频率响应位移幅值敏度分析的伴随法

Sensitivity Analysis for Frequency Response Amplitude with Adjoint Method

频率响应位移幅值的敏度分析通常采用直接法,一次敏度分析只能计算出对一个设计变量的偏导数,这在设计变量很多的拓扑优化中因敏度分析计算量太大而显得不适用,本文推导了频率响应位移幅值敏度分析的伴随法,一次敏度分析可计算出对所有设计变量的偏导数,算例表明伴随法计算结果与直接法及差分法结果符合得很好,用伴随法分析敏度在结构拓扑优化中可以大幅提高计算效率。

The direct method is always adopted to analyze sensitivity of displacement amplitude with frequency response, the partial derivatives with respect to a single design variable can be obtained from a sensitivity analysis, thus it is not suitable for the topology optimization with many design variables. An adjoint method for sensitivity analysis of displacement amplitude with frequency response is developed and the partial derivatives with respect to all design variables can be obtained via a sensitivity analysis. The numerical examples reveal that the results from the adjoint method agree with those from direct method and difference method very well with a lighter computing task.