结构拓扑优化应力敏度分析的伴随法

发布时间：2018-04-28 23:14

本文选题：连续体结构拓扑优化 + 应力约束　；参考：《应用力学学报》2017年05期

【摘要】：针对受应力约束的连续体结构拓扑优化问题,推导了应力敏度分析的伴随法公式;并以算例形式,将伴随法计算的应力敏度结果与差分法结果进行对比,验证了所推导公式的准确性,应力敏度分析结果表明了应力对设计变量的偏导数具有局部性特点。在此基础上,以受应力约束重量极小化为目标的结构拓扑优化为例,对比分析了应力一阶Taylor近似与满应力法的优化效果。结果表明:相比满应力法,应力一阶近似能使结构应力在更多的部分达到许用应力,得到的最优结构重量更轻。对设计变量数目巨大的应力约束连续体结构拓扑优化问题,由于应力约束数目可以通过准有效约束初选及不考虑删除单元的应力约束等方式减少,通常比设计变量数目小很多,应用应力敏度分析伴随法可以显著提高计算效率。
[Abstract]:In order to solve the topological optimization problem of continuum structure constrained by stress, the adjoint method formula of stress sensitivity analysis is derived, and the stress sensitivity results calculated by the adjoint method are compared with the results of the difference method in the form of an example. The results of stress sensitivity analysis show that the partial derivative of stress to design variables is local. On this basis, the optimization results of stress first order Taylor approximation and full stress method are compared and analyzed with the example of structural topology optimization in which the weight is minimized by stress constraints. The results show that compared with the full stress method, the stress first order approximation can make the stress reach the allowable stress in more parts, and the weight of the optimal structure is lighter. For the problem of topological optimization of continuum structures with large number of design variables, the number of stress constraints can be reduced by means of quasi-effective constraints and stress constraints without consideration of deleted elements, which is usually much smaller than the number of design variables. The adjoint method of stress sensitivity analysis can significantly improve the computational efficiency.
【作者单位】：湖南城市学院土木工程学院;北京工业大学工程数值模拟中心;
【基金】：国家自然科学基金(11672103) 湖南省自然科学基金(2016JJ6016)
【分类号】：O302

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