Efficient equilibrium-based stress recovery for isogeometric laminated Euler–Bernoulli curved beams.

Laminated curved composite parts, used, e.g., in the spar and ribs in aircraft and wind turbine blades, are typically subjected to high interlaminar stresses. This work focuses on a two-step procedure to study laminated Euler–Bernoulli curved beams discretized via Isogeometric Analysis (IGA). First, we solve a (planar) Euler–Bernoulli curved beam formulation in primal form to obtain the tangential and transverse displacements. This formulation features high-order PDEs, which we can straightforwardly approximate using either an IGA-Galerkin or an IGA-collocation approach. Starting from the obtained displacement solution, which accounts for bending-stretching coupling, we can directly compute the normal stress only, while we do not have information concerning the transverse shear stress state, typically responsible for delamination. However, by imposing equilibrium in strong form in a curvilinear framework which eases the post-processing, eliminating the need for coordinate changes, we can easily recover interlaminar transverse shear stresses at locations of interest. Such a posteriori step requires calculating the high-order displacement derivatives in the equilibrium equations and, therefore, demands once again higher-order regularity that can be easily fulfilled by exploiting the high-continuity properties of IGA. Extensive numerical tests prove the effectiveness of the proposed approach, which is also aided by the IGA's superior geometric approximation. • Two-step local equilibrium-based stress recovery for laminated Euler-Bernoulli beams. • 3D constitutive model reduction with exact integration through the beam thickness. • High-order PDEs in primal form and recovery requirements easily handled via IGA. • Coupled membrane-bending problem solved via IGA Galerkin and Collocation approaches. [ABSTRACT FROM AUTHOR]