结构动力响应灵敏度分析伴随法一致性问题研究

摘要

研究结构瞬态动力响应灵敏度分析伴随法可能存在的一致性问题，具体考虑先微分后离散与先离散后微分两种敏度分析方法的计算精度、收敛速度及一致性等。基于动力响应分析的时域显式法基本思想，以更简洁方式推导先离散后微分的伴随法计算列式。结果表明，先微分后离散伴随法一致性问题是由计算中所用动力响应结果仅在离散时间点满足运动方程产生的，存在的一致性问题不影响该方法的可靠性及应用。%The inconsistency issue of adjoint variable methods (AVMs)for sensitivity analysis of transient dynamic responses was investigated.The differentiate-then-discretize and discretize-then-differentiate approaches were considered, focusing on their computational accuracy,convergence rates and result consistency.Based on the basic idea of the explicit time-domain method for dynamic analysis,a concise discretize-then-differentiate AVM formulation was presented.It is found that the inconsistency of the differentiate-then-discretize approach is caused by the fact that numerical solutions for dynamic responses satisfy equations of motion only at integration points in the time domain.However,despite this consistency problem,this approach is still reliable for sensitivity analysis of dynamic responses.