Optimization of Glulam Beams with Spatially Dependent Polymorphic Uncertainty Modeling of Structural Inhomogeneity in Virtual Boards

Research output: Contribution to book/conference proceedings/anthology/reportConference contributionContributedpeer-review



Several uncertainties are induced by the natural growth of wood. The properties of timber components are affected by naturally varying material characteristics. In addition, structural inhomogeneity has to be accounted for solid wood components. Structural inhomogeneity is dependent on, e.g., natural fissures, inclusions, and especially branches that pervade wooden boards. Those pervasions result in timber boards containing multiple scattered knots.
Polymorphic uncertainty models are required to account for diverse uncertainty characteristics. Natural variability and lack of knowledge are persistent for the uncertainty modeling of natural materials, such as wood. To incorporate those aleatoric and epistemic uncertainty characteristics, uncertainty analyses are performed based on combined fuzzy and stochastic models. In this contribution, fuzzy probability based random fields are proposed as polymorphic uncertainty approach, with respect to spatial dependencies of the uncertain variables. Methods for the simulation of timber boards are introduced, where knots are established referred to the specific position of the tree trunk axis and spread over the components.
Glulam beams, containing multiple slats of wooden boards, are investigated for bending load cases as numerical example. The tensile zone is simulated with knots in the timber boards. The basic deterministic solution is performed with a local-orthotropic material formulation, with respect to the grain directions of the wood matrix and knots. Therefore, the knots are discretized separately in the FE mesh. Distinct material properties and grain directions are assigned to the discrete knots and to the surrounding wood matrix, while the grain directions are dependent on the tree trunk axis.
Both, stochastic and fuzzy models are used in field formulations for the spatially dependent polymorphic uncertainties. The knottiness of timber boards – specified by parameters of knot geometry, location and incidence – is dependent on the wood grade. In this contribution, methods for decision making of glulam beam designs are suggested. For this purpose, several design variables are examined. First, the knottiness or wood grade, where a higher grade results in reduced structural inhomogeneity, and second, the thickness of the slats in the glulam beam are considered. Both aspects influence the reliability and robustness of the component, but affect the costs. The maximum endurance of the glulam beam under bending is desired. Therefore, an optimization of the glulam beam design is performed, with respect to the multiple conflicting objectives.


Original languageEnglish
Title of host publicationProceedings in Applied Mathematics and Mechanics
Publication statusPublished - 24 Mar 2023

Publication series

SeriesProceedings in applied mathematics and mechanics : PAMM

External IDs

Mendeley 17ea655a-cc3d-36d1-bd0d-d7023d2e15ad
ORCID /0000-0002-1304-7997/work/142246694