تجزیه و تحلیل المان محدود الوار شامل شاخه های - رویکردی به مدل دوره دانه و تاثیر در رفتار سازه

Wood, as a naturally grown material, is affected by growth inhomogeneities like branches. Especially in solid timber or glulam beams, knots lead to a decrease in stiffness and strength. In this contribution, approaches to model knots and the grain course in an FE-simulation are presented. Based on these methods, the influence of knots is evaluated by structural analyses. For validation, the numerical results are compared to experimental data. Since knots often initiate damage in structural timber parts, a failure criterion is applied in the area of the knots.

Recently, different numerical models to analyze wooden structures by means of an FE-analysis have been developed and published. These methods include material models on different length scales to simulate damage and failure as well as to capture the hygro-mechanical behaviour, see e.g. [1]. Most of the models are restricted to perfect timber and wood products free of inhomogeneities. To analyze timber structures made of solid or sawn timber, the existing models need to be enhanced in order to capture growth inhomogeneities like branches or knots (as branches are called in construction timber). Besides, even wood products like glue-laminated timber are affected by branches since every layer is made of sawn timber containing knots. Regarding glue-laminated girders, layers in the tensile zone are most likely to fail outgoing from knots. Fig. 1 shows failure in timber boards evolving from knots. Thus, the main objective of the work at hand is the combination of material models for timber with approaches to describe branches and knots in an FE-analysis.Several methods to capture inhomogeneities like branches in a structural analysis are already known. As a simple option, knots can be considered by means of reduced mechanical material parameters, e.g. the longitudinal elasticity modulus, due to a knottiness factor. According to [2], knottiness can be determined mechanically or visually [3]. By knottiness, strength classes and related material parameters are defined for a structural part made of timber. To capture local differences within a component of timber, the total knot area ratio (TKAR [4]) might be applied, whereas knottiness is determined section-wise. In [4], boards are divided into knot and clear wood sections based on the TKAR to determine a distribution of material parameters like the longitudinal elasticity modulus along the board length. The direct modelling of knots and grain deviation in an FE-analysis is even more detailed. Studies of single knots are documented e.g. in [5] and [6]. An approach to capture arbitrary knots is presented e.g. in [7]. Here, a method to capture an arbitrary number of knots varying in position and shape in structural members made of timber is presented, whereas each knot is described in particular in the FE-model. Moreover, a geometrical description and methods to numerically determine the grain course in the area of branches are introduced. The models are applied to analyze the mechanical behaviour of timber boards from [8].

In this article, models and methods to analyze timber be means of FEM are presented. Beside the numerical description of the material characteristics on a macroscopic length scale, an approach to consider branches and knots in the structural analysis as well is introduced. Based on a geometrical model, the fibre direction is determined numerically in the area of knots by the so-called Stream Line Approach. A direct validation by experimentally measured fibre orientations has to be done in the future. Therefore, the tracheid effect might be applied [32] and [33]. This kind of experimental investigation is very complex and costly and was performed only for small specimen until now. However, the comparison to experimentally tested timber boards shows that the method delivers reliable results. With the determined fibre course, structural responses regarding loading are computed. The knots are described in a regular FE-mesh by integration points. This method has numerical benefits and is shown to be reliable, at least in the elastic regime. Aspects of how to model knots, as holes or filled with material, and the connection of knots and surrounding wood remain open questions and subjects of future work. For modelling failure initiated by knots, plasticity formulations and cohesive elements are applied. It is shown, that the regular mesh works well in combination with plasticity. However, to simulate brittle failure at tensile loading cohesive elements should be applied. To distinguish knots and surrounding wood, an automatic meshing procedure for timber boards is introduced. This Stream Line meshing is restricted to boards without splay knots located far from pith until know. The development of the SL-meshing is work in progress. By using equipotential lines similar to the stream lines, meshing in transverse direction can be improved. By using quadratic shape functions with 20-node-elements, streamline curves and knot shapes could be modelled more accurately. In addition, a suitable adaptive meshing procedure will be developed to simulate brittle failure [28]. The crack path can be determined more precisely by using a mesh modification as in [27], The application of the models to experimentally tested timber boards shows that the methods work well. However, the numerical results depend on the chosen material properties. The choice of these parameters is always questionable since the data available are restricted. Beside, the properties are naturally varying. By introduction of appropriate uncertainty models, this lack of information can be considered in a structural analysis as well [13]. This development is work in progress and will be published in the near future.