Pseudo_Rigid_Body_Flexible_Beam

Pseudo-Rigid Body for Flexible Beam Analysis

Overall Summary

The code models a structure consisting of 10 connected segments. Joints are placed between the segments with constraints that allow some degrees of freedom. A force-driven node is defined at the end, with forces applied and ramped up over time. The study runs an inverse dynamics simulation with force-dependent kinematics, aiming to analyze how forces act on the structure as it moves according to a predefined driver.

Overview of the code:

1. Global Reference Frame

• A global reference frame (GlobalRef) is defined for the whole model.
• A visual reference frame is created, with Visible = On and a small scale for display (ScaleXYZ = {0.05, 0.05, 0.05}).

2. Segments Definition (AnySeg)

• The code defines 10 segments (S1 to S10). These segments likely represent sections of a mechanical structure like a beam or limb.
• r0 defines the position of the segment in 3D space.
• Mass is set to 0, which means these segments are massless.
• Jii (moments of inertia) are also set to zero, indicating no rotational inertia is considered for these segments.
• Each segment has two reference nodes (N1 and N2), representing the start and end points of the segment.
• AnyDrawPLine is used to visually draw each segment, with a specified color (RGB = {0.92, 0.77, 0.07}).

3. Joints Between Segments (AnyStdJoint)

• The segments are connected through standard joints (AnyStdJoint), with the first joint (GRefS1) connecting the global reference frame to the first segment.
• For the joints between segments (e.g., S1S2, S2S3), constraints are defined. These constraints describe how the segments are connected, with some degrees of freedom fixed (Hard) and others dependent on forces (ForceDep).
• Reaction.Type defines whether or not reaction forces are applied in different directions.

4. Force and Springs

• A folder (ForceAndSprings) contains definitions for forces applied in the system.
• Stiffness is defined as a constant value for the springs connecting the segments, with a negative value indicating a restoring force.
• The ConstraintForce simulates the force between the last segment (S10) and a driven node (DriveNode). This force is applied with a gradual ramp-up using cosine functions.
• There is also an alternative method (ConstraintForce2) provided for applying the constraint force, but it is commented out.

5. Driver Definition (Driver)

• A driver (driver_tip) is defined to move the tip of the system (the last segment S10).
• This driver specifies target positions (DriverPos = {0.5, -0.3, 0, 0, 0, 0}) for both linear and rotational components.

6. Study Setup

• An AnyBodyStudy object is defined, which sets up the inverse dynamics simulation.
• Gravity is set to zero (Gravity = {0, 0, 0}), meaning this is a gravity-free simulation.
• The simulation runs from time tStart = 0 to tEnd = 1, with nStep = 200 steps.
• The inverse dynamics study involves force-dependent kinematics (ForceDepKinOnOff = On), with specific perturbation and step sizes for the Newton method.

7. Output (Commented)

• An AnyOutputFile is prepared but commented out. If uncommented, this section would save the positions of the segment reference nodes and some characteristics (like stiffness) to a file named example.txt.

Please cite this as:

@Article{biomechanics4030040,
AUTHOR = {Hahnemann, Yannis and Weiss, Manuel and Bernek, Markus and Boblan, Ivo and Götz, Sebastian},
TITLE = {Advancing Biomechanical Simulations: A Novel Pseudo-Rigid-Body Model for Flexible Beam Analysis},
JOURNAL = {Biomechanics},
VOLUME = {4},
YEAR = {2024},
NUMBER = {3},
PAGES = {566--584},
URL = {https://www.mdpi.com/2673-7078/4/3/40},
}