On finite element implementation of geometrically nonlinear Reissnerʹs beam theory: three-dimensional curved beam elements Original Research Article

Finite element implementation of the three-dimensional finite-strain beam theory of Reissner is considered in this work. In contrast with some earlier works on the subject, discussed here are the beam elements whose reference axes are arbitrary space-curved lines. We have shown that an improved representation of curved reference geometry significantly increases the accuracy of the results. However, it also makes the choice of non-locking finite element interpolations somewhat more delicate. A hierarchical displacement interpolation proposed here is proved to be capable of eliminating both shear and membrane locking phenomena. A very satisfying non-locking performance is demonstrated for a set of problems in nonlinear elasto-statics.