THEORETICAL FORMULATION AND COMPUTATIONAL IMPLEMENTATION OF CURVED FINITE ELEMENTS FOR ADVANCED ANALYSIS OF STEEL PLANE ARCHES
Advanced Analysis, Spread Plasticity, Steel Plane Arches, Curved Finite Elements, Finite Element Method, Numerical Methods.
Given the growing relevance of structural reliability analysis models and performance-based methodologies, more comprehensive and accurate paradigms for structural analysis and design must be explored. The use of steel arches remains relevant, experiencing an increase in 2021 compared to previous years, in their application in civil engineering projects. Steel arches are a material capable of providing both improved quality and cost-effectiveness to projects. The present research aims to develop a theoretically precise formulation for curved finite elements, focused on the analysis of arches and modeling of initial imperfections in planar frames.The proposed formulation encompasses the consideration of second-order effects for geometric nonlinearity and the distribution and spreading of plasticity using the plastic zone method for material nonlinearity. Furthermore, it aims to allow for significant displacements and rotations at nodes, as well as large elongations and curvatures in the bars, while accounting for the impact of initial residual stresses. The computational implementation aims to elucidate the structure's behavior, enabling the complete tracing of the nonlinear equilibrium path through incremental and iterative numerical methods.The theoretical development will be based on the idealization of bar behavior using the Euler-Bernoulli model and the updated Lagrangian formulation, which employs the Corrotational technique for a consistent derivation of the tangent stiffness matrix for curved elements. To achieve the desired results, the computational implementation combines the Newton-Raphson method with the arc-length control method of Riks.Through numerical examples, the efficiency of the method will be verified, and its accuracy will be assessed in comparison with models present in the literature. Thus, the research aims to contribute to the advancement of structural analysis in situations of nonlinearity, especially in planar arches with significant deformations and the behavior of nonlinear materials, including residual stresses.