提出了一种新的梯度分析方法。针对梯度类优化设计中非线性参数梯度计算困难的问题,利用复变量求导法,把隐式函数的梯度分析过程转化为函数值的计算,显著提高了梯度计算的精度。相对于常规的基于有限差分的梯度计算方法,该方法更为高效。利用建立的复域梯度分析方法,结合经典的最速下降优化方法,给出了结构刚度优化方法。数值算例表明,所给出的方法可以高效可靠地实现结构的刚度优化。 A new gradient analysis method is proposed. In order to solve the difficult problem of nonlinear parameter gradient calculation in gradient class optimization design, the method of multivariate derivative is used to transform the gradient analysis process of implicit function into the calculation of function value, which significantly improves the accuracy of gradient calculation. Compared with the conventional finite difference-based gradient calculation method, this method is more efficient. Using the established gradient analysis method of the complex domain, combined with the classical steepest descent optimization method, the structural stiffness optimization method was given. Numerical examples show that the proposed method can achieve structural stiffness optimization efficiently and reliably.