The purpose of this study is the selection of appropriate bases for the generalized coordinates of a linear and nonlinear deformable bodies in multibody system to improve the computational efficiency for the dynamic analysis. The dynamic equations of a beam-like deformable body which has a rigid body motion coupled with elastic deformation are derived by the principle of virtual work. These deformable bodies are discretized by finite elements. To reduce the number of generalized elastic coordinates resulting from the discretization, the vibrational normal modes, the load-dependent Ritz vectors, the derivative modes and the nonlinear static modes are employed for various dynamic systems. For the impact system, the load-dependent Ritz vectors are tried as a basis for the generalized coordinates of a deformable body. Each of these vectors is obtained from the deflection by a unit force applied at the special point of the elastic body. The impact surfaces of two bodies are modeled as a nonlinear spring-damper system. Comparisions of computational results are presented for three examples. Then it is shown that the load-dependent Ritz vectors provide efficient bases for the analyses of the impact problems. For the nonlinear deformable system, three dynamic cases are presented. In case of the rotating beam analysis, the vibrational normal modes and their derivatives at initial, and steady state configurations are tried as a reduction bases. Two examples are carried out and it is shown that the computational efficiency are increased when the steady state modes and derivatives are added to the reduction bases. In the analysis of fixed-fixed beam with a step loading case, the normal modes and derivative modes at the static equilibrium and the nonlinear static mode are employed. The solutions of this reduction models are converged to the FEM full model solution but the other solutions of the reduction model are not. In the nonlinear mechanism analysis, only the vibrational modes and their derivative are employed. Two examples, such as a slider crank and four-bar mechanisms, are presented to illustrate the effect of geometric nonlinearities. The solutions of the bases well represent the nonlinear behavior of the deformable body.
