Study On Basis Functions In Parameterized Level Set Method And Its Application In Solid-shell Topology Optimization

With development of Computer Aided Design and Computer Aided Engineering,the methods of structural design,analysis and construction are also advancing rapidly.Among them,continuum structural topology optimization based on finite element analysis and optimization has gradually become a research hotspot in shape generation of all kinds of architectural and civil structures.Structures generated by this method can not only meet certain aesthetic needs,but also increase material consumption efficiency.Therefore,the application of this method in architectural and civil design is gradually increasing.The level set method is a popular algorithm in the field of structural topology optimization,and the parameterized level set method(PSLM)studied in this dissertation has attracted much attention of researchers because of its relatively good numerical stability,free opening in the design area and relatively smooth boundary.Basis functions are an important part of the parameterized level set method,but there are few researches on them.In this dissertation,minimum compliance problem is adopted.Based on the parameterized level set method,the effects of different basis functions on the optimization results,computational efficiency and numerical stability are systematically studied,and the parametric way of using shape functions in finite element analysis is proposed for expression of level set function as basis functions.Then,the updating mode of the method is improved.The specific contents are as follows:Firstly,on two-dimensional structured mesh,the original parameterized level set method based on multiquadric radial basis functions(MQRBFs)is used for structural optimization,and the 88-line open-source code is adopted to analyze the characteristics of objective function,volume fraction and topology changes in optimization process.Secondly,the effects of multiquadric radial basis functions,compactly supported radial basis functions(CSRBFs),B-spline functions and shape functions in finite element analysis on optimization results and process are studied and compared,and shape functions in finite element analysis are proposed for parametric expression as basis function.Through the reseach of updating pattern of Cardinal Basis Function,this dissertation proposes updating mode using nodal value of level set function as variables.The updating mode is different from that of original parameterized level set method,which avoids need of inversing coefficient matrix of the basis function in each iteration.Besides,this dissertation also adopts local optimal condition criterion,and introduces the local optimal condition coefficient to replace approximate reinitialization scheme in the parameterized level set method.Then,the value of the local optimal condition coefficient in the minimum compliance problem is put forward.Additionally,topology optimization of 2D structures and 3D solid structures is carried out by using the proposed updating mode and the local optimal condition coefficient.Finally,solid-shell coupling structures are optimized based on adopting the proposed updating mode and the local optimal condition coefficient.In finite element analysis model,the solid structure is discretized by linear T4 element,the shell structure is discretized by DKT plate element and linear triangular membrane element(T3)with translational degrees of freedom,and Multipoint Constraint algorithm(MPC)is used to couple the solid and shell interface.Through the above research,this dissertation draws three main conclusions.Firstly,different basis functions have little effect on optimization results,and shape functions in finite element analysis as basis functions lead to higher computational efficiency.Secondly,the updating mode based on nodal value of level set function and local optimal condition can further improve computational efficiency of the parameterized level set method.Thirdly,since high dimensional function is used in the parameterized level set method to express topology of structures,and there is no need to solve Hamilton-Jacobian equation,this method can naturally deal with the fusion of holes in 3D solid space and holes in 3D surface space.