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基于固体各向同性材料惩罚密度插值模型,建立近似支撑框架模型,以最大刚度为优化目标,以优化体积比及工程限值为约束条件,对支撑框架结构进行了优化。工程限值约束包括最大、最小尺寸约束,对称性约束以及顶点位移约束等。研究结果表明:当支撑框架中斜撑的斜交角度为39°~59°时,框架具有较好的抗侧刚度;当优化体积比为0.3时,优化后结构顶点位移较原设计域增加19%。引入工程限值约束条件能使拓扑优化后的结果有效应用于实际工程,优化后结构具有框架形态,无不易建造的细微结构,减少了低效材料分布,从而降低造价。
Based on the penalty density interpolation model of solid isotropic material, an approximate support frame model is established, and the maximum stiffness is taken as the optimization objective. The optimization of the support frame structure is achieved by optimizing the volume ratio and the engineering limit. Engineering limit constraints include maximum and minimum size constraints, symmetry constraints, and vertex displacement constraints. The results show that the frame has good lateral rigidity when the skew angle of support brace is between 39 ° and 59 °. When the optimized volume ratio is 0.3, the displacement of the optimized structure increases by 19% %. The introduction of engineering constraints can make the results of topological optimization effectively applied to practical projects. The optimized structure has the form of frame and the subtle structure that is easy to be built, reducing the distribution of inefficient materials and reducing the cost.