For a finite element to be legitimate in a linear analysis, it must exhibit zero strains and zero forces when subjected to rigid body motions. Such a requirement is usually checked by the patch test. However, for a finite element to be qualified for a nonlinear analysis, the initial forces acting on the element must rotate or translate with the rigid body motion, while the magnitudes of the initial forces remain unchanged, so as to preserve equilibrium of the element during the rigid body motion. A procedure will be described for testing the validity of finite elements to be used in nonlinear analyses with regard to the rigid body movements. As an illustration of the rigid body motion concept, a three-dimensional beam-column with warping effect will be derived and tested using an updated Lagrangian procedure.

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