Simplified ultimate strength estimation method of rectangular plates under combined loads

Abstract

A simple method for estimating the ultimate strength of rectangular plates under combined biaxial and shear loads is proposed. Although numerous studies have been conducted to predict the ultimate strength of plates, most conventional methods rely on empirical approaches that involve plastic correction of the elastic buckling strength or curve fitting through nonlinear finite element analysis (NLFEA) or experimental test results. For a more rational design of hull structures, it is important to develop an estimation method with a more theoretical basis corresponding to physical phenomena, such as post-buckling and yielding behavior, the effects of initial imperfections and material properties as well as the elastic buckling strength. Although some methods with the more theoretical basis were developed in previous studies, they often require numerical iterations such as the Newton-Raphson method to obtain load-deflection relationships. Our approach entails a thorough observation of the buckling and collapse behavior obtained from a series of NLFEA calculations, rather than merely investigating the magnitude of the ultimate strength derived from NLFEA. By applying the elastic-large deflection theory and considering the identified buckling modes, analytical solutions that describe the elastic post-buckling behaviors are derived. The ultimate strength is predicted by assessing the yield at pre-defined locations corresponding to the classified collapse modes. The proposed semi-analytical method eliminates the need for numerical iterative methods to obtain load-deflection relationships and provides a simple estimation of the ultimate strength. The accuracy of the proposed method is validated through a comparison with NLFEA results.