Abstract: Gaussian copula hypothesis is used for the traditional Rackwtiz-Fiessler method; Meanwhile, the traditional reliability calculations in first order reliability methods(FORM) always have to be conducted in independent standard normal space. So the generalized Rackwitz-Fiessler method is presented based on the elliptical copula family. This generalized Rackwitz-Fiessler method can accomplish the transformation of random vector from physical random space to the standard spherical space. In order to make the FORM be suitable to this new standard spherical space, the geometrical interpretation of reliability index in independent standard normal space is extended to standard spherical space. Examples show that the generalized method is more applicable than traditional method, and the calculated failure probability is also closer to the real case under the sufficient dependence information.

Key words: generalized Rackwitz-Fiessler method;Gaussian copula hypothesis;elliptical copula hypothesis;generalized first order reliability method