Joint Creation and Demonstration in LS-DYNA

Aim:

To demonstrate spherical, revolute, cylindrical, and translational joints between two rigid bodies and two deformable bodies. 

Theory:

A distinguishing feature of multibody systems is the presence of joints that impose constraints on the relative motion of the various bodies of the system. Most joints used in practical applications can be modelled in terms of the so-called lower pairs like spherical, revolute, cylindrical, and translational joints.

Spherical Joint:

The spherical joint is used for allowing free rotation in two planes at the same time while preventing translation in any direction, including rotating in those planes. The relative motion of the rigid bodies is constrained so that nodes that are initially coincident remain coincident. In the below figure, the socket’s node is not interior to the socket—LS-DYNA does not require that a rigid body’s nodes be interior to the body.

Revolute Joint:

A revolute joint is one degree of freedom kinematic pair used frequently in mechanisms and machines. The joint constrains the motion of two bodies to the pure rotation along a common axis. As shown in the below figure, Nodes 1 and 2 are coincident; nodes 3 and 4 are coincident. Nodes 1 and 3 belong to rigid body A; nodes 2 and 4 belong to rigid body B. The relative motion of the two rigid bodies is restricted to rotations about the axis formed by the two pairs of coincident nodes. This axis is labelled the “centerline”.

Cylindrical Joint:

A cylindrical joint is two degrees of freedom kinematic pair used in mechanisms. It provides a single-axis sliding function as well as a single axis rotation, providing a way for two rigid bodies to translate and rotate freely. This joint is derived from the rotational joint by relaxing the constraints along the centerline. This joint admits relative rotation and translation along the centerline as shown in the below figure.

Translational Joint:

A Translational joint provides a linear sliding movement between two bodies. This is a cylindrical joint with the third pair of off-centerline nodes which restrict rotation. Aside from translation along the centerline, the two rigid bodies are stuck together.

Procedure:

The different types of joints are created between two rigid bodies in LS-DYNA using the keyword *CONSTRAINED_EXTRA_NODES and between two deformable bodies using *CONSTRAINED_NODAL_RIGID_BODY.

1. Joints between Two Rigid Bodies:

1) Spherical Joint:

1) Open LS-PrePost, using options under Element and Mesh->Shape Mesher-> Entity->Sphere Shell, create two parts as shown in the below figure. The elements of the outer sphere shell are deleted using option Element editing to get the necessary shape.

2) The material and section are assigned to the parts. For material, the *MAT_RIGID card is used.

3) A pair of nodes is created using the option under Element Tools->Node Editing->Create, i.e node 305 and 306. Node 305 is constrained to part 1 and node 306 to part 2 using *CONSTRAINED_EXTRA_NODES card as shown in the below images.

4) The spherical joint is created using *CONSTRAINED_JOINT_SPHERICAL card with one node pair i.e node N1 is 305 for part 1 and Node N2 is 306 for part 2.

5) The initial velocity of 20 mm/ms is assigned to the moving part in the rotational X, Y, Z-axis.

6) The *CONTROL_TIMESTEP Card is activated with the value of the Initial time step size (DTINIT) is set as 0.01 ms.

7) The *CONTROL_TERMINATION is given with termination time is set as 5 ms.

8) The keyword file is saved using the suitable name with the ‘.k’ extension and made to run in LS-DYNA run.

2) Revolute Joint:

1) Open LS-PrePost, using options under Element and Mesh->Shape Mesher-> Entity->4N Shell, create two parts as shown in the below image.

2) The material and section properties assigned to the parts are the same as that of the spherical joint.

3) Two pairs of nodes are created using the option under Element Tools->Node Editing->Create, i.e node 101-102 and 103-104. The nodes 101 and 103 is constrained to part 1 and nodes 102 and 104 to part 2 using *CONSTRAINED_EXTRA_NODES card as shown in the below image.

4) The revolute joint is created using *CONSTRAINED_JOINT_REVOLUTE card with nodes N1 and N3 of part 1 and nodes N2 and N4 of part 2.

5) The nodes of part 1 as shown in the below image is constrained in all degrees of freedom.

6) The *BOUNDARY_PRESCRIBED_MOTION_NODE card is given at the node on part 2 as shown in the image given below. Also, the LCID or curve ID is given.

7) The control timestep is defined using the LCTM curve as shown below image.

8) The termination time is set to 10 ms. The keyword file is saved using the suitable name with the ‘.k’ extension and made to run in LS-DYNA run.

3) Cylindrical Joint:

1) Open LS-PrePost, using options under Element and Mesh->Shape Mesher-> Entity->Cylinder Shell, create two parts as shown in the image given below.

2) The material and section properties assigned to the parts are the same as that of the spherical joint.

3) Two pairs of nodes are created using the option under Element Tools->Node Editing->Create, i.e node 321-322 and 323-324. Nodes 321 and 323 are constrained to part 1 and nodes 322 and 324 to part 2 using the *CONSTRAINED_EXTRA_NODES card.

4) The cylindrical joint is created using *CONSTRAINED_JOINT_CYLINDRICAL card with nodes N1 and N3 of part 1 and nodes N2 and N4 of part 2.

5) The initial velocity of 10 mm/ms is assigned to part 1 in the X-axis.

6) The value of the Initial time step size (DTINIT) is set as 0.01 ms which is the same as the spherical joint. The termination time is set as 5 ms. Finally, the keyword file is saved using a suitable name with the ‘.k’ extension and made to run in the LS-DYNA run.

4) Translational Joint:

1) Open LS-PrePost, using options under Element and Mesh->Shape Mesher-> Entity->Box Shell, create two parts as shown in the image given below.

2) The material and section properties assigned to the parts are the same as that of the spherical joint.

3) To define the Translational joint three pairs of nodes are created. Using the option under Element Tools->Node Editing->Create, two pairs of nodes are created 1001-1002 and 1003-1004 which is coincident and collinear. The third pair 1005-1006 is coincident and slightly away from the axis of the other two pairs but in-between the two pairs. The nodes 1001, 1003 and 1005 are constrained to part 1 and nodes 1002, 1004 and 1006 to part 2 using *CONSTRAINED_EXTRA_NODES card.

4) The translational joint is created using *CONSTRAINED_JOINT_TRANSLATIONAL card with nodes N1, N3 and N5 of part 1 and nodes N2, N4 and N6 of part 2.

5) The initial velocity of 10 mm/ms is assigned to part 1 in the X-axis same as the cylindrical joint.

6) The value of the Initial time step size (DTINIT) is set as 0.01 ms which is the same as the spherical joint. The termination time is set as 5 ms. Finally, the keyword file is saved using a suitable name with the ‘.k’ extension and made to run in the LS-DYNA run.

2. Joints Between Two Deformable Bodies:

The steps required to create a joint between two deformable bodies are the same as that of rigid bodies except few changes i.e,

*MAT_ELASTIC material card is used instead of *MAT_RIGID card.

2) Instead of using *CONSTRAINED_EXTRA_NODES card *CONSTRAINED_NODAL_RIGID_BODY (CNRB) is used to constrain the nodes to the necessary part.

3) The initial velocity is assigned using *INITIAL_VELOCITY card instead of *INITIAL_VELOCITY_RIGID_BODY card.

1) Spherical Joint:

1) The parts for spherical joint are created and assigned with section and material properties similar to the spherical rigid joints, but the *MAT_ELASTIC card is used instead of the rigid one.

2) Using Create Entity>>Constrained>>Nodal Rigid Body (CNRB) option the nodes generated are linked between two deformable parts for creating a spherical joint.

3) The spherical joint is created using *CONSTRAINED_JOINT_SPHERICAL card with one node pair i.e node N1 is 305 for part 1 and Node N2 is 306 for part 2.

4) The initial velocity of 20 mm/ms is assigned to the moving part in the rotational X, Y, Z-axis same as spherical rigid joints.

5) The value of the Initial time step size (DTINIT) is set as 0.01 ms which is the same as the spherical joint. The termination time is set as 5 ms. Finally, the keyword file is saved using a suitable name with the ‘.k’ extension and made to run in the LS-DYNA run.

2) Revolute Joint:

1) The parts for the revolute joint are created and assigned with section and material properties, but the *MAT_ELASTIC card is used instead of the rigid one.

2) Two pairs of nodes are created using the option under Element Tools>>Node Editing>>Create, i.e node 101-102 and 103-104. The nodes 101 and 103 is constrained to part 1 and nodes 102 and 104 to part 2 using *CONSTRAINED_NODAL_RIGID_BODY under the create Entity option.

3) The revolute joint is created using *CONSTRAINED_JOINT_REVOLUTE card with nodes N1 and N3 of part 1 and nodes N2 and N4 of part 2. The nodes of part 1 are constrained in all degrees of freedom using boundary SPC set and boundary prescribed motion is assigned to node 173 similar to revolute rigid joints.

4) The control timestep is defined using the LCTM curve same as the rigid revolute joints and the termination time is set as 10 ms.

5) Finally, the keyword file is saved using a suitable name with the ‘.k’ extension and made to run in the LS-DYNA run.

3) Cylindrical Joint:

1)  The parts for the cylindrical joint are created and assigned with section and material properties, but the *MAT_ELASTIC card is used instead of the rigid one.

2) Two pairs of nodes are created using the option under Element Tools>>Node Editing>>Create, i.e node 321-322 and 323-324. The nodes 321 and 323 are constrained to part 1 and nodes 322 and 324 to part 2 using *CONSTRAINED_NODAL_RIGID_BODY under the create Entity option.

3) The cylindrical joint is created using *CONSTRAINED_JOINT_CYLINDRICAL card with nodes N1 and N3 of part 1 and nodes N2 and N4 of part 2.

4) The initial velocity of 10 mm/ms is assigned to part 1 in the X-axis same as the rigid cylindrical joint.

5) The value of the Initial time step size (DTINIT) is set as 0.01 ms which is the same as the spherical joint. The termination time is set as 5 ms. Finally, the keyword file is saved using a suitable name with the ‘.k’ extension and made to run in the LS-DYNA run.

4) Translational Joint:

1)  The parts for the translational joint are created and assigned with section and material properties, but the *MAT_ELASTIC card is used instead of the rigid one.

2) To define the Translational joint three pairs of nodes are created. Using the option under Element Tools>>Node Editing>>Create, two pairs of nodes are created 1001-1002 and 1003-1004 which is coincident and collinear. The third pair 1005-1006 is coincident and slightly away from the axis of the other two pairs but in-between the two pairs. The nodes 1001, 1003 and 1005 are constrained to part 1 and nodes 1002, 1004 and 1006 to part 2 using *CONSTRAINED_NODAL_RIGID_BODY under the create Entity option.

3) The translational joint is created using *CONSTRAINED_JOINT_TRANSLATIONAL card with nodes N1, N3 and N5 of part 1 and nodes N2, N4 and N6 of part 2.

4) The initial velocity of 10 mm/ms is assigned to part 1 in the X-axis same as the rigid translational joint.

5) The value of the Initial time step size (DTINIT) is set as 0.01 ms which is the same as the spherical joint. The termination time is set as 5 ms. Finally, the keyword file is saved using a suitable name with the ‘.k’ extension and made to run in the LS-DYNA run.

Results:

1. Joints between Two Rigid Bodies:

1) Spherical Joint:

2) Revolute Joint:

3) Cylindrical Joint:

4) Translational Joint:

2. Joints Between Two Deformable Bodies:

1) Spherical Joint:

2) Revolute Joint:

3) Cylindrical Joint:

4) Translational Joint:

Conclusion:

1) The keyword files necessary to demonstrate spherical, revolute, cylindrical, and translational joints between two rigid bodies using the *CONSTRAINED_EXTRA_NODES card in LS Pre-Post.

2) Also, the keyword files necessary to demonstrate spherical, revolute, cylindrical, and translational joints between two deformable bodies are created in LS Pre-Post using the *CONSTRAINED_NODAL_RIGID_BODY card.

3) Finally, we have simulated all joints for two rigid bodies and two deformable bodies using the LS-Run. We also obtained the animations for all the joints for both rigid bodies and deformable bodies.