Analytical and semi-analytical methods for buckling and bending of steel elastomer sandwich plates

Abstract

This thesis has been written about the analytical and semi-analytical formulae as an alternative to finite element analyses in computing lateral deflection, buckling loads and ultimate capacity of steel elastomer sandwich plates. Since the introduction of sandwich plates in the aerospace industry several decades ago, the shipbuilding industry is now finding a use of their own for this type of construc- tion. The major classification societies are all in the process of creating rules for the design of sandwich plates for use in the maritime industry and in this process Det Norske Veritas has created the classification note CN.30.11 Steel Sandwich Panel Construction. The thought behind these rules is to use formulae in the design of the sandwich panels instead of the more time consuming finite element method. The work in this thesis has involved finding the proper analytical formulae for buckling and bending of simply supported sandwich plates from relevant theory and comparing the results from these formulae with the finite element method. The formulae have been implemented in a Visual Basic-automated Excel spread-sheet which has been made available as a supporting tool for the classification note. Another part of the thesis has been to develop a semi-analytical method, using a Rayleigh-Ritz approach, for more accurate buckling strength assessments. This model can be used for both simply supported and clamped plates and calculates eigenvalues for all combinations of in-plane normal and shear forces. It also can accurately account for pre-stresses in the buckling analyses. The results from the analyses are presented along with the underlying theory in this thesis. For the analytical models the results show a good agreement between the formulae and the finite element method for most cases, with the closed form formulae often being a bit conservative on the safe side. The results for the Rayleigh-Ritz model also show very good agreement with the finite element method. Some problems were encountered in the modelling procedures of sandwich plates in ABAQUS, especially with the solid element models. This can be the cause of some of the difference between the analytical and finite element models in the results.