There are at least two failure modes of a bow because of stability reasons (terminology yet unclear) :
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"Snapping": Bows with narrow limbs and deep recurves will snap around because of torsional instability, making the bow difficult or impossible to brace and draw.
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"Flip flop": Bow has an instable tiller at brace height and "flip flops" around vertically between two stable configurations.
Stability is an important reason for the failure of a bow design, in addition to material failure. It would be great if some measures of stability could be calculated for each failure mode that show how far the bow is from being unstable.
Determining the stability of a FEM system is not that difficult, it is typically done by investigating the determinant of the tangent stiffness matrix or equivalent metrics. The problem for VirtualBow is that the bow is modelled planar and symmetric, so it doesn't include the degrees of freedom in which the instability might happen.
Solution 1: Secondary FEM system
Build a fully 3d fem model of the bow limb. Perform the simulation with the 2d model, apply the states to the 3d model and investigate the tangent stiffness matrix. This adds a lot of complexity.
Solution 2: Linear stiffness matrix
Maybe it would already be enough to compute a 6x6 stiffness matrix of the limb tip with regards to three spatial displacements and rotations and check the stability of that. Assume the current state of the limb as the initial state and use only linear kinematics. Inspiration: https://www.sciencedirect.com/science/article/pii/S2452321617305000
There are at least two failure modes of a bow because of stability reasons (terminology yet unclear) :
"Snapping": Bows with narrow limbs and deep recurves will snap around because of torsional instability, making the bow difficult or impossible to brace and draw.
"Flip flop": Bow has an instable tiller at brace height and "flip flops" around vertically between two stable configurations.
Stability is an important reason for the failure of a bow design, in addition to material failure. It would be great if some measures of stability could be calculated for each failure mode that show how far the bow is from being unstable.
Determining the stability of a FEM system is not that difficult, it is typically done by investigating the determinant of the tangent stiffness matrix or equivalent metrics. The problem for VirtualBow is that the bow is modelled planar and symmetric, so it doesn't include the degrees of freedom in which the instability might happen.
Solution 1: Secondary FEM system
Build a fully 3d fem model of the bow limb. Perform the simulation with the 2d model, apply the states to the 3d model and investigate the tangent stiffness matrix. This adds a lot of complexity.
Solution 2: Linear stiffness matrix
Maybe it would already be enough to compute a 6x6 stiffness matrix of the limb tip with regards to three spatial displacements and rotations and check the stability of that. Assume the current state of the limb as the initial state and use only linear kinematics. Inspiration: https://www.sciencedirect.com/science/article/pii/S2452321617305000