一种新型线性化迭代算法及其在结构优化准则方程组求解中的应用

 求解一元非线性方程的埃特金算法是一种线性化自动迭代算法，其每次迭代需要计算两次函数值。将其推广到结构优化非线性准则方程组的迭代求解，可实现结构优化迭代求解的完全自动化。为克服其每次迭代需要两次结构分析的缺点，构造了一种新型线性化迭代解法，称为Atiken Chen算法，该算法利用前次结构分析信息，每次迭代只需一次结构分析，从而大大提高了结构优化迭代计算的效率与自动化程度。算例验证了该算法的可行性和优越性。

New linear iterative algorithm and its application in seeking solution of criterion equations of structural optimization

Aitken algorithm, exploited to solve nonlinear equations with one variable, is an automatic linear iterative algorithm, in which each iteration needs computing function values twice. Extending it to iterative solution of structural optimization nonlinear criterion equations, complete automatization of iterative seeking solution for structural optimization can be implemented. To eliminate the defects of requiring two structural analysis for one iteration, a new type of linear iterative algorithm, called Atiken Chen algorithm, is constructed. This algorithm utilizes the information of the last iteration and merely needs one structural analysis for each iteration, through which the computing efficiency and degree of automatization of structural optimization interaction computation are greatly enhanced. Feasibility and superiority of this algorithm have been demonstrated by illustrations.