BEC: A 2-node fast converging shear-deformable isotropic and composite beam element based on 6 rigid-body and 6 straining modes

We present a 2-node isotropic and composite shear-deformable beam element 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 straining modes which describe the element's kinematics. Only a sparse 6 x 6 natural stiffness matrix needs to be formed while congruent transformations, 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 temperature is also given. In addition, simplified and partly simplified geometrical stiffnesses are established which permit the study of nonlinear phenomena such as buckling and large displacements. Throughout the formulation 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 validation with reference solutions, applications are made to isotropic and composite beams, frames and three-dimensional composite beam structures. The theory presented indicates a new direction in finite element analysis and structural mechanics in general.