论文部分内容阅读
针对目前在结构可靠性计算中被广泛应用的传统响应面法存在计算量大,精确度不高,容易产生奇异解,必须知道功能函数才能计算等问题。首先根据最小二乘原理,在只需知道设计验算点对应的功能函数值的情况下,利用权函数的紧支性、非负性、光滑性、递减性等性质,在影响域内应用选取的设计验算点,提出了用移动最小二乘法通过迭代生成响应面函数,然后结合一阶可靠性方法,计算结构的最大失效点与可靠性指标。通过反复迭代,直到计算的相邻两次的可靠性指标满足所给的误差为止。给出了切实可行的算法,该算法不需要知道功能函数,甚至不需要知道功能函数的类型就可以进行计算。算例表明,文中方法以较少的迭代次数,可以获取高精度的最大失效点与可靠性指标。
In view of the fact that the traditional response surface method which is widely used in structural reliability calculation has a large amount of calculation, low accuracy and is easy to generate singular solutions, it is necessary to know that functional functions can be calculated. First of all, according to the principle of least squares, we only need to know the value of the function corresponding to the design checkpoint, then use the selected function in the influence domain, such as the tight support, the nonnegative, the smoothness and the degeneracy. Check point, the response surface function is generated by iteratively using the moving least square method, and then the maximum failure point and the reliability index of the structure are calculated by combining the first-order reliability method. Through repeated iterations, until the calculated reliability index of two adjacent times satisfies the given error. A practical algorithm is given. The algorithm does not need to know the function, and does not even need to know the type of the function to calculate. The example shows that the method can get the maximum failure point and reliability index with fewer iterations.