Trefftz and RBF-based formulations for concrete beams analysis using damage models

In this work a hybrid-Trefftz formulation and a meshless approach based on the use of radial basis functions (RBF) are applied to the analysis of reinforced concrete beams. Resorting to the Mazars model, the concrete is represented by an elastic medium with progressive damage. In the hybrid-Trefftz formulation a stress field that satisfies a priori the equilibrium equations on the domain is used. The displacements on the static boundary are independently approximated, resulting in a governing system where the operators have to be integrated over the domain of the problem. In what concerns the meshless approach, radial basis functions are used to approximate the displacement fields but, as a collocation procedure is used, no integrations are required. A numerical example illustrates the results obtained with both techniques.