Explicit Structural Topology Optimization Based On Boundary Element Method

As one of the emerging innovative design method,topology optimization has contributed tremendous strength to the application of aerospace,automotive,marine and so on.However,the traditional implicit topology optimization method has many problems in solving engineering problems,such as too many design variables,high computational cost,difficulty in extracting structural geometry information of optimization results and high coupling degree of geometrical model and the associate analysis model,which once hindered the development of topology optimization to engineering field.To solve these problems,the topology optimization method(Movable Morphable Voids Method-MMVs),which is explicitly described by the structure boundary in this paper,can provide a good solution.This method can provide a specific function description for the structure boundary,which can obtain the boundary geometry information directly and simply.However,the traditional topology optimization methods mostly use finite element analysis with fixed grid background in structural response analysis,which will lead to the inconsistency between the geometrical model and the analysis model,resulting in the lack of accurate geometric information in the process of structural analysis,and the post-processing optimization results will destroy the optimality of the structure.On the other hand,most scholars have done a lot of research on the optimization problem of fixed loads,while the design-dependent load problem has less research work because of the complexity of the optimization problem.For the above problems,the following research is carried out for this paper based on the explicit topology optimization framework and combined with the boundary element method:Firstly,the boundary element method(BEM)is used to replace the finite element method(FEM)in the MMVs method,and the BEM is used to divide the boundary into elements,which has the advantages of high accuracy and efficiency.The topology optimization analysis is realized by the direct coupling of BEM and MMVs.Since the geometrical model and analysis model are consistent throughout the whole optimization process,this method has the advantages of explicit description of structural boundary,fewer variables of topology optimization design,fewer degrees of freedom in structural response analysis,and higher accuracy in structural response analysis.Secondly,considering that the traditional topology optimization method needs to restore the loading surface first in solving the design dependent load problem,this paper presents a load-dependent explicit topology optimization method based on the boundary element method.With the natural explicit characteristics of MMVs method,in each iteration step,the pressure load can be accurately applied through the external normal vector parameters of the structure boundary and the node coordinate information of boundary element.Compared with the optimization method based on SIMP framework,no additional processing is required to solve the problem of load imposition.Through the study of the above problems,this paper develops and improves the topology optimization method based on the explicit moving morphable voids framework,and provides a new idea for maintaining the consistency of geometrical model and analysis model in the process of optimization analysis.It also provides a new theoretical model for solving engineering problems by the explicit topological optimization method.