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.

Elastic and Inelastic Analysis of Frames with a Force-Based Higher-Order 3D Beam Element Accounting for Axial-Flexural-Shear-Torsional Interaction

João Saraiva Esteves Pacheco de Almeida

When one of the dimensions of a structural member is not clearly larger than the two orthogonal ones, engineers are usually compelled to simulate it with refined meshes of shell or solid finite elements that typically impose a large computational burden. The alternative use of classical beam theories, either based on Euler-Bernoulli or Timoshenko’s assumptions, will in general not accurately capture important deformation mechanisms such as shear, warping, distortion, flexural-shear-torsional interaction, etc. However, higher-order beam theories are a still largely disregarded avenue that requires an acceptable computational demand and simultaneously has the potential to account for the above mentioned deformation mechanisms, some of which can also be relevant in slender members. This chapter starts by recalling the main theoretical features of a recently developed higher-order beam element, which was combined for the first time with a force-based formulation. The latter strictly verifies the advanced form of beam equilibrium expressed in the governing differential equations. The main innovative theoretical aspects of the proposed element are accompanied by an illustrative application to members with linear elastic behaviour. In particular, the ability of the model to simulate the effect of different boundary conditions on the response of an axially loaded member is addressed, which is then followed by an application to a case where flexural-shear-torsional interaction takes place. The beam performance is assessed by comparison against refined solid finite element analyses, classical beam theory results, and approximate numerical solutions. Finally, with a view to a future extension to earthquake engineering, an example of the element behaviour with inelastic response is also carried out.

Springer International Publishing2017

Elastic and Inelastic Analysis of Frames with a Force-Based Higher-Order 3D Beam Element Accounting for Axial-Flexural-Shear-Torsional Interaction

João Saraiva Esteves Pacheco de Almeida

Springer International Publishing2017