Bionic Topology Optimization Method For Structural Stiffener Layout Based On Optimality Criterion

As a new topology optimization method, the adaptive growth technology, which is based on the growth and branching mechanism of branching systems in nature, has been applied to the stiffener layout design of plate and shell structures and has been expected to have great development and application prospects. However, because of the limitations of the current technology, the application of the adaptive growth method is limited to the simple design problems. Firstly, because of the heuristic optimization iteration formula, the current design method has several parameters needed to be determined in advance, and the design result depends on these parameters to some extent. As a result, it is difficult to deal with multi-condition and multi-objective topology optimization problems. Secondly, the current ground structure which is the initial design modal of design problems is imperfect and can not be applied to the design problems of the inner surface load case of plate structure and the three-dimensional box structure. Meanwhile, the differential method is used to calculate the design sensitivity when ANSYS is taken as the tool to analyze the performance of structure, the accuracy and efficiency of the design algorithm should be improved.Focused on the the shortcomings of the current adaptive growth technique, this paper studies geometric model and optimization mathematical model of plate and shell structures and box structures; and an optimization iteration formula on the basis of KKT(Karush- Kuhn-Tucker) condition are derived. The construction of the ground structure which is based on the load conditions is studied and the design sensitivities of the stiffeners are solved by means of analytical method. The iterative formula based on the optimality criterion is applied to deal with the design problems of the minimum compliance, the maxmization natural frequency, and the multi-conditions and multi-objective. Moreover, the adaptive growth technology is applied to the stiffener layout design of box structures, and several typical design examples are demonstrated to validate the effectiveness of the suggested method. The engineering application is also studied, which is the inlet structure of electrostatic precipitator. The result show that the compliance of the optimal design of inlet structure is increased by 18.83% and the first-natural frequency is increased by 4.78% on the condition of the volume is decreased by 4.1%. It is found that the suggested new method overcomes the shortcomings of the current adaptive growth technique and can solve the complex topology design optimization problems of multi-condition and multi-objective. Typical examples show that the adaptive growth technology can effectively solve the stiffener layout of plate and shell structures and three-dimensional box structure, and the suggested technology improves the effectiveness and applicability of the adaptive growth technology.