Application of stochastic finite element approaches to wood-based products

Abstract

Due to the natural growing process of wood, the mechanical properties of wooden boards are subject to high variability, mainly introduced by knots and the resulting deviation of the wood fibre directions around them. This variability has a great impact on the serviceability limit state performance of wood-based products, such as glued-laminated timber, and thus should be considered within design concepts. Numerous applications of random process models for numerically representing the fluctuation of the mechanical properties along wooden boards can be found in the literature. But, the corresponding mechanical probabilistic investigation, however, is limited almost exclusively to Monte Carlo simulations so far. For this reason, the focus of this work is laid on alternative probabilistic approaches, in particular the perturbation and the spectral stochastic finite element method. Both methods are combined with several discretization methods for the random process, programmed in a consistent environment, and compared to the Monte Carlo simulation, regarding computational effort as well as quality of results. For this purpose, the second-order moments (mean and standard deviation) of the system response of a glued-laminated timber beam with random lamination stiffness are computed. The performance of the different approaches is compared and, in particular, the influence of the variability of the ‘raw’ material on the structural response is shown. Well-known effects, such as the decrease in the variability of effective properties of GLT with increasing number of lamellas, are numerically reproduced and quantified. Moreover, a significant influence of the correlation length, specifying the rate of material property fluctuation within each lamella, on the effective stiffness of the resulting glued-laminated timber beams is demonstrated.