Implementation of 3D Bernoulli beams

The objective of this project is to implement structural elements within the finite element library Akantu. A preliminary work has already been done, working with 2D Bernoulli beams. The main goal of the proposed project is to add 3D Bernoulli beams to the structural mechanics model of the library, and to validate the code by writing simple test cases that are comparable to analytical results. Depending on the efficiency of the student some other structural elements could be added in a second time.

 

Responsables:

Jean-François Molinari (LSMS), [email protected]

Guillaume Anciaux (LSMS), [email protected]

Student:

Fabian Barras, [email protected]

Final Results

Bernoulli model for beams is included in the theories of thin structures that assume the conservation of the planar cross sections after deformation. This assumption is widely used in structural mechanics to predict the response of prismatic beams. For Finite Element analyses, 3-D objects relatively complex satisfying Bernoulli’s assumption can be studied only with curvilinear elements representing their geometric references (their axes). Moreover theory of Bernoulli beams enables a considerable reduction of the mesh size. In return, a more sophisticated element should be constructed.

This semester project consisted in the implementation of a 3-D Bernoulli beam element within the Finite Element library of Akantu. Axial and flexural theories for Bernoulli beam and Saint-Venant theory for torsion were followed for the model construction.

After its implementation and validation, the robustness of the developed element was evaluated on a complex 3-D structure. In collaboration with I-Bois laboratory, a 36 meters timber tower was analyzed with almost 20’000 3-D Bernoulli beam elements. The comparison with commercial Finite Element software shows the consistence of the developed element but also the great potential of Akantu library in structural analyses.
 

Deformation of the timber tower computed on Akantu (left) and on RFEM(C) software (right). Scale 150x.