Direct probability integral method for static and dynamic reliability analysis of structures with complicated performance functions

For structural reliability assessment, some performance functions are fairly complicated, which leads to disjoint failure domains, discontinuous structural responses and multiple design points. Thus, such a problem is difficult to be solved by some existing methods, i.e., the design point-based methods and surrogate model-based methods, etc. Although the stochastic sampling-based methods can tackle this issue, much computational effort is needed. In this paper, a novel approach, direct probability integral method (DPIM), is proposed to address static and dynamic reliability assessment for structures with complicated performance functions. The DPIM is established based on the decoupled computation of probability density integral equation and structural physical equation. Firstly, by introducing the point selection technique based on generalized F discrepancy and the smoothing of Dirac delta function, the probability density integral equation is solved directly to calculate the probability density functions (PDFs) of static and dynamic responses of structures with complicated performance functions. Then, the failure probability for static system is acquired by integrating the PDF curve of structural response over failure domain. For stochastic dynamic system, the dynamic reliability assessment is fulfilled efficiently by DPIM combining with extreme value distribution. Finally, six representative examples indicate that DPIM is much more efficient than Monte Carlo simulation to attack the reliability estimation issue of structures containing complicated performance functions. •DPIM is proposed to estimate reliability of complicated performance functions.•DPIM can efficiently fulfill reliability analysis with discontinuous structural responses.•For structural reliability analysis with MPPs, DPIM avoids complex MPPs searching.•Dynamic reliability is assessed by DPIM combining with extreme value distribution.