Large Rigid Body Kinematics with Small Deformations -- a Nonlinear Problem Linearly Solved

Abstract

Simulations of transient structural response are generally performed either with direct transient or modal linear analysis. The former approach entails the direct tracking of all individual degrees of freedom, the other a cost-effective bypass of this expensive endeavor in modal space, possible only if the response is linear. The present paper offers an escape from the expenses and inconvenience of direct integration for problems that are rendered nonlinear by large rigid body motion (rotations) and where the loads can be specified in a body-fixed frame and are known prior to the analysis time span (a slew maneuver may belong to this class of problems). In particular, a numerical recipe to assess via linear steps the responses of a structure subjected to large transient rigid body motion is presented. The procedure consists of two steps. First, a linear analysis in a body-fixed frame is performed. As the real structure tumbles, the output of this linear procedure will develop unrealistic and extreme features as dictated by large input fed into relations built on small angle approximations. This garbled output is corrected with a simple linear operation in the second step, and the valid solution expressed in the body-fixed reference results. For the procedure to be applicable, structural response must be sufficiently linear in a body-fixed frame (this implies small deformations), and Coriolis and centrifugal force effects must be insignificant.