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Reliability analysis method for convex set structures based on reduced base concept

DOI：

 作者 单位 E-mail 张正 吉首大学土木工程与建筑学院 zz419600@126.com 吴曼颖 吉首大学土木工程与建筑学院 wumanying911@126.com 毕仁贵 吉首大学物理与机电工程学院

针对椭球凸集参数域结构的可靠性分析问题，提出了一种基于减基概念的快速求解方法。该方法首先将椭球参数域进行坐标正交变换，获得标准的椭球域及其相应的矩形域，在矩形域采样且通过坐标逆向变换获得原椭球参数域的样本参数点集，并以此构建结构的减基空间及其相应的减基算法，随后在标准椭球域产生均匀的等概率抽样点，并通过坐标逆向变换和相应的减基算法进行蒙特卡洛减基模拟来分析结构的可靠度及其可靠域。该方法由于是在低维的逼近空间中进行椭球参数域结构的位移向量解分析，故而较之有限元法能够获得较大的计算效率。文中的算例测试并验证了该方法的有效性。

Aiming at the reliability analysis of parameter structure with ellipsoidal convex set, a fast solution method is proposed based on the reduced basis concept. Firstly, the standard ellipsoid domain and its packaged rectangular domain are obtained by the orthogonal coordinate transformation in the original ellipsoid parameter domain. Secondly, sampling is conducted in the rectangular domain and the sample parameter point set is obtained in the original ellipsoid parameter domain by the inverse coordinate transformation, and then the structural reduction space and its associated reduction algorithm are constructed. Subsequently, the uniform sampling points with equal probability are conducted in the standard ellipsoid domain, and then the reliability and its reliable domain of the structure are analyzed by Monte Carlo reduction simulation using the inverse coordinate transformation and corresponding reduction algorithm. Because this method is used to analyze the displacement vector solutions of parametric structure with ellipsoidal convex set in low-dimensional approximation space, it is more efficient than the finite element method. An example is given to test and verify the effectiveness of the proposed method.
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