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结构稳健优化设计中,一个关键的环节是分析结构响应量的概率特性,即计算响应的均值和方差。常用的方法主要有泰勒级数法、蒙特卡洛法以及数值积分法等。其中泰勒级数法精度较差,不适用于参数方差较大的随机结构,而蒙特卡洛法和高斯积分法计算量又过大。为了提高结构稳健性分析的计算效率,将结构位移的二项级数近似技术引入到高斯积分方法之中,提出一种结构位移均值及方差的计算方法。同时,用伴随向量法推导了相关的灵敏度计算公式。通过一个算例与已有的方法进行了比较,表明该方法较大程度上减少了高斯积分法的计算量,而与泰勒级数法相比,该方法又具有较高的计算精度,并且其灵敏度计算不再需要重分析,计算量较少。
One of the key aspects of robust structural optimization is the analysis of the probabilistic characteristics of the structural response, ie, the mean and variance of the response. Commonly used methods are mainly Taylor series, Monte Carlo method and numerical integration method. Among them, the Taylor series method has poor accuracy and is not suitable for random structures with large variance of parameters. However, the Monte Carlo method and the Gaussian integration method take too much calculation. In order to improve the computational efficiency of structural robustness analysis, the binary series approximation technique of structural displacement is introduced into the Gaussian integral method, and a method of calculating the mean and variance of structural displacements is proposed. At the same time, the associated sensitivity calculation formula is deduced by the following vector method. An example is compared with the existing methods, which shows that this method reduces the computational complexity of the Gaussian integral method to a great extent. Compared with the Taylor series method, this method has higher computational accuracy, and its sensitivity Calculations no longer require reanalysis, less computation.