Exact integration of uniaxial elasto-plastic laws for nonlinear structural analysis

The recently formulated fiber-free approach [1,2] is used for the analytical integration of non-linear elastic and elasto-plastic normal stresses acting on beam cross sections. It is based on the subdivision of the section in suitable subdomains, which are updated during the analysis of the structural model, and the use of analytical formulas which require the constitutive law to be integrated four times as a maximum. In particular we illustrate the application of the fiber-free approach to the well known concrete model by Mander et al. [3] since its expression belongs to the set of countinous functions which do not admit a primitive. Some representative numerical tests highlight the correctness and the computational efficiency of the fiber-free approach with repsect to the traditional fiber approach, to date the only existing method to perform a non-linear sectional analysis.