A Study On Topology Optimization Of Moving Morphable Components Method With Growth Mechanism

Structural topology optimization is widely used in industrial design as a technology for designing structures with high strength,high stiffness and high-performance.It is not only the pillar of innovative development of precise manufacturing industry and engineering design,but also the key support technology of upgrading defense industrial equipment.Many scholars have made important achievements in the topology optimization field.However,the results obtained by most current topology optimization methods often depend on the initial design of the problem.In order to avoid the influence of adverse initial design on optimization results,it is better to optimize with a more complex or superior initial design.Whereas,it is difficult to set up a superior initial design and the design variables may increase due to the more complex initial design.To solve this problem,the traditional implicit topology optimization algorithms such as “Bubble method” are adopted to avoid the influence of the initial design on the optimization results,in terms of introducing holes into the design domain to obtain the optimized structure.However,material is merely subducted during the optimization process and excess boundary evolution calculation of holes in the later stage of optimization will reduce the optimization efficiency.On the other hand,it is difficult to impose manufacturability constraints such as feature size control under the implicit geometric description framework.The explicit topology optimization methods such as Moving Morphable Components(MMC)method have the advantages of explicit geometric description of optimization results,easy to impose manufacturability constraints,and less design variables.Since the number of components is fixed initially,it is difficult to obtain satisfactory optimization results when the number of components is insufficient or the components’ distribution is unfavorable.Therefore,upgraded MMC method with growth mechanism is established in this work,in which no specific component layout is needed in this method.The topological derivatives of growing components are derived to introduce new components into the design domain to form the optimized structures.By utilizing this method,the dependence of results on initial design can be greatly alleviated.Specific contents of this thesis are listed as follows:A MMC method with growth mechanism is developed in 2D case and a set of explicit geometric description of components are used as basic design blocks.The topological derivative of embedded hard components in infinite soft matrix is derived as the introduction mechanism of new components under fixed background grid.Subsequently,the shape optimization of the original component or the introduction of the new component is determined under a growth criterion containing competition mechanism.In order to solve the problem of unstable objective function value caused by introducing components into the optimization process,the technologies of partition and size factor adjustment of growth components are developed.The effectiveness and accuracy of this method are verified through several numerical examples.MMC method with growth mechanism is developed for 3D condition.In order to reduce the amount of finite element analysis and design variables for the 3D problem,loading path identification algorithm and redundant degree of freedoms removal techniques are introduced.Thus,the islanding components and redundant freedom degrees outside the loading path can be deleted,the number of design variables is reduced,and the calculation efficiency is improved.the analytic sensitivity is derived by introducing the K-S function to calculate the topological description function of the structure,and the iterative stability of the optimization process of the 3D MMC method with growth mechanism is improved.Compared with the traditional 3D MMC method,superior results can be obtained in the cases of a small volume constraint and coarse finite element meshing,thus the dependence of the initial component layout is reduced.On basis of the above work,the topology optimization of plate is studied by using MMC method with growth mechanism.In this study,the thin plate element and equivalent stiffness model are used for finite element analysis,which the calculation amount of finite element analysis is deceased and the calculation accuracy is improved.Since the plate is subjected to the transverse load in the design domain,the optimization result of the traditional MMC method is greatly affected by the angle of initial component layout.However,the MMC method with growth mechanism can effectively solve this problem.Meanwhile,the proposed method is applied to explore the distribution form of natural plant veins,and the mechanical principle behind the unique phenomenon of vein distribution is given from the perspective of mechanics.