Problem of Determination of Optimal Supports Position for Jumbo Flat Glass with Free Edges

Abstract

Recent trends in architecture are characterized with wide applications of laminated glass plates in facing systems of high-rise buildings, where the plates are oriented in both vertical and horizontal planes. This paper deals with mathematical description of optimization problem for location of finite number of rigid supports horizontally placed on jumbo flat glass plate with free edges. Associated state problem corresponding to Kirchhoff’s hypothesis of plate theory is solved. Further the optimization problem for finding location of the finite number of rigid supports, with respect to the condition for minimal deflection of the plate in the sense of 1 C -norm, is solved. Theoretical results are used in numerical simulation by the finite element method (FEM). It allows us to reduce the computation time for solution of real projects. Further application of such results is for example in the area of automatic handling in the flat glass production in the case of engineering design for location of vacuum gripping heads components of handling devices.