Rigid elements and multi-point constraints are used to constrain one or more degrees of freedom to be equal to linear combinations of the values of other degrees of freedom.
Rigid elements are equations generated internally by OptiStruct. Users provide the connection data only. Rigid elements function as rigid bodies; therefore they are also known as rigid bodies or constraint elements. Internally, they are treated the same way as multi-point constraints.
The RROD element can be used to model a pin-ended rod which is rigid in extension. One equation of constraint will be generated for this element. The RBAR element can be used to model a rigid bar with six degrees of freedom at each end. From one to six (depending on user-input) equations of constraint will be generated by OptiStruct for this element.
The RBE1 and RBE2 elements are rigid bodies connected to an arbitrary number of grid points. The number of equations of constraint generated is equal to or greater than one, depending on the dependent degrees of freedom selected by the user. For the RBE1 element, the independent degrees of freedom are six components of motion that must be jointly capable of representing any general rigid body motion of the element; whereas for the RBE2 element, the independent degrees of freedom are the six components of motion at a single grid point.
The RBE3 element provides for specification of from one to six equations of constraint developed from the relation that the motion at a "reference grid point" is the least square weighted average of the motion at other grid points. This element is generally used to "beam" loads and masses from a reference point to a set of grid points.
Multi-point constraints are equations in which the user explicitly provides the coefficients of the equations. Each multi-point constraint is described by a single equation that specifies a linear relationship for two or more degrees of freedom. Multiple sets of multi-point constraints can be provided in the bulk data section. In the subcase information section, the multi-point constraints are assigned to the specific load case using the MPC statement.
The bulk data entry MPC is the statement for defining multi-point constraints. The first coordinate mentioned on the card is taken as the dependent degree of freedom (i.e. the degree of freedom that is removed from the equations of motion). Dependent degrees of freedom may appear as independent terms in other equations of the set, however, they may appear as dependent terms in only a single equation.
Some uses of multi-point constraints are:
· To enforce zero motion in directions other than those corresponding to components of the global coordinate system. In this case, the multi-point constraint will involve only the degrees of freedom at a single grid point. The constraint equation relates the displacement in the direction of zero motion to the displacement components in the global system at the grid point.
· To describe rigid elements and mechanisms such as levers, pulleys, and gear trains. In this application, the degrees of freedom associated with the rigid element that are in excess of those needed to describe rigid body motion are eliminated with multi-point constraint equations. Treatment of very stiff members as being rigid elements eliminates the ill-conditioning associated with their treatment as ordinary elastic elements.
· To be used with scalar elements to generate nonstandard structural elements and other special effects.
When using rigid elements or multi-point constraints, users must make sure that the following requirements are satisfied:
· A dependent degree of freedom cannot be in the SPC.
· A dependent degree of freedom in any rigid element or multi-point constraint cannot be defined as a dependent degree of freedom in any other rigid element or multi-point constraint.