A 3D solid-like frame finite element applied to steel structures under high temperatures

• Development of 3D frame FEM based on positions and unconstrained vectors.
• For Physical and Geometrical analysis of 3D steel structures at high temperatures.
• Definition and implementation of thermo-plastic model.
• Successful analysis of structures under fire with literature comparisons.

This study presents the development of a finite element formulation based on positions to deal with steel structures under high temperatures. The nonlinear thermal analysis is done regarding cross sections using two-dimensional flat elements while the three dimensional structural members are modeled by physical and geometrical nonlinear solid-like frame elements of any order. The thermal analysis consists in achieving, along time, the temperature profile at frame elements cross sections that affects the constitutive relations and, consequently, residual stresses at the structural mechanical equilibrium. The proposed element presents a geometrically exact description for large displacements and rotations by means of translations and generalized vectors nodal parameters. The adopted three dimensional Thermo-elastoplastic constitutive relation is based on the von Mises yielding surface for which the temperature dependence is established and an alternative flow rule is developed. Several examples are presented in order to validate the formulation and to show its good results.