Isogeometric configuration design sensitivity analysis of finite deformation curved beam structures using Jaumann strain formulation

Abstract

Using an isogeometric approach, a continuum-based configuration design sensitivity analysis (DSA) method is developed for curved Kirchhoff beams with multi-patch junctions. Under the total Lagrangian formulation, large deformations considering the initial curvature of curved beams are described by geometrically exact beam theory (GEBT) and Jaumann strain formulation. In the isogeometric approach, the higher order continuity and the exact description of initial geometry are naturally embedded using NURBS basis functions. In multi-patch models, C0-continuity of physical displacement or C1-continuity of displacement component at junction is weakly imposed using the Lagrange multiplier method. The superior accuracy of isogeometric analysis (IGA) is verified through the comparison with the results of finite element analysis (FEA) using cubic Hermite interpolation. In the DSA, a material derivative is utilized and the kinematical description of GEBT is consistently employed to express orientation design variations. Contrary to the IGA-based DSA, the Hermite basis function explicitly depends on design in the FEA-based DSA due to its element length parameter. Moreover, since the design velocity field is approximated using the nodal velocity imposed at nodal tangential vector, the amount of design perturbations should be very small to obtain precise design sensitivity.