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提出利用线性凸区概率的组合,计算结构可靠性的新方法,从而以较好的精度实现设计点附近非线性程度较高时结构可靠性的计算。以重要抽样方向为进给方向,以通过设计点和主线性逼近极限状态超平面与坐标轴的交点的方向为搜索次线性化点方向,构建线性凸区。利用事件概率方法,推导了线性凸区可靠性的计算方法,进而获得以线性凸区可靠性的组合计算结构可靠性的近似方法。算例表明方法简单可行,有效实用,具有较高的计算精度。
A new method to calculate the structural reliability by using the combination of the probability of linear convex regions is proposed to calculate the structural reliability with good accuracy near the design point with a high degree of nonlinearity. Taking the important sampling direction as the feed direction, a linear convex region is constructed by searching the direction of the sublinear point by the direction of the intersection of the design point and the principal linear approximation limit state hyperplane with the coordinate axis. Using the method of event probability, the method of calculating the reliability of linear convex regions is deduced, and the approximate method of calculating the structural reliability by the combination of the reliability of linear convex regions is obtained. The examples show that the method is simple and feasible, effective and practical, and has high computational accuracy.