abaqus software. Several examples of buckling behaviours, including primary Levy-type plates, edge point-supported plates, as well as single and two interior point-supported plates are provided as guidelines for future design purpose.