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Natural building materials, such as naturally shaped tree trunks, have been used in construction since ancient times. Wood is primarily processed as a long, thin product due to its growth and structure, leaving many parts unused. These neglected parts, like branches, can be used for load-bearing structures. However, they require a new parametric description due to material and geometric behaviour differences. It's crucial to transfer these geometries into the calculation model accurately. The surface is described using NURBS based on image data to realise this. Applying the Scaled Boundary Isogeometric Analysis (SBIGA) can directly use these geometries for structural analysis. This method combines the concepts from the scaled boundary finite element method (SBFEM) with the isogeometric analysis (IGA). In this technique, two-dimensional surfaces are scaled to a centre point. When used in the context of thin, long structures, obtuse-angled polyhedrons occur within a patch, leading to numerical condition problems. This motivates this contribution to modify the conventional SBIGA towards a generalised scheme. This work introduces a generalised SBIGA approach, employing a scaling centre line instead of a scaling centre point. This enables the analysis of slender, curved objects without additional structure partitioning, simplifying the preprocessing while improving the performance. [ABSTRACT FROM AUTHOR]

Components for timber constructions are usually based on simple geometrical shapes. In the production, bifurcated or curved components of the tree crown remain unused. Recently, building botany has evolved as a new discipline of living construction design. Therefore, trees are lead in the right shape to join as a load‐bearing structure interconnected with conventional parts. For the structural analysis, geometric features such as curvature or bifurcations exhibit unique static capabilities. It is crucial to transfer these geometries into the calculation model accurately. The structure can be depicted through three‐dimensional scanning techniques. A fundamental model (point cloud) is created in this process. This is the base for a Non‐uniform rational B‐spline (NURBS) model, existing as a 2D surface within a 3D space. Using the novel generalized scaled boundary isogeometric analysis (GSBIGA)‐approach, numerical disadvantages of conventional scaled boundary methods can be reduced. This method employs a scaling center line instead of a scaling center point. A growth simulation is used to describe the leading process. The present approach is based on an isotropic growth model applied to wooden growth applications. Therefore, the deformation gradient is split multiplicatively into an elastic and a growth part. The formulation for modeling volumetric growth is located on the kinematic level. [ABSTRACT FROM AUTHOR]

Combining tradition and innovation, timber plays essential roles in building structures for architecture and engineering. Tree branching geometries and timber in its natural state often serve as sources of inspiration. However, the mechanical properties of naturally grown timber, inherently inconsistent and geometrically varied, remain insufficiently studied, particularly for construction and simulations. This knowledge gap perpetuates the prevalent use of straight, uniformly harvested timber while neglecting curved and bifurcated elements with smaller cross-sections. This research investigates the potential of naturally grown timber in structural design, emphasizing the importance of understanding the natural characteristics and growth patterns of trees to optimize timber use. The developed methodology leverages noninvasive technologies, such as computerized tomography (CT), to precisely capture the geometrical and material properties of wood. These data sources are then integrated to visualize cross-sectional geometries and material properties, forming the basis for our analytical approach. Utilizing generalized scaled boundary isogeometric analysis, the methodology enhances the accuracy and efficiency of simulations, aligning structural design with natural growth principles. This approach not only fosters sustainable resource practices by promoting the use of major tree parts but also transforms discarded materials into valuable resources. The paper concludes with a demonstration of this methodology applied in a practical construction scenario. [ABSTRACT FROM AUTHOR]