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Rotation Formulations for Dynamic Relaxation – with Application in 3D Framed Structures with Large Displacements and Rotations, Proceedings of the International Symposium of the IASS-APCS Symposium, Seoul, South Korea, 2012
Dynamic relaxation (DR) has been widely used as a powerful method for structural analysis and form-finding. Compared with the direct stiffness method, one advantage of DR is that there is no need to compose a global stiffness matrix; for DR, every node of the structure can be seen as a single particle constrained by forces generated by the interactive mechanism of the structural members. The equations of motion for particles are much easier to consider than the direct stiffness approach, especially when structures undergo large displacements and rotations.

However, most applications of DR are restricted in the field of cable, membrane, hanging chain structures. The common feature behind these structures is that only three degree of freedom (3-DOF) nodes are used. And for 3-DOF nodes, no bending moment but translational forces can be applied.

In this paper, we propose the rotation formulations for DR. The description of motion of one particle is then separated into two parts, the translational and the rotational. Therefore, additional rotation degree of freedom is introduced into the computation system and we can use DR to simulate structure systems composed of 6-DOF nodes.
We further show how we apply the 6-DOF DR, with the beam mechanism, to the simulation of framed structures. Validity is examined through examples of structures which undergo large displacements and rotations.
Ansprechpartner: Li, J. .; Knippers, J.
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