Isotropic growth model for generalized scaled boundary isogeometric analysis on slender structures

• Published in: Proceedings in applied mathematics and mechanics Vol. 24; no. 2
• Main Authors: Spahn, Florian, Kolisch, Florian, Praster, Maximilian, Balmayor, Elizabeth Rosado, Klinkel, Sven
• Format: Journal Article
• Language: English
• Published: 01.08.2024
• ISSN: 1617-7061; 1617-7061
• DOI: 10.1002/pamm.202400200

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.