On stochastic finite elements for structural analysis

A stochastic finite element method for fatigue reliability analysis of gear teeth subjected to bending

“…Recently, the SFEM has been extensively used in the static and dynamic structural analysis (Shinozuka and Wen 1972;Shinozuka and Astill 1972;Araujo and Awruch 1994;Sanker et al 1993). In addition, by incorporating certain reliability analytical model, the SFEM can be applied as the most effective means for the reliability analysis of complex structural systems with uncertain system parameters (Mahadevan 1992;Brenner and Bucher 1995).…”

Probabilistic analysis of linear elastic cracked structures with uncertain damage

“…Moreover, even for low level of uncertainty, they are not capable to provide for the skewness of the probability density function of the structural response, which is usually strongly non-Gaussian also in the linear case with uncertain parameters modelled as Gaussian. To overcome these shortcomings, improved procedures have been developed (see for example [3][4][5][6][7][8]), aiming at enhancing accuracy while keeping tolerable the computational cost. Recently, a very interesting approach for the probabilistic characterization of truss structures with uncertain geometrical and mechanical properties has been proposed in [9].…”

Chaos–Galerkin solution of stochastic Timoshenko bending problems

“…In early approaches, finite element solutions were obtained via Monte Carlo simulation: samples of random system response were computed based on samples of random system parameters. Perturbation and Galerkin methods were used in this context [7]. These methods allowed representation of uncertainty in system parameters by means of random fields.…”