映射变换法的收敛性证明及其在抗力分项系数计算中的应用

Proof of convergence of mapping transformation method and its application to calculation of partial safety factor for resistance

通过对映射变换法的迭代计算步骤进行分析,证明映射变换法可以避免设计验算点超出随机变量定义域情况的出现,保证迭代收敛.在此基础上,探讨了映射变换法在计算分项系数设计表达式的抗力平均值及相应的抗力分项系数中的应用,给出了采用映射变换法计算抗力平均值的迭代计算步骤与相关公式.算例分析表明,该方法在避免设计验算点超出随机变量定义域、保证迭代收敛方面是有效和可行的,且易于利用计算机程序实现.

Through analyzing the iterative calculation steps, it is proved that mapping transformation method could avoid the case of that the design checking point to be beyond the domain of random variables and ensure the convergenece. On this basis, the application of mapping transformation method to the calcula- tion of mean resistance and its corresponding partial safety factor was discussed. The iterative calculation steps and formula for calculating mean resistance by mapping transformation method were given. The case studies show that the mapping transformation method is not only effective and feasible in avoiding the case that the design checking point is beyond the domain of random variables , but also easy to program.