A Formulation of the Global Equations of Motion of a Deformable Body.

摘要

The global equations of motion for a deforming body are cast in a form which is attractive for many studies. The deforming body is assumed a continuum,but its constitutive behavior is left totally general. Equations treated represent the conservation of linear and angular momenta and kinetic energy. The motion -including deformation -of the body is of unrestricted magnitude. A translating and rotating reference frame is defined in terms of the linear and angular momenta of the body,and the global equations of motion are transformed in terms of parameters which are defined relative to this reference frame. It is defined so that the body possesses zero momenta as seen by an observer fixed in the reference frame. It is also shown that for a given motion,this choice of reference frame minimizes the kinetic energy of the body measured relative to the reference frame. The global equations are represented in a form similar to the classical rigid-body equations,which are shown to follow on the assumption of zero stretching. Finally,the conditions for 'steady'motion are developed. Solutions are presented for steady motion and when the angular velocity has only steady direction.