Research On Multiscale Topology Optimization Method For Structure Based On Parameterized Level Set

Topology optimization is capable to generate product prototype according to the requirements during conceptual design stage.It is the most prospects in modern structural design,and has been widely utilized in the fields of aerospace,architecture,shipbuilding and machine manufacturing.To meet the requirements of new structure,processes and manufacturing,multiscale topology optimization method based on the scale-separation design idea has become an important research direction in the structural optimization field.However,there are still some problems such as complex model expression,difficult in analysis,difficult in synchronization of multiscale optimization,poor continuity and low accuracy.In this paper,multiscale topology optimization is studied from the aspects of model representation mechanism,structural analysis model,optimization method and parallel computing technology.The main research work is as follows:(1)For the problems of complex model representation and difficult analysis under scale separation,the skeleton-unified isomorphic microstructures are yielded by reconstructing level set function and interpolating shape for the basic microstructure.Additionally,the period intervals of microstructures are adaptively adjusted,so that the skeletons of multiple types can be connected in series by cell nodes.Then a well-connected multiscale representation mechanism is presented,realizing the dimensional reduction of design parameters.The homogenization method and interpolation strategy are combined to construct a multiscale analysis model,laying a theoretical foundation for large-scale structural topology optimization.(2)The hierarchical scheme is adopted in multiscale topology optimizations,leading to a lag of optimization information and difficulty of synchronous optimization among different scales.Therefore,an optimization mechanism based on surrogate model of effective property is proposed.Based on the mathematical relation between geometric models and macroscopic equivalent properties for the isomorphic microstructures,the surrogate model of effective property is established from the characteristic sample data.The model establishes an effective connection between micro configuration and macro performance,thereby breaking through the design bound and eliminating the lag of optimization information.Thus,the synchronous optimization of multiscale structure is realized.(3)For the problem of low continuity in multiscale optimization,a structure representation method via surface cutting is presented,in which the multiscale structure is generated from the intersection between cutting surface and basic lattice structure defined by parameterized level set.Additionally,a relative density-based sample extraction method is researched.Subsequently,the analysis model of effective property for cutting microstructure is established by combining the periodic processing and homogenization algorithm.With the help of continuity of level set surface,the structure is optimized with high-order continuity of geometry.(4)For the accuracy issue,the non-uniform rational B-Splines are employed as the interpolation function of the parameterized level set.With the continuity of B-Splines,the physical fields are approximated precisely,and the analysis accuracy is improved.For the low computational efficiency of high-order elements,the GPU parallel method is researched,and the parallel algorithm of multiscale topology optimization is proposed to accelerate the processes such as effective property analysis,stiffness matrix calculation,and optimization solution.The GPU/CPU speedup ratio reaches 61 times at 100,000 degrees of freedom,effectively improving the computational efficiency.Based on the theories and methods above,a software system architecture and core algorithm module are studied.The function module of the surrogate model-based optimization,the surface cutting-based optimization and the NURBS-based optimization with parallel algorithm is developed with Visual C++ development.Then a prototype system of multiscale topology optimization is realized.The system is validated by the engineering cases,and provides a reference for realizing the independent design tool of optimization-driven design analysis.