dc.description.abstract
A common approach for optimising the load-bearing behaviour of glued laminated timber (GLT) beams, with respect to an efficient use of the raw material, is producing combined GLT beams. Thereby, stronger boards, categorised based on a preceding strength grading method, are used for the outer layers of the beam, whereas weaker boards are used to fill the less stressed inner layers. This method, however, leaves room for improvement. Especially the omission of the real morphology of a board (e.g. knot groups and their position) and their location in the final beam setup is significant, since only this information together with the actual loading situation allows for a proper evaluation of weaknesses in the GLT beam. For example, a certain knot which reduces the strength grading class of a single board might be located in a not highly stressed region in the GLT beam and, thus, is actually negligible when considering its load-bearing behaviour. For this reason, the objective of this thesis had been to develop an optimisation strategy for GLT beams, able to take actual mechanical property distributions as well as the occurring stress states in the final GLT beam within each individual board into account. To achieve this, the GLT beams are analysed using a two dimensional finite element (FE) model, giving access to the strain and stress field of each wooden board. Subsequently, this information is exploited to find optimal GLT beam setups out of a defined sample of wooden boards. As the complexity and the computational effort of this combinatorial optimisation task quickly increases with the number of beams and wooden boards, a class of special algorithms, namely metaheuristic search methods, where introduced. In particular, local search, iterated local search, tabu search, and genetic algorithms where considered and are discussed in detail. In a first step, the algorithms are assessed on a simplified problem, which assumes homogeneous material properties for each board and, thus, allows the usage of beam theory. Next, based on this simplified model, the solvability by deterministic algorithms, instead of metaheuristic, non-deterministic algorithms is discussed. In order to solve the original problem (with inhomogeneous stiffness distributions) within a reasonable time, the evaluation of the computationally costly FE model is bypassed by defining two types of metamodels, which are capable of approximating the FE model’s results after an initial training phase on previously calculated results. All algorithms are tested multiple times, allowing a statistical validation of each method. This validation results in a preference for iterated local search, as an algorithm being capable of quickly finding moderately good results, and genetic algorithms, being capable of finding good results, however needing more computation time. Comparing the results obtained from various optimisation approaches to commonly used methods within the production of GLT beams, on average an improvement of 15 to 20% could be obtained, meaning that by using the same sample of wooden boards, the maximum deflection of the worst GLT beam is smaller by this value. Summarised, it can be said that the used metaheuristic search methods are applicable to this optimisation task and deliver good results within a reasonable time. Furthermore, due to the general nature of the proposed algorithms and definitions, they are applicable and expandable to a wide range of different optimisation tasks in timber engineering.
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