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就桁架结构而言,本文在结构变化定理的基础上提出了计算杆内力、杆应力和节点位移关于杆面积偏导数(梯度)的一组公式.与已有的计算结构响应的梯度公式比较,在一般情形下,用本文公式进行计算所需的附加载荷个数最少,因而计算量也小.这对于广泛使用响应梯度的许多优化方法有减少机时的实用价值.另外,我们还将导出的梯度公式用于满应力设计,得到一个改进的满应力迭代公式.算例表明与简单应力比法相比,改进的方法大大地减少了收敛于满应力设计所需的结构重分析次数.
For the truss structure, based on the structural change theorem, this paper proposes a set of formulae for calculating the rod internal force, rod stress and joint displacement with respect to the partial derivative of the rod area (gradient). Compared with the existing gradient formulas for calculating the structural response, In the general case, using this formula to calculate the minimum number of additional loads, and therefore the amount of calculation is also small. This is widely used for many gradient optimization methods have reduced the practical value of the machine. In addition, we will also export The gradient formula is used for the full-stress design and an improved full-stress iterative formula is obtained. The calculation example shows that compared with the simple stress ratio method, the improved method greatly reduces the number of structural reanalysis required to converge to the full-stress design.