J. Argyris et al., BEC - A 2-NODE FAST CONVERGING SHEAR-DEFORMABLE ISOTROPIC AND COMPOSITE BEAM ELEMENT BASED ON 6 RIGID-BODY AND 6 STRAINING MODES, Computer methods in applied mechanics and engineering, 152(3-4), 1998, pp. 281-336
We present a 2-node isotropic and composite shear-deformable beam elem
ent in space-the element BEG. The formulation is based on the natural
mode finite element method whereby the 12 Cartesian degrees of freedom
(6 per node) are transformed to 6 natural rigid-body and 6 natural st
raining modes which describe the element's kinematics. Only a sparse 6
x 6 natural stiffness matrix needs to be formed while congruent trans
formations, performed on the computer, transform the natural stiffness
to the local and global Cartesian coordinates with significant impact
on computational efficiency and economy. Initial load due to temperat
ure is also given. In addition, simplified and partly simplified geome
trical stiffnesses are established which permit the study of nonlinear
phenomena such as buckling and large displacements. Throughout the fo
rmulation no locking or any other parasitic phenomena were encountered
. Although a general formulation is adopted, the model is applied here
to a solid beam section. The theory is implemented in our structural
analysis code SANI (Structural Analysis and Information). Following va
lidation with reference solutions, applications are made to isotropic
and composite beams, frames and three-dimensional composite beam struc
tures. The theory presented indicates a new direction in finite elemen
t analysis and structural mechanics in general.