Force-based higher-order beam element with flexural-shear-torsional interaction in 3D frames. Part II: Applications

The specific features of the proposed force-based formulation derived in the companion paper, which is applied for the first time to higher-order beam theories, are herein thoroughly validated. Introductory numerical examples illustrate the influence of mesh refinement, boundary conditions, and slenderness ratios for isotropic linear elastic response. Specific higher-order effects—unique to the developed element—are then suitably interpreted, as well as the formulation appropriateness to consider distributed loads and to model three-dimensional behaviour, which is verified with solid finite element analyses. Extensive comparisons against existing proposals, namely other refined higher-order beam theories, emphasize the performance of the proposed approach. Finally, the nonlinear response of the element with a multiaxial J2 linear plasticity material model is analysed, highlighting its advantages in relation to a classical force-based Euler–Bernoulli beam using a one-dimensional plastic material model with kinematic hardening.

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