A solid-beam finite element and non-linear constitutive modelling

The successful concept of solid-shell formulations which brings up several advantages with respect to classical shell elements is transferred to beam structures. The resulting three-dimensional solid-beam element possesses eight nodes with only displacement degrees-of-freedom. A reduced integration concept is worked out which accounts for the presence of two thickness directions. The relevant locking phenomena are treated by a combination of the assumed natural strain method and the enhanced assumed strain method. It is shown at which points the steps to derive the solid-beam formulation deviate from the derivation of the corresponding solid-shell. Validations for elasticity and elasto-plasticity with a reference to classical beam finite elements are provided. In particular beam structures with arbitrary four-sided cross-section can efficiently be modelled by using only one element within the cross-section. If more complex cross-sections are modelled by using several elements within the cross-section, the formulation shows a superior performance compared with standard solid elements.