| This thesis is concerned with the development of an elasto-plastic large deformation finite element formulation for multibody system applications. The method is based on the finite element absolute nodal coordinate formulation that uses global position vector gradients to describe the orientation and deformation of the finite element. In order to formulate the nonlinear kinematic constraint equations in terms of the absolute coordinates, joint coordinate systems whose axes are defined using the gradients are introduced. In particular, a new formulation for the sliding joint between two very flexible bodies is developed. As an application of the computer algorithms developed for the large deformation analysis, cable problems are considered. The results obtained using the finite element formulation are compared with the results obtained using the classical cable theory.; A Lagrangian plasticity formulation based on J 2 flow theory is presented in this investigation. It is demonstrated that the principle of objectivity, which is an issue when existing finite element formulations using rate-type constitutive equations are used, can be automatically satisfied when the stress and strain rate are directly calculated in the Lagrangian descriptions using the absolute nodal coordinate formulation. Furthermore, since this formulation does not suffer from the problem of coordinate redundancy and allows for the use of non-incremental solution procedures, the principle of work and energy are satisfied without the need of taking any special measures. It is also shown that the consistent Lagrangian elasto-plastic tangent moduli derived in the thesis lead to better convergence of the iterative Newton-Raphson procedure used in the full implicit integration methods. |
