Analysis and development of nonlinear Finite Elements for modelling steel structures at ambient and elevated temperature

This thesis work aims to successively analyze and develop "ex novo" problems concerning the use of finite elements for the analysis of issues characterized by high plasticity, geometrical and material nonlinearity, large displacements and rotations; all combined with the effect of temperature on the material mechanical properties. The ultimate objective of the work is the analysis and development of nonlinear Finite Elements devoted to the modelling of steel structures at ambient and elevated temperature. Three different experiences will be analyzed in this elaborate; each of them characterised by specific issues that may be involved in the analysis via finite element method of steel structures at ambient and elevated temperature. At the same time innovative aspects that are related, for example, to the particular typology of the analyzed case study (first case) or in the methodology used in the treatment of the problem (second and third case) are investigated. The thesis structure chronologically retraces this path and the results and the experience gained from each of them were exploited to ultimately implement a thermomechanical finite element that is expression of all the tackled problems. The thesis consists of a collection of three papers that have been published or submitted on each of the investigated topics. In detail: - In the first paper, a commercial finite-element code, of the type "multipurpose", such as ANSYS has been used for the analysis of innovative cold-formed, laterallyrestrained steel rectangular hollow flange beams subjected to monotonic bending test. The numerical analysis has been carried out by means of the direct comparison with experimental tests on real scale specimens; that has allowed the detection of some phenomenological problems that have been included in the model calibration. From a numerical point of view, this work has at first allowed to deeply investigate the plastic problem by means, for example, the appropriate identification of the constitutive laws for the material, the correct choice of hardening law and yield surface, and their impact on the model. The local buckling problem typical of these profiles has been evaluated, through the use of shell elements. Furthermore, the effect of the global and local imperfections, which have been introduced in the model with different amplitudes, has been deeply investigated by evaluating their effect on the ultimate load. The calibration of the model finally allowed to perform a series of parametric analyses in order to extend the results to an extended range of profiles, characterized by different slenderness. - In the second paper, the thermal problem has been introduced with the support of a finite element software, designed specifically for thermomechanical analysis (SAFIR). The case study is, in this case, based on a multi-storey steel-concrete composite open car park subjected to localized fire of vehicles. With this study, not only the plastic problem has been analyzed but also phenomena such as the effect of high geometrical nonlinearity and large displacements on the structure in addition to the temperature effect on materials mechanical properties. The case study has been used to evaluate the assumptions and the issues that arise when developing an innovative integrated modelling methodology between a computational fluid dynamics (CFD) software applied to compartment fires and a finite element (FE) software applied to structural systems. Particular emphasis has been given to the weak coupling approach developed between the CFD code fire dynamics simulator (FDS) and the FE software SAFIR. - In the third and last paper all the experiences obtained from the previous works have been focused on the implementation, inside the MATLAB environment, of a thermomechanical beam finite element based on the co-rotational beam theory for the analysis of two-dimensional frames heated under high temperature and subjected to plastic deformation and to the effect of geometrical nonlinearity. The finite element is mainly aimed at the study of steel structures, with double-symmetrical profiles such as IPE or HE cross sections, and could then be used as a modelling tool for typical frames subjected to thermal actions. The element implements both Euler-Bernoulli and Timoshenko beam theories and can analyse slender to moderately stocky structures. A co-rotational formulation was used for describing the beam kinematic. The degradation of the steel mechanical properties at high temperature according to the Eurocode 1993-1-2 was considered by integrating the material constitutive law based on a predetermined temperature field in the cross section. An improved displacement predictor for estimating the displacement field at the beginning of each time step was successfully implemented and allowed to significantly decrease the computational time. Furthermore, advanced path-following methods that detect secondary equilibrium paths owing to instability occurrence were implemented in order to analyse the elasticplastic post-buckling behaviour of compressed steel elements at high temperature without the need of introducing geometrical imperfections. In order to show the potential of the developed finite element by highlighting the practical implications, a parametric analysis was performed to show whether the element could reproduce the EN1993-1-2 buckling curve. Validation against experimental and numerical data obtained with commercial software like ABAQUS and SAFIR is thoroughly shown in the paper.