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

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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.

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Acknowledgments

The authors gratefully acknowledge the financial support of the Austrian Research Promotion Agency (FFG, project number 832803 and 839858) and the wood industry partner CEI-Bois (through the platform ‘Building with Wood’) for funding the research work within project ‘MechWood 2’. Moreover, the authors want to thank Prof. Anders Olsson from Linæus University for his valuable feedback.

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  1. Institute for Mechanics of Materials and Structures, TU Wien, Karlsplatz 13, 1040, Vienna, Austria

    Georg Kandler, Josef Füssl & Josef Eberhardsteiner

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  1. Georg Kandler
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Correspondence to Georg Kandler.

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Kandler, G., Füssl, J. & Eberhardsteiner, J. Stochastic finite element approaches for wood-based products: theoretical framework and review of methods. Wood Sci Technol 49, 1055–1097 (2015). https://doi.org/10.1007/s00226-015-0737-5

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