The Multibody Dynamics Interface

The interface (

), found under the branch (

) when adding a physics interface, is intended for analysis of mechanical assemblies. The parts in the assembly can be rigid or flexible, and are connected by various types of joints, gears, chains, springs, or dampers. Flexible parts can be defined using solid, shell, or beam elements. There are many types of joints, such as hinges or ball joints, which can be used based on the type of connection required between components. There are many types of gears, such as spur, helical, bevel, worm, or rack, which can be used for power transmission. Computed results are displacements, velocities, accelerations, joint forces, gear contact forces, and — in flexible parts — stresses. The joints can be given properties such as spring constants, damping, friction, and limits on movement. The gears pairs can also be given properties such as gear mesh stiffness, mesh damping, backlash, transmission error, and friction.

The Linear Elastic Material is the default material model. It adds the equations for the displacements in a linear elastic solid and has a Settings window to define the elastic and inertia properties of a material. As an alternative, a domain can be made into a rigid body, using the Rigid Domain material model. A rigid domain adds the rigid body dynamics equations and has a Settings window to define inertia properties of a material.

With the Nonlinear Structural Materials Module, you can also incorporate nonlinear material models like hyperelasticity or plasticity by adding a Solid Mechanics interface to the model.

When the interface is added, these default nodes are also added to the — , (a boundary condition where boundaries are free, with no loads or constraints), and (only applicable for flexible domains). Then, from the toolbar, add features that implement other multibody dynamics properties. You can also right-click to select physics features from the context menu.

The is the default physics interface name.

The is used primarily as a scope prefix for variables defined by the physics interface. Refer to such physics interface variables in expressions using the pattern <name>.<variable_name>. In order to distinguish between variables belonging to different physics interfaces, the name string must be unique. Only letters, numbers, and underscores (_) are permitted in the field. The first character must be a letter.

The default (for the first physics interface in the model) is mbd.

	From the 2D approximation list select Plane stress or Plane strain (the default). Plane stress is relevant for structures which are thin in the out-of-plane direction, such as a thin plate. Plane strain is relevant when the 2D model can be considered as a cut through an object which is long in the out-of-plane direction. This information is needed if the components are flexible and modeled using Linear Elastic Material. For more information see the theory section. When modeling using plane stress, the Solid Mechanics interface solves for the out-of-plane strain displacement derivative, , in addition to the displacement field u. When combining Multibody Dynamics with other types of physics, there is often an assumption that the out-of-plane extension is infinitely long. This is the case in for example Acoustic-Structure interaction problems. In these cases, Plane strain is usually the correct choice.

	For 2D components, enter a value or expression for the Thickness d. The default value of 1 m is suitable for plane strain models, where it represents a unit-depth slice, for example. For plane stress models, enter the actual thickness, which should be small compared to the size of the plate for the plane stress assumption to be valid. In Acoustic-Structure Interaction problems, the Thickness should be set to 1 m. Use a Change Thickness node to change thickness in parts of the geometry if necessary.

From the list, select or . Use to treat the mechanical behavior as quasi static (with no mass effects — that is, no second-order time derivatives). Selecting this option gives a more efficient solution for problems where the variation in time is slow when compared to the natural frequencies of the system.

Enter the coordinates for the xref (variable refpnt). The resulting moments (applied or as reactions) are then computed relative to this reference point. During the results and analysis stage, the coordinates can be changed in the section in the result nodes.

Specify initial values for a rigid body translation and rotation. The values specified here are, as a default, inherited by the initial values settings for and .

Use this section to automatically generate physics nodes in the Multibody Dynamics interface. This functionality makes the model setup easier and more robust for systems with many rigid bodies or gears.

By using the button (

), you can automatically create and nodes.

The has the following options:

The option (

) automatically creates nodes for geometrically disconnected objects. The input controls for which geometric objects to create a rigid domain. It is by default set to , which creates rigid domain for all objects in the selection of the physics interface. All available domain selections are also listed in the list, which makes it possible to create rigid domains for a subset of objects. Select the check box to add a subnode to each auto-generated node. The of the created rigid domains is automatically set to zero when this check box is selected.

The option (

) automatically creates a node for every gear geometry part present in the geometry sequence. This option requires that the gear geometry is built from the COMSOL . The domain selection for the auto-generated node is same as the gear geometry part. Relevant definitions and parameters are retrieved from the gear geometry part, and entered in the settings for the corresponding gear node. The and does not affect the option.

The option (

) automatically creates nodes from the geometry based on the shape of the boundaries. This option requires nodes created under . If the and are of same standard shape, this option creates one node for each active present. The possible shapes of boundaries for automatic joint creation are listed under .

	The Creating Joints Automatically section describes the details of creating various joint types from the geometry.

In this section you can modify the postprocessing defaults for the interface.

You can select a from the list of all rigid domains, attachments, and gears used in the model. It is used to visualize the relative motion of objects with respect to the selected body.

The variables u_ref, v_ref, and w_ref, being the three components of the displacement field with respect to the reference body, are available in the result menus. Also, the variables mbd.disp_ref and mbd.vel_ref contain the total displacement and velocity with respect to the reference body, respectively.

When you change the reference body, you need to update the solution before you can access the new definitions of these variables. To do that, right-click the node and select (

) (or press F5).

This is an information table that displays the name of all the joints used in a model and their source and destination attachments. This table summarizes all the connections present in a model and can be used to review the connections.

This is an information table that displays the number of degrees of freedom and constraints introduced by rigid domains and joints. You can use this information to determine whether you model has an appropriate number of constraints or not when running pure rigid body analysis.

The contents of the columns are:

The last two rows of the table contain a summary. In the row, the number of DOFs, prescribed conditions, and constraints are summed.

The row contains the net number of degrees of freedom of the model — that is, the difference between all degrees of freedom and the constraints and prescribed motions. A negative net number of degrees of freedom indicates that the mechanism is overconstrained and is not shown. In that case, the net number of constraints is instead displayed.

Some constraints are conditional and are not present during the whole analysis. Such constraints are counted in the summary table, irrespective of their actual status.

The contents of the table do not change if you suppress any of the contributing features from the settings in the study step.

In general, and if there are flexible bodies in the system, the model’s total number of degrees of freedom increase significantly. Such degrees of freedom are not accounted for in the summary.

The physics interface uses the global spatial components of the u as dependent variables in the flexible domains. The default names for the components are (u, v, w) in 3D. In 2D the component names are (u, v), and in 2D axial symmetry they are (u, w). You can, however, not use the “missing” component name in the 2D cases as a parameter or variable name because it is still used internally.

You can change both the field name and the individual component names. If a new field name coincides with the name of another displacement field, the two fields (and the interfaces which define them) share degrees of freedom and dependent variable component names. You can use this behavior to connect a Multibody Dynamics interface to a Shell directly attached to the boundaries of the solid domain, or to a Solid Mechanics interface sharing a common boundary.

A new field name must not coincide with the name of a field of another type (that is, it must contain a displacement field), or with a component name belonging to some other field. Component names must be unique within a model except when two interfaces share a common field name.

Each rigid domain, attachment, and joint also adds a number of global dependent variables depending on the number of ODEs needed to represent its motion.

In the Multibody Dynamics interface you can choose not only the order of the discretization, but also the type of shape functions: Lagrange or serendipity. For highly distorted elements, Lagrange shape functions provide better accuracy than serendipity shape functions of the same order. The serendipity shape functions, however, give significant reductions of the model size for a given mesh containing hexahedral, prism, or quadrilateral elements.

The discretization order applies to the flexible bodies. The default is to use shape functions for the . If you want to compute stresses with good accuracy, increase the shape function order to or .