Stochastic finite element approaches for wood-based products: theoretical framework and review of methods

Abstract

As a result of the natural growing process of wood, each timber lamella shows a high variability in its mechanical properties, particularly strength and stiffness. It is assumed that those properties are governed by a random process and, subsequently, that the effective stiffness of glued laminated timber also varies randomly. Therefore, a probabilistic approach is necessary. Hence, the latest achievements in probabilistic timber engineering are reviewed and compared. Numerous works rely on random process models for the representation of stiffness and/or strength distributions in single timber lamellas. The statistical evaluation of those random process models, however, is limited almost exclusively to Monte Carlo simulation (MCS) so far. Therefore, this work aims at giving an overview of alternative ways to compute the effective stiffness, by reviewing the framework of stochastic finite element methods. Random process models for the representation of the stiffness distribution in single lamellas are discussed, and the two most promising alternatives to the MCS for computation of effective stiffness parameters, the perturbation and the spectral stochastic finite element method, are evaluated in terms of accuracy and efficiency. Finally, this paper shows alternative and more efficient ways of exploring the stochastic nature of wood, delivering a new basis for more reliable design concepts for timber products.