TIME-DEPENDENT RELIABILITY ANALYSIS OF STRUCTURE WITH PERFORMANCE MUTATIONS BASED ON PROBABILITY DENSITY EVOLUTION METHOD AND ITS APPLICATION

Structural performance changes dramatically due to structure damaging or strengthening locally, and performance function becomes discontinuous, which causes much difficulty in time dependent reliability analysis. In this work, time-dependent reliability analysis method for structure with performance jump discontinuities is developed in the frame of probability density evolution theory. Firstly, Heaviside step function is introduced to rewrite a piecewise function into a general function. Secondly, a generalized density evolution equation (GDEE) for margin of ultimate limit capacity (ULC) is derived, where one of the coefficients is a Dirac #x003b4;function. In fact, this equation is a piecewise partial difference equation with infinite coefficient, which is very difficult to solve. Thirdly, approximation of Dirac #x003b4;function by Dirac #x003b4;sequences is introduced into the analytical solution of GDEE, and it becomes feasible to obtain the numerical solution for probability density function (PDF) for margin of ULC. And then, one dimensional integral formula for time dependent reliability analysis of structure with performance jump discontinuities is proposed, and the probability density evolution method (PDEM) is built up. Finally, the proposed method is used to analyze time-dependent reliability of strengthened structure, and its efficiency and precision are verified by comparing with Monte Carlo method (MCM), where a cantilever beam strengthened with carbon fiber sheet is taken as example.