Generalised scaled boundary isogeometric analysis - a method for structural analysis of naturally shaped timber structures

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.