Numerical weight function method for the structural analysis of ships: a speedy direct calculation with condensed structural information

The weight function method was originally derived for crack problems to calculate stress intensity factors for arbitrary loading conditions. In this article, a numerical weight function method has been extended to formulate the structural response analyses of two-dimensional elasticity, plate-bending, and three-dimensional plate-structures by using the finite-element method. The solution procedure is based on the well-known Maxwell–Betti reciprocal theorem, which is applied to the original and properly defined auxiliary problems. The present numerical weight function may be considered as a finite-element version of a Green’s function in an integral equation solution scheme. Although ship structures are certainly analysed by the finite-element method in a practical design procedure, the weight function approach has not yet been realized. The method is very useful for the analysis of structures subjected to a vast range of loading conditions, because structural responses can simply be calculated by the inner product of the universal weight function and load vectors. The validity and convergence characteristics of the present method are investigated by two-dimensional elastic and plate-bending problems, respectively. Finally, the method is applied to the calculation of the response amplitude operator of a stress component at a critical structural detail of a double-hull tanker, and the speed and efficiency of the method are quantitatively discussed based on the practical results.