A new approach for numerical analysis of flexible space frames subjected to impact forces is presented. The method is particularly effective in the analysis of large-amplitude vibration and dynamic stability found in extremely flexible structures.
The proposed method of analysis is based on a concept of updated material frame, which allows the algorithm of handling large rotations exceeding 360" and extensions longer than 100 per cent without numerical difficulty and the need for iterations. Thus, an efficient explicit integration finite element algorithm can be adopted. The method is convenient for non-linear and inelastic material models.
The basic coding procedure is similar to the popular co-rotational approach. Existing codes can be easily modified to solve transient dynamic problems. The modification steps necessary for the implementation are outlined in the paper.
Several numerical examples are presented. Comparison with the standard co-rotational approach and large deformation finite element formulations, such as the updated Lagrangian approach, are presented.
JNTRODUCTTON
Formulations for the finite element analysis of structures undergoing large deflection have been proposed for both static and dynamic One which is widely used is the co-rotational formulation. This method uses the approach that it is easier to treat large deflection of thin-walled structures by separating the rigid-body (or approximate rigid-body) displacements of the ith element, df, from the total displacements, di, of the element leaving only the deformation displacements, df , as
(1) allowing the application of infinitesimal strain4eformation relations to the material properties. The separation is accomplished by using convected, or co-rotational, co-ordinate systems.69
Earlier formulations based on convected co-ordinates were introduced by Argyris et aL8 for the static analysis of large displacement but small-deformation problems using an incremental approach. Transient dynamic analyses were proposed by Belytschko and Hsieh' using a total formulation. This latter formulation has been proven effective in dynamic analyses with moderate rotations. A large number of references", l 1 and general purpose computer codes, such as DYPLAS and WHAM,'* STRAW,13 and DYNA3DI4 have been reported in recent years.