PROJECTION FLEXION-TORSION

Connection type PROJECTION FLEXION-TORSION provides a rotational connection between two nodes. It models the bending and twisting of a cylindrical coupling between two shafts. In this case the response to twist rotations about the shafts may differ from the response to bending of the shafts. Connection type PROJECTION FLEXION-TORSION is similar to connection type FLEXION-TORSION. Whereas the FLEXION-TORSION connection has rotation parameterization angles consisting of total flexion, torsion, and sweep, the PROJECTION FLEXION-TORSION connection has rotation parameterization angles consisting of two component flexion angles and a torsion angle. The flexion angle of the FLEXION-TORSION connection is the resultant flexion angle resulting from the two component flexion angles of the PROJECTION FLEXION-TORSION connection. Connection type PROJECTION FLEXION-TORSION cannot be used in two-dimensional or axisymmetric analysis.

The flexural part of the connection resists angular misalignment of the two shafts, whereas the torsional part of the connection resists relative rotations about the shafts. Connection type PROJECTION FLEXION-TORSION can be used in conjunction with connection type PROJECTION CARTESIAN when modeling the response of bushing-like or spot-weld-like components.

Related Topics
Connector elements
Connector element library
In Other Guides
*CONNECTOR BEHAVIOR
*CONNECTOR SECTION

ProductsAbaqus/StandardAbaqus/ExplicitAbaqus/CAE

Description

Figure 1. Connection type PROJECTION FLEXION-TORSION.

The PROJECTION FLEXION-TORSION connection does not impose kinematic constraints. The PROJECTION FLEXION-TORSION connection describes a finite rotation by three angles: flexion 1, flexion 2, and torsion (α1, α2, and β). However, the flexion 1, flexion 2, and torsion angles do not represent three successive rotations. The two component flexion angles (α1 and α2) make up the total flexion angle between two shafts and measure the angle of misalignment of the two shafts. The torsion angle measures the twist of one shaft relative to the other.

The first shaft direction at node a is e3a, and the second shaft direction at node b is e3b. Let the two shafts form an angle α, called the total flexion angle. Then,

α=cos-1(e3ae3b),    where    0απ.

The flexion angle is a rotation by α about the (unit) rotation vector,

q=1sinαe3a×e3b,    where    sinα=e3a×e3b.

The PROJECTION FLEXION-TORSION connection is formulated in terms of the unit vector normal to a plane, e3, and two unit vectors spanning this plane, e1 and e2. See Figure 1. The plane with normal vector e3 is referred to as the flexion-torsion plane. The component flexion angles α1 and α2 are determined from α and q by projection onto the two in-plane directions:

α1=α(e1q)    and    α2=α(e2q).

The torsion angle in a PROJECTION FLEXION-TORSION connection can be understood from a finite successive rotation parameterization 3–2–3. In terms of the 3–2–3 parameterization the total flexion angle is the second successive rotation angle, and the torsion angle is the sum of the first and third successive rotation angles. The torsion angle β between the two shafts is defined as

β=tan-1(e2ae1b-e1ae2be1ae1b+e2ae2b)+mπ,

where positive torsion angles are rotations about the positive e3-direction and m is an integer.

The PROJECTION FLEXION-TORSION connection avoids the singularity that occurs in the sweep angle of the FLEXION-TORSION connection when the total flexion angle α vanishes. As a result, the PROJECTION FLEXION-TORSION connection is better suited for defining bushing-like behavior for flexion response that varies with the direction of q in the flexion-torsion plane.

The available components of relative motion ur1, ur2, and ur3 are the changes in the two flexion angles and the torsion angle and are defined as

ur1=α1-α10,    ur2=α2-α20,    and    ur3=β-β0,

where α10, α20, and β0 are the initial flexion component angles and torsion angle, respectively. The connector constitutive rotations are

ur1mat=α1-θ1ref,    ur2mat=α2-θ2ref,    and    ur3mat=β-θ3ref.

The kinetic moment in a PROJECTION FLEXION-TORSION connection is

mprojflex-tor=m1e1+m2e2+m3e3.

Summary

PROJECTION FLEXION-TORSION
Basic, assembled, or complex: Basic
Kinematic constraints: None
Constraint moment output: None
Available components: ur1,ur2,ur3
Kinetic moment output: m1,m2,m3
Orientation at a: Required
Orientation at b: Optional
Connector stops: θ1minα1θ1max,
  θ2minα2θ2max,
  θ3minβθ3max
Constitutive reference angles: θ1ref,θ2ref,θ3ref
Predefined friction parameters: None
Contact force for predefined friction: None