Form-finding as a modelling tool for shaping mechanical components: A feasibility case study of an axial-flow compressor blade

This paper reports on an exploratory study to assess the capability of a novel, form-finding methodology for generating optimal shapes of shell-type structures subjected to complex load regimes, using an axial-flow, compressor blade as a case study. The methodology exploits the natural principle of ‘form follows force’, in which the structural form is shaped according to the forces acting on it. Such forms, or objects, which are found in nature, are known to have optimal strength and stiffness characteristics for a predominant load regime. Our methodology makes use of a direct relationship between form and force, offered by the Laplace–Young equation that describes shapes of minimal surface membranes, such as soap films. Unlike structural optimisation in which the form is modified within its initially prescribed shape, form-finding literally finds the shape within prescribed boundary conditions. This is the first application of the methodology to modelling mechanical components, such as a compressor blade. The blade shapes obtained by this method correspond, in the first instance, to a minimal form and, subsequently, a minimal form subjected to a known (empirically determined) pressure profile. The behaviour of the blades is studied under a variety of loads and includes modal analysis. In view of the methodology adopted, attention is directed to structural performance. The results, compared against a ‘control’ blade produced by a conventional design/optimisation method are very encouraging; they indicate that the proposed methodology has the potential to improve significantly the current blade design process.