基于Epsilon算法加速的导重法拓扑优化求解研究

Convergence acceleration of guide-weight method on solving topology optimization models using Epsilon-algorithm

针对拓扑优化模型求解过程中需要多次迭代才能得到满足一定精度要求的收敛结果的问题,提出了一种基于向量Epsilon算法加速迭代序列收敛的方法。在求解大型连续体结构拓扑优化过程中,依据导重法迭代格式首先迭代了k次,然后对所得到的迭代序列的后m项作Epsilon算法运算,将所得到新向量作为下次导重法迭代的初始值,以此类推直到满足收敛条件。通过两个算例验证了所提出方法的有效性。计算及研究结果表明,用Epsilon算法加速后的迭代格式求解拓扑优化问题能够减少迭代次数,具有更高求解效率。

Aiming at the problem of too much times of iterations to get the convergence results satified the accuracy required at the process of solving topology optimization models, a convergence acceleration method was proposed using vector epsilon-algorithm based on Guide-weight method. In the procedure of calculate large continuous structural topology optimization problems, k iterations were done according to the guide-weight method, then vector epsilon-algorithm was applied to the sequence of last m terms to obtain a new vector which was regarded as a initial value of next iteration until convergence. The developed method was verified by two examples. The results indicate that epsilon-algorithm can solve topology optimization problems with less iteration and high efficiency.