An isogeometric implicit G1 mixed finite element for Kirchhoff space rods

In the paper we present a multi patch isogeometric mixed element with implicit geometric continuity at the ends for the analysis of non polar Kirchhoff space rods. Rotations are introduced at the ends of the element analogously to the Hermitian interpolation, performing a change of basis for the configuration space. A mixed method in which the internal forces are interpolated by means of an L2 projection leading to a B̄ formulation is used to cope with the membrane-flexural locking that affects the solution. The efficiency of the method in avoiding locking and instabilities is investigated. The formulation adopted has the advantage with respect to other formulations that a non full global stiffness matrix is obtained. This approach appears very appealing for efficient analyses of general assemblies of 3D non polar elements.