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constraints Command

This command is used to construct the ConstraintHandler object. The ConstraintHandler object determines how the constraint equations are enforced in the analysis. Constraint equations enforce a specified value for a DOF, or a relationship between DOFs. The degrees of freedom can be broken down into UR, the retained DOF's, and UC, the condensed DOF's:

The other constraints commands are used for ALL other cases, such as the case of non-homogeneous single-point constraints using the sp command, multi-point constraints, imposed motions and multi-support excitation. For such cases, the relationship between DOF's can be written as:UC=CRCUR. Where CRC is a matrix of constants.

The following constraints handlers are currently availble:

Of the different methods, "the Lagrange multiplier method is more attractive than the transformation method if there are few constraint equations that couple many DOF. However, Lagrange multipliers are active at the structure level, but transformation equations can be applied at either the structure level or element by element. The latter has the appeal of disposing of constraints at an early stage, when the matrices are small and manageable". (Cook)

"In comparison with Lagrange multipliers, penalty functions have the advantage of introducing no new variables. However, the penalty matrix may significantly increase the bandwidth of the structural equations, depending on how DOF are numbered and what DOF are coupled by the constraint equations. Penalty functions have the disadvantage that penalty numbers must be chosen in an allowable range: large enough to be effective but not so large as to provoke numerical difficulties". (Cook)

More information and examples on these methods are discussed in detail in the Cook book.

In This Chapter

Plain Constraints

Penalty Method

Lagrange Multipliers

Transformation Method

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