A global formulation for complex rod structures in isogeometric analysis

• A spatial rod formulation for multi-patch complex structures is proposed.
• The formulation is suitable for multi-patch assembling and post-processing.
• The curvature and torsion are considered in the formulation.

Linear elasticity analysis of complex rod structure in the framework of isogeometic analysis is researched. An efficient global formulation for spatial Timoshenko rod structure is proposed, in which the general geometric form of complex rod structure with arbitrary curvatures and torsions described by multi-patches is adopted. The Frenet–Serret formula is used for the derivatives of direction vector with respect to the arc length of the rod, and a concise local strain formula with respect to the global control variables is obtained. The element stiffness matrices are calculated in global coordinate system therefore they can be assembled directly, which makes present formulation suitable for multi-patch connection. The performance with respect to the number of quadrature points are tested, and the results indicate that reduced integration schemes could be adopted to improve the performance. The effectiveness of proposed formulation is verified by numerical analyses of complex structures. Comparison with the local form formulation shows that the proposed formulation has less computational cost for multi-patch simulation, and is easier to be post-processed as well.