Advances in Structural Loadflow Visualisation and Applications to Optimal Shapes

Abstract : Currently there is no generally accepted procedure for calculation of structural loadpaths, which would show how remote loads are equilibrated through a structure and could provide insight into how well a structure is performing its intended load-carrying functions. Kelly and Elsley have recently proposed a method for computing loadflow orientations and loadpaths using finite element results, which is based on iterative solutions of non-linear equations. In this paper, we have enhanced their theoretical formulation and general procedure by deriving explicit expressions for computing loadflow orientations. The new equations produce more accurate loadflow orientations compared to the prior approach and improve the fidelity of calculated loadpaths. In a series of benchmark problems, we have investigated non-optimal and optimal holes in plates using loadflow visualisation to identity their key features. We found that recirculation is apparent for non-optimal hole shapes, whereas no recirculation zone is present for optimal shapes. Although very highly refined finite element meshes were utilised, the implications are that even more refined meshes are required to fully capture the complex behaviour that exists in recirculation zones. The removal of the recirculation zone for a non-optimal shape leads to a better shape, but the improvement in peak stress is insignificant. The calculation of loadflow orientations using the new equations is simple, and could be used with any finite element analysis code, while a plotting package is required to display loadpaths. Loadflow visualisation is a powerful tool for use by structural designers to improve their understanding of structural performance, the application of which can potentially result in worthwhile improvements in structural efficiency.