Dynamics of Systems of Deformable Bodies

摘要

A mathematical description of the dynamic behavior of systems of interconnected deformable bodies is presented. The displacement field of a body is resolved into a displacement field due to a rigid body motion and a displacement field due to deformation. In order to get an unambiguous resolution, the displacement field due to deformation is required to be such that in cannot represent rigid body motions. This is achieved by prescribing either displacements due to deformation of selected particles or mean displacements due to deformation. Starting from the equations of motion of a particle of the body, a variational formulation of the equations of motion of the free body is derived. These equations are simpler is the mean displacements due to deformation are equal to zero. Approximate equations of motion are obtained by approximating the displacement field due to deformation by a linear combination of a set of assumed displacement fields. Three methods for generating assumed displacement fields are described: the assumed-modes method, the finite element method, and the modal synthesis method.