Shape optimisation of loaded curved beams using a new geometry-based parametrisation

Abstract

This work proposes an optimisation platform, consisting of a recently proposed parametrisation and a modified gradient-based optimiser to optimise curved beams. This parametrisation technique defines a curve by a series of alternative straight and circular arcs through the points of tangency. The design variables are the coordinates and radii of the curved (transitional) sections. The relationships between the design variables and the points of tangency are formulated analytically. This technique can be used to parametrise the neutral axis of a beam or its outer shape directly. The advantage of this parametrisation method is that the derivatives of most geometrical and mass constraints can be formulated analytically allowing effective use of gradient-based optimisers. Numerical results are used to demonstrate the performance of the proposed optimisation platform. It is shown that the algorithm can remove redundant curved sections or add necessary curved sections provided that enough design freedom is included in the initial design. The capabilities of the platform in dealing with geometrical constraints are demonstrated. By directly parametrising the outer curves, the proposed platform is capable of optimising beams with variable cross sections as well.