Research On Parametric Level Set Method For Structural Topology Optimization

The technique of structural topology optimization has overcome the problems in traditional structural design,such as long cycle,high cost,low material utilization and difficulty in structural innovation,etc.The optimal configuration can not only meet the different design requirements,shorten the period of product designing,but also improve the performance of the structure effectively,decrease the cost of development.Therefore,the technique of structural topology optimization has become an important approach of structural design,and it is currently widely used in the fields of aviation,machinery,biology and materials,etc.However,the optimal configuration of topology optimization methods based on finite element mesh often has the problems of jagged boundaries,checkerboard,grayscale elements and so on,and the optimization results cannot be directly processed and manufactured.The parametric level set method can solve these problems effectively.The topological results have clear boundaries and complete geometric information,which is convenient for processing and manufacturing.At the same time,it overcomes the numerical difficulties in the traditional level set method.Based on the requirements of engineering application and structural design,parametric level set method is utilized to focuse on the single material and multi-material topology optimization of steady-state heat conduction structures,the single material and multi-material topology optimization of thermo-elastic structures which subjected to high temperature and high pressure,and the topology optimization design of the bridge structures with different design areas.The main research work is as follows:(1)To solve the problem of low efficiency of the traditional level set method for topology optimization of steady-state heat conduction structures.A topology optimization design method for steady-state heat conduction structures based on parametric level set method is proposed.The interpolated coefficients of Compactly Supported Radial Basis Function(CSRBF)are used as design variables,The optimization model is built to minimize the heat dissipation under the volume constraint.The sensitivity analysis based on shape derivative is carried out and the optimization process is given.Finally,under the conditions of non-design related load and design related load,the topology optimization designs of optimal heat dissipation for steady-state heat conduction structures under different boundary conditions are carried out.The results of the examples show that the parameterized level set method has higher computational efficiency,and demonstrate the feasibility and effectiveness of the parametric level set method for topology optimization of heat conduction structures.The optimization results provide the basis for improving the structural heat dissipation design.(2)To solve the problems of overlap of different materials,complex calculation,etc.A new Multi-Materials Level Set(MMLS)interpolation model is proposed.Based on interpolation model,the optimization model of multi-material steady-state heat conduction structures under the volume constraints of different materials is built,and the minimum heat dissipation is conducted as the objective function.And the sensitivity analysis of heat dissipation and the volume of different materials with respect to design variables are derived.Finally,under the conditions of non-design related load and design related load,the optimal heat dissipation for multi-material steady-state heat conduction structures under different boundary conditions is carried out.The boundaries of optimal configuration are clear,smooth,and the topological configuration is easier to manufacture,which verify the feasibility and effectiveness of the proposed method.The method can be extended to the optimization designs of multi-material with different requirements,such as light weight,economy and high performance,etc.(3)The topology optimization problems of single material and multi-material thermo-elastic structures based on parametric level set method are studied.According to the thermo-elastic theory,the definition and expression of the structural compliance for the thermo-elastic problem are given.The equivalent thermal load is applied as a body force to the structure field.Then optimization models of the single material and multi-material thermo-elastic structures based on parametric level set method are established,and the sensitivity analysis is carried out.The Young's modulus and thermal expansion coefficient of the materials are interpolated by MMLS model.Finally,the thermo-elastic topology optimization designs of single material and multi-material for both fixed beam and Michell beam under different thermal loads are carried out.The results of the examples show that the coupled field is more complicated than the single physics optimization problem,the necessity of structural topology optimization considering thermal load is verified.The effectiveness of the proposed method is demonstrated.Meanwhile,the effects of thermal loading on structural topological configuration and structural compliance are investigated.This method can also be extended to the structural optimization of multi-coupling fields such as thermo-electricity and thermo-magnetic,etc.(4)To solve the problem of difficulty in dealing with holes and complex irregular region in structural topology optimization.A free design region topology optimization method based on parametric level set method is proposed.The implicit functions of the irregular design area and non-design area of the structure can be composed by a series of implicit functions of basic geometry through the combination of R functions.The implicit function is represented by the parametric level set function formed by the interpolation of the radial basis function.Therefore,the interpolation coefficients of the compactly supported radial basis functions are treated as the design variables,and the topology optimization model of free design region is constructed and the sensitivity analysis is performed.This method is utilized to the form finding of different types of arch bridge.The topological configurations obtained by this method are basically consistent with the structures in actual projects,and the rationality and effectiveness of method are verified,and it provides the basis for engineering design.Innovations(1)The topological optimization of steady-state heat conduction structures is carried out by using the parametric level set method,and the topological optimization model for minimizing the degree of heat dissipation under volume constraints is established.The heat dissipation design of heat conduction structures is carried out under the conditions of non-design-related loads and design-related loads.Numerical examples show that the parametric level set method is efficient,the boundaries of optimal topological configurations are clear and smooth,and the engineering practicability is strong.(2)A new multi-phase material level set function interpolation model is proposed,and a topology optimization model is established to minimize the degree of heat dissipation under different material volume constraints.The boundaries of optimal topological configurations are clear and smooth,and there is no redundancy between different materials,which is convenient for manufacturing.(3)The topological optimization of thermo-elastic structures of single-phase and multiphase materials is carried out by using the parametric level set method.The coupling field topological optimization model is established to minimize the structural compliance under the volume constraint,and young's modulus and thermal expansion coefficient are interpolated in the multiphase material thermo-elastic optimization model.The boundaries of optimal topological configurations are clear and smooth,and there is no redundancy among the multiphase materials.It provides a theoretical basis for coupling optimization of multiple physical fields.(4)The R function is introduced to model the implicit level set function.Both the irregular design region and the non-optimal region of the structure can be combined by the implicit function of the basic geometric figure through multi-level Boolean operation.Combined with the parametric level set method,the irregular design region and the topology optimization of the non-optimal region are realized.It provides an effective method for optimization design of practical engineering.