Transient Response of Inelastically Constrained Rigid-Body Systems

Abstract

An energy rate balance is employed to develop the incremental equations of motion for a shock loaded, inelastically constrained rigid-body structural system. Lagrangian multipliers provide the coupling mechanism necessary to reduce the overall system of equations to a set of modified rigid-body equations which include the nonlinear geometric and structural material effects. Kinematic material hardening and a modified yield criteria are used. Examples illustrate the technique and are compared with experimental results.

Large displacement, transient analysis of space frames

“…The components of the b, and b3 vectors given above are in terms of the xi co-ordinates of that node at time step j . Using equation (5) with the [k] matrix defined in the previous time step, the components are transformed to global co-ordinates ; the vector 4" is then found by a vector product.…”