Stochastic Finite Elements Via Response Surface: Fatigue Crack Growth Problems

A stochastic finite element method based on an extended response surface technique is coupled with fracture mechanics concepts to evaluate the lifetime of a cracked structural component subjected to cyclic loading. For a complex structure the relationship between the fracture mechanics parameters and the crack depth can only be obtained by numerical approaches based on the discretization of the continuum into finite elements. As a consequence, any random field describing the stochastic nature of the input parameters has to be discretized into stochastic finite elements. An extended response surface approach is used to characterize in closed form the numerical input-output stochastic relationship. This information is used to define a fatigue crack growth model for the evaluation of the lifetime probability distribution function.