Ultimate Strength Analysis of Thin Plated Structures Using Eigen-functions

Abstract

In order to increase the safety of plates structures such as ships, ultimate strength analysis should be performed taking into account of local failures of buckling and yielding of component plate elements. Direct application of the finite element method still needs enormous computation time and is not economical to use at the design stage, even most advanced computers are provided. In order to achieve this purpose, one of the authors proposed the “Idealized Structural Unit Method (ISUM)” and proved its usefulness by many applications. The previous rectangular plate element was developed based on the numerical results on buckling and post-buckling and formulation of its stiffness equation was complicated. In this paper, a new rectangular plate element has been developed. The formulation of its stiffness equation has been performed completely analytically for buckling and post-buckling behaviors by introducing eigen-functions, being paid attention to use only one or two parameters to reduce computation time. For partial yielding of the element, the plastic node method is introduced. This new element can be applied to the complete range of the behavior incluing buckling, post-buckling, ultimate strength and post-ultimate strength. The numerical results indicate that necessary computation time is very short for any aspect ratios and the accuracy is very high in comparison with FEM. There is some improvement is expected to reduce higher shear force at the ultimate strength under a combined action of compression and shear.