Substructure equations of motion
Having adopted an appendage idealization, one can proceed formally to derive its equations of motion. Since it is the variational nodal deformations u j and β j (j = 1,...,n) which represent the appendage unknowns, the equations of motion of the appendage ultimately consist of the 6n scalar second order differential equations of motion for the n nodal bodies. The present section, however, has the intermediate objective of providing an expression for the interpolation function relating the variational deformation function \(\bar \omega \) of a finite element to the variational deformations at its nodes, and in terms of this relationship providing expressions for the forces and torques applied to the nodal bodies by the adjacent finite elements.
KeywordsInertial Reference Frame Finite Element Equation Inertial Acceleration Consistent Mass Matrix Nodal Body
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