| As a scientific and efficient computational tool,topology optimization can find the structural topological configuration with the best target performance in a given design space.It is the most powerful method for lightweight design of structures.The design has broad application prospects.However,the traditional structural topology optimization design can not meet the needs of modern industrial products for “shape topology integration”,“CAD/CAE integration” and “topological description parameterization”.How to reasonably describe the structure topology,enable it to achieve integration with CAD,improve optimization efficiency,conveniently control geometric features,and solve challenging structural optimization problems has become a hot topic in the field of structural topology optimization.In this paper,the mobile deformable cavity algorithm is used as the entry point,and a new method in the field of topology optimization,"feature mapping topology optimization method" is studied.Firstly,the topology description method of parametric geometric feature mapping is studied,and a topology optimization method based on mobile deformable cavity is constructed.Secondly,the modeling characteristics are deeply studied,and efforts are made to improve the optimization efficiency and avoid the initial dependence of parameters.Finally,the method is extended to the isogeometric analysis and geometric nonlinear problems.The main work of the thesis is as follows:(1)Starting from the description method of structural topology,the high-level geometric parameterization method is used to describe and model the structure topology,realize the explicit and clear description of the boundary,and explore the geometric description ability of the cavity.The linear optimization of the mobile deformable cavity topology is constructed and the analytical sensitivity is derived.Structural optimization of the structure including the satellite support legs was carried out using a mobile deformable cavity.A smooth post-processing method is proposed for the boundary smoothness of the optimization results.(2)Improve the mobile deformable cavity algorithm to make it more stable,reliable,fast and efficient,and the optimization mechanism is more scientific and reasonable.The mutual independence of the sensitivity solution is analyzed,and the boundary motion characteristics are controlled by the explicit method.Multi-resolution finite element is introduced,which makes full use of the characteristics of topology description and analysis grid decoupling.The analysis grid is subdivided to obtain the material grid,and the subdivision material grid is used to perceive the material distribution,and the rough analysis network is used.Perform a finite element analysis.Using the fast marching method to calculate the neighborhood of the explicit boundary,limiting the range of the topological description function and the sensitivity calculation,and improving the computational efficiency.An automatic cavity introduction mechanism suitable for the mobile deformable cavity optimization frame is designed.The optimal position of the cavity is calculated based on the bidirectional progressive structure optimization principle,and the optimal timing of cavity introduction is derived based on the level set method.(3)In order to realize the unification of the design model and the computational model and ensure the geometric information integrity,the research of the mobile cavity method is further extended to the isogeometric analysis.In this framework,the multi-resolution geometric analysis method is further developed,and an artificial material model based on Greville collocation is established to interpolate the Young's modulus and density field of the material.The geometrical mesh is used to construct the material distribution field to improve the accuracy,while the coarse mesh is used for the geometric analysis to reduce the amount of computation.Numerical examples show that the mobile deformable cavity method has been successfully extended to isogeometric analysis,and geometric analysis such as multi-resolution can achieve high-resolution design with lower computational cost.(4)The problem of geometric nonlinear topology optimization is studied by using the mobile deformable cavity method.The nonlinear topology optimization problem formula under the framework is established and the sensitivity of the structural response is derived.The cavity modeling method is used to delete the invalid cells in the design domain to avoid the convergence problem caused by low density elements.Further,in order to enhance the stability of the optimization process,the boundary motion control technology is continuously adopted,so that the success rate of the iteration is guaranteed.The end flexible structure and the compliant mechanism are separately designed and analyzed for structural features under geometric nonlinearity.(5)Using a multi-output compliant mechanism model,an optimized design of a“flexible mechanical gripper” was carried out,and the physical object was obtained by3 D printing,and then a multi-scene actual crawling experiment was carried out.Experiments show that the deformation of the structure under displacement drive is consistent with the nonlinear calculation results.The optimization design results in both good deformation ability and sufficient stiffness,so that the structure can grasp the object well.In summary,this thesis takes the mobile deformable cavity algorithm as the research object,and conducts an in-depth study on the feature map topology optimization method.The scientific and reasonable topology description and modeling methods are expounded,and the generalized feature mapping algorithm improvement strategy is proposed,and the hotspots and difficult areas of structural optimization are actively explored.This paper further enriches and develops the topology optimization method system,which has great theoretical significance and practical value for promoting and improving the design capability and application level of topology optimization methods. |
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