Topology/shape optimisation of axisymmetric continuum structures – a metamorphic development approach

A novel topology/shape optimisation method for axisymmetric elastic solids, based on solid modeling and FE analysis, is presented. Optimal profiles of minimum-mass axisymmetric structures are sought by growing and degenerating simple initial structures subject to response constraints. The rates of the growth and degeneration are controlled based on the current objective and constraint functions of the optimisation problem under consideration. The optimal structures are developed metamorphically in specified infinite design domains using both quadrilateral and triangular axisymmetric finite elements that are ideally suited for modeling continua involving curved boundaries.The robustness of this fully automatic method is studied and validated with the first example of seeking the optimal shape of a centrally suspended axisymmetric object with minimum strain energy caused by self-weight. Then the method is applied to a practical industrial design problem: the design of a turbine disk. The variations of load and boundary conditions caused by shape change in these problems, including the gravitational and centrifugal loads, and temperature distribution are accommodated in the optimisation procedures. Thus, the design model closely resembles the real design problem. The results demonstrate the success of the method in generating optimal but realistic solutions to practical design problems.