ABSTRACT
Performance of structure will change dramatically as local damage or strengthen happens, and performance function will become unsmooth. Obviously, the time dependent reliability analysis for this kind of structure becomes very difficult. In this work, time dependent reliability analysis method for structure with performance mutations 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 consists of Dirac δ function. In virtually, this equation is a piecewise partial difference equation with infinite coefficient, and is very difficult to solve. Thirdly, approximation by Dirac δ sequences is introduced into the analytical solution of GDEE, 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 mutations is proposed. 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.
