考虑位移要求的大型三维连续体结构拓扑优化数值技术研究

A RESEARCH ON THE NUMERICAL TOPOLOGY OPTIMIZATION TECHNOLOGY OF LARGE THREE-DIMENSIONAL CONTINUUM STRUCTURES CONSIDERING DISPLACEMENT REQUIREMENTS

大型复杂三维结构拓扑优化设计既具有理论意义,又具有重要的应用价值。基于等效转换的非奇异的结构优化模型,研究结构位移要求的最小结构重量设计问题。首先,介绍了位移约束的三维结构优化准则和公式。而后,为了提高拥有数万个单元以上的三维结构的计算效率,结合结构位移计算的迭代方法,在分析用于结构特性参数计算模型的基础上,建立了一套三维结构拓扑优化的求解策略和算法。最后,给出了几个典型和复杂的三维结构的拓扑优化设计算例。算例表明求解策略和算法是正确和有效的,且具有广泛的工程应用前景。

The topology optimization of large and complex structures is important in theory and application. Based on the idea that finite elements with artificial material property are inserted around the cavities and boundaries of the structure to approximately transform the singular topology optimization model into a non-singular one, this paper has made a research on the topology optimization problem of large three-dimensional continuum structures considering displacement requirements. First, a criterion and a set of formulas of three-dimensional structures with displacement constraints are introduced. Then, in order to solve calculation efficiency problem of large structures with more than ten thousand degrees of freedom, a strategy and its algorithm of three-dimensional structural topology optimization designs are proposed based on analyzing the computation model of structural properties and combining with the iteration method of structural displacement calculations. Finally, several examples of typical and complex three-dimensional structural topology designs are given. These ex＇amples show that the proposed method is valid and effective for complex three-dimensional structural topology optimizations, and is of engineering application value.