An effective optimization procedure for finding structural shapes and topologies that minimize structural compliance and weight subject to stress and deflection constraints is presented. This new approach, called `Metamorphic Development' (MD), can allow a structure to grow and degenerate towards an optimum topological layout. In this method, the optimization can start from the simplest possible geometry (layout) or any degree of development of the structure rather than from a complex ground mesh. The structure is then developed metamorphically using rectangular and triangular elements that can be of any specified sizes. Examples demonstrate the potential of the MD optimization procedure to generate innovative solutions to structural design problems. Results are given and the growth and degeneration histories during optimization are illustrated.@en

As an extension of the Evolutionary Structural Optimization [ESO] method, the bidirectional ESO [BESO] method has effectively addressed various topology optimization problems. It is observed in ESO/BESO applications that the optimal solution obtained strongly depends on the finite element mesh. This paper presents an improved BESO methodology incorporating a means of controlling the optimization process in order to satisfy a constraint on structural perimeter and thus to solve this size effect problem. Numerical tests are conducted on three examples at different levels of finite element discretization. Solutions convergent with respect to the grid refinement are obtained, especially when the perimeter bound is sufficiently low. Simpler topologies consisting of fewer and larger structural members and holes are generated when a more restricting constraint is imposed. Therefore, it is concluded that BESO combined with perimeter control is capable of suppressing mesh dependency and controlling the structural complexity for topology optimization problems.@en

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.@en

In this study, optimal shapes of intersecting pressure vessels are sought using a novel topology/shape optimisation method, called Metamorphic Development (MD). An industrial benchmark design problem of finding the optimal profile of variable thickness that connects a spherical shell pressure vessel to a cylindrical nozzle is considered. Two types of intersecting structures, distinguished by flush and protruding nozzles, are investigated. The optimum profiles of minimum mass intersecting structures are found by growing and degenerating simple initial structures subject to stress constraints. The optimisation seeks to eliminate the stress peaks caused by the opening. The optimised structures are developed metamorphically in specified infinite design domains using both rectangular and triangular axisymmetric finite elements that are ideally suited for modelling continua with curved boundaries. It is shown that the design with a protruding nozzle would produce a better stress distribution than the design with a flush nozzle. The results demonstrate the success of the method in generating suitable, practical solutions to the design problem.@en