For a structure that is symmetric about a plane, anti-symmetric loading causes anti-symmetric displacements. All degrees of freedom that are equal when symmetric are opposite when anti-symmetric, and all degrees of freedom that are opposite when symmetric are equal when anti-symmetric. Thus the specification of the anti-symmetric degrees of freedom simply uses the opposite signs from the symmetric case.
Consider the example of a structure that is symmetric with respect to a plane normal to the X axis, but now subjected to anti-symmetric loading. One Equal Constraint and one Opposite Constraint must be defined for each pair of joints that is symmetrically located with respect to the plane. The degrees of freedom that would be specified for the Equal Constraints are UX, RY, and RZ, and for the Opposite Constraint, degrees of freedom UY, UZ, and RX. The constraint types would be switched to model the symmetric case.
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