GEOMETRIC NONLINEAR ANALYSIS OF TRUSS SYSTEMS WITH RIGID BODY MOTIONS

Many truss systems are both structures and mechanisms. So it is hard to solve these problems using the classical FEM theory. Aiming at dealing with the geometric nonlinear effect of these systems, this paper presents a co-rotational method using a series of coordinate systems which include global coordinate, body-fixed coordinate, element coordinate, node coordinate and section coordinate. It is supposed that the cross-section nodes are rigidly connected, namely the transformation matrix between the node coordinate and the section coordinate is invariable, thus the rotational concept is clearer. Subsequently, the deformational conversion relationship between element coordinate and global coordinate is attained based on the finite rotation theory, and it is shown that the large rotation and deformation are appropriately converted into small strain effect. Then, the nonlinear formulation of the residual forces is obtained. In addition, this paper gives a new augmented constraint method which is widely used in multi-body dynamics to deal with complicated displacement boundary conditions. Finally, four numerical examples are given to verify the method of this paper.