Project start: 1.10.2025.

Beam structures are widely used in many engineering fields, such as mechanical engineering, shipbuilding, construction, aerospace, and biomechanics. These areas are in great need of the development of new numerical tools for simulating their response. The term „inhomogeneous cross-sectionbeam-type structure“ suppose the laminated sections, and more recently, a significant group so-called FG (Functionally Graded) beams, with an isotropic and continuous material distribution of material properties across the cross-section.

Due to their slenderness, beam structures are suspective to buckling and the loss of stable deformation form, making numerical simulations during the design phase of utmost importance for cost optimization and resource savings. Assessing the load-carrying capacity of the structure, along with predicting the onset of failure and the reasons for its collapse, is one of the main objectives of this project proposal.

The project is envisioned as a contribution to the field in terms of developing new and improving the existing numerical models applicable for simulating the buckling of beam-type structures under geometrically nonlinear response regimes, considering the variable mechanical and thermal environment. Special attention will be given to types of beam structures with inhomogeneous cross-sections made from increasingly popular materials, such as carbon nanotubes or graphene nanoplatelets.

The new numerical model that is to be developed, will be based on the existing one that the project team members have been working on and improving for several years. It is based on the Euler-Bernoulli and Timoshenko beam theories, as well as Vlasov's theory of torsion, and includes warping as a specific feature of thin-walled profiles. Simulating the response of nonlinear beam members under large spatial rotations is enabled by incorporating a nonlinear displacement field, using corotational and UL-updated Lagrangian incremental formulations. The model will also predict the variation of the centroid and shear center positions, which are tipical for cross-section inhomogeneity.