Research On Topology Optimization Of Continuum Structure Based On SR Model

Topology optimization is an advanced design method that achieves optimal structural performance in a given design area based on boundary and load conditions while meeting specific constraints.Density method is one of the most commonly used topological optimization methods.Due to the complex structure of the topology optimization results,it is often difficult to prepare it using traditional manufacturing processes.Additive manufacturing is the preferred manufacturing technology for the topology optimization results.However,the relaxation of design variables or numerical instability in the solving process of density method will hinder the generation of clear and effective topology optimization configurations.As a result,the printed parts are inconsistent with the design requirements,which reduces the printability of the topology optimization results to a certain extent.In this paper,the density method in the topology optimization method of continuum structures is used as the research object.In the process of optimization of single-phase materials and multi-phase materials,in order to suppress the intermediate density units,checkerboards and grid dependence caused by the relaxation of design variables or numerical instability,a new material interpolation model is proposed.Based on this model,the morphological filtering technology based on imageology and the algorithm for topology optimization of multi-phase materials are studied.Based on this,combined with the additive manufacturing technology,the optimization method of the manufacturing process based on the topology optimization results is studied.Finally,a prototype system for structural topology optimization is developed and verified.Specific research content includes:(1)Based on SIMP(Solid Isotropic Microstructures with Penalization)model and RAMP(Rational Approximation of Material Properties)model,which are two kinds of material interpolation models commonly used in density method,an SR weighted interpolation model is proposed.The SR model takes full advantage of the high efficiency of the SIMP model and the high stability of the RAMP model.The problems that the SIMP model easily converges to a local optimal solution and the RAMP model has low execution efficiency are solved,thereby more effectively suppressing the intermediate density units in the optimization results.(2)The morphological filtering technology based on SR model is studied,and the morphological filters based on imageology are constructed.Among them,the expansion and corrosion filters are used as the basic filters.By performing these two basic filters in sequence,the advanced filters,namely the open,close,open-close and close-open filters are obtained accordingly.Then,the morphological filters are combined with the SR model to effectively suppress the checkerboards and grid dependence phenomena while effectively filtering out the intermediate density units,and obtain the optimization results with clear boundary.Finally,the effectiveness of the method is verified by numerical examples.(3)A mathematical model for topology optimization of multi-phase materials is established based on the SR model.Then,a sensitivity-based material phase alternative solution method is proposed,which quickly and accurately obtains the ideal local optimal solution of the optimization problem.Based on this,the quantitative evaluation index for topology optimization of multi-phase materials is proposed,and the optimization results are evaluated accordingly.(4)Combining with the structural characteristics of the topology optimization configurations,a two-stage process decision model for additive manufacturing oriented to the results of topology optimization is proposed.From the perspective of additive manufacturing process,screen out the most suitable manufacturing process for the topology optimization results,and infer the best molding strategy based on the effect of printed parts.The surface roughness,printing time and printing cost of printed parts are reduced,and the product quality of printed parts is improved.(5)The topology optimization prototype system based on SR model is developed in MATLAB programming environment to realize unified structural analysis and optimization,and validated the models and methods described in this paper.The limitation of the narrow selectivity of the current structural topology optimization analysis system is solved.