Optimal positioning of internal point-supports in Levy-type plates for buckling load maximisation

Abstract

The buckling capacity of plates can be enhanced by appropriately placing discrete point-support(s) at optimal locations. However, determining the optimal locations of point-supports to achieve maximum buckling coefficients is a challenging problem, as it couples the analysis procedures for buckling and optimisation. This paper investigates the optimal positioning of point support(s) in Levy-type plates subjected to in-plane loads for maximum buckling coefficients and presents a novel and efficient solution framework for this problem. The framework is based on the application of the one-dimensional impulse function approach (1D IFA) in combination with the particle swarm optimisation (PSO) method. As shown previously [1], the 1D IFA is a suitable method for the secure handling of multiple point-supports and changing their locations in rational plate buckling analyses. Using the presented framework, a set of demanding analytical solutions for the buckling of Levy-type plates with arbitrarily positioned single or multiple point-supports subjected to linearly varying in-plane loads are first verified against convergence and comparison studies. Subsequently, buckling results are presented for a wide range of rectangular plates with various numbers of point-supports and various combinations of mixed edge support conditions. The results for the optimal locations of point-supports include surprising findings, including (a) some of the optimum solutions can be achieved when the point-supports are positioned over a line of finite length, rather than at discrete points; (b) there can be multiple solutions for one specific aspect ratio and edge condition; (c) some of the optimum solutions for the location of point-supports are not symmetric with respect to symmetry axes of geometry and/or loading.