Level Set-based Topology Optimization Method For Architectural Structure Design

For architectural structure design,digital structural performance design based on the continuum structure topology optimization method can combine the structural mechanical analysis with structural design,and help architects introduce the concept of structural performance optimization in the schematic design phase naturally.This paper focus on solving some key problems when applying the level set-based topology optimization method into architectural structure design.Firstly,this paper adopts the existing level set-based topology optimization method using a reaction diffusion equation.And this paper proposes that the computational formula of topological derivative for the mean compliance minimum problem under the fixed external load,can be given by the differential derivation of finite element equation,which is also adopted in the evolutionary structural optimization method using the compliance criterion.Secondly,this paper proposes that the level set function of curved shell structure can be discreted by using a local polynomial,and then the reaction diffusion equation-based level set method can be used to solve the topology optimization problem of curved shell structure.Then there is no need to solve the Hamilton-Jacobi equation using the transformation of curvilinear coordinate system.For the finite element mechanical analysis of curved shell structure,this paper uses the four-node flat shell element from the combination of DKQ plate element and four-node membrane element with drilling degree of freedom.Thirdly,this paper proposes that the level set function used in the reaction diffusion equation-based level set method can be parameterized by the radial basis functions,and gives the update form of level set function.And then this paper proposes that the parameterized level set-based topology optimization method can be used to solve the pattern repetition and symmetry constraints in the topology optimization problem with independent interpolations in each subdomain and mapping relationship between subdomains,because the sample points of radial basis functions can be selected independently from the finite element mesh nodes and have no need of mesh connection.Finally,for the design-dependent self-weight load problem,this paper also adopts the computational formula of topological derivative for the mean compliance minimum problem considering the self-weight load based on the differential derivation of finite element equation from evolutionary structural optimization method using the compliance criterion.And the approximate topological derivative is used in the level set-based topology optimization method using a reaction diffusion equation.Moreover,this paper analyses the important influence of the penalty factor of material interpolation model on the volume constraint of the optimization problem.It is proven by the numerical example that a totally void structure can be obtained for the structure only considering self-weight load using the proposed method.