Elasto-plastic deformations in multibody dynamics

The problem of formulating and numerically solving the equations of motion for a multibody system undergoing large motion and clasto-plastic deformations is considered here. Based on the principles of continuum mechanics and the finite element method, the equations of motion for a flexible body are derived. It is shown that the use of a lumped mass formulation and the description of the nodal accelerations relative to a nonmoving reference frame lead to a simple form of these equations. In order to reduce the number of coordinates that describe a deformable body, a Guyan condensation technique is used. The equations of motion of the complete multibody system are then formulated in terms of joint coordinates between the rigid bodies. The kinematic constraints that involve flexible bodies are introduced in the equations of motion through the use of Lagrange multipliers. In this paper the following general rules will apply: (a) Matrices and higher order tensors are in boldface upper-case characters. (b) Column and algebraic vectors are in boldface lower-case characters. (c) Scalars are in lightface characters. (d) Summation convention is applied when tensors are written on component form. (e) Left superscript denotes the configuration in which an event occurs. (f) Left subscript denotes the configuration to which an event is refered to.