Reply To: Dynamic Analysis of a bow

[peteroznewman]

Hello Philipp,

Transient Structural can solve this problem using multiple steps. Let’s agree on a coordinate frame: X is horizontal along the direction the arrow will shoot, Z is also horizontal and Y is vertical.

First, draw the bow in CAD using its 3D solid shape before the bowstring had been attached because the unstrung bow shape has no stress, which is the assumption at the beginning of all typical Static Structural models. 

Let’s make some simplifying assumptions for this first model. Assume the bow is symmetric top to bottom and left to right.  Assume the bow is made of a uniform isotropic material.  The bow should be thick near the handle and taper toward the ends. Draw the bow string from tip to tip using a line between the ends of the unstrung bow. You may use any CAD system to draw the 3D unstrung bow shape, but you must be in SpaceClaim (or DesignModeler) to draw the bowstring line because you need to assign a cross-sectional property to the string, which will be a circle with the diameter of the bowstring. Also draw the arrow body. For simplicity, let that also be a line body with a circular diameter equal to the arrow body. The arrow tail should be located at the place where the string will be on the X axis after it has been pulled back to shoot the arrow.

Create two planes of symmetry to reduce the geometry to 1/4 of the size of the full 3D shape. One plane is horizontal to cut the bow into a top and bottom half, one plane is vertical to cut the bow into a left and right half. Delete all the solid bodies except for the top right piece.

Create another horizontal plane some short distance above the center plane to cut the bowstring. In step1 of the simulation, this end of the bowstring will be pulled down along the Y axis to the center plane, flexing the bow and creating tension in the bowstring.

In Mechanical, insert a Symmetry region on the XY plane and set that to have a Z normal and select the cut face in that vertical plane. Select the horizontal cut face at the center of the handle and apply a Fixed Support.

Use a Displacement to pull the end of the bowstring down along the Y axis by the distance that the string was cut above the horizontal center plane. The end of the bowstring will also have a Z = 0 setting in the Displacement BC to keep the string centered, but the X direction will be Free.

Use a Displacement BC on the arrow tip and tail that sets Y and Z to 0 and leaves X Free.  In Engineering Data, set the Density of the arrow to be 1/4 of the true density because we want the mass of the arrow to be only 1/4 of its true mass because we are only simulating 1/4 of a bow.  In Engineering Data, set the density of the bowstring to be 1/2 of the true density because we are only simulating 1/2 of the bowstring since only one symmetry plane cuts the string while two symmetry planes cuts the arrow.

In step 2 of the simulation, the string is pulled back to the tail of the arrow, further flexing the bow.  In step 3 of the simulation, contact between the string and the arrow, which was deactivated for steps 1 and 2, is made active. Finally in step 4 of the simulation, the Displacement that pulled the string back is deactivated and the dynamic event of the arrow launch is simulated.

Steps 1, 2 and 3 all have an analysis setting of Time Integration Off, which means they behave like Static Structural where time has no physical meaning. Step 4 has Time Integration On so that the tension in the string accelerates the mass of the arrow.

This is how I imagine the simulation might be built. I haven’t tried this myself, so some modifications may be required to get it to work. There are other ways that this can be accomplished. Let us know how it is going.