Topology Optimization: Applications of VFLSM and SESO in the Generation of Three-Dimensional Strut-and-Tie Models

This article presents the analysis of Strut-and-Tie Model (STM) in reinforced concrete 3D structures based on the study of topological optimization, so that the problem is formulated with the Smooth-ESO (SESO) discrete method, whose removal heuristic is bidirectional with discrete optimization procedure, and the Velocity Field Level Set Method (VFLSM), which is an inheritance of the classical continuum Level Set Method (LSM), but advances the design limits with a velocity field constructed from the rate of the design variables and base functions. The proposed approach is to couple both methods in conjunction with the Method of Moving Asymptotes (MMA), used to control the various design constraints that are the minimization of compliance and the Von Mises stress that has demonstrated more rational STM results. Additionally, it has been formulated a methodology for the automatic generation of optimal of 3D STM by using sensitivity analysis obtaining via derivatives of the Von Mises stress fields, finding the force paths prevailing compression in the directions of the strut and the tensile in the directions of the ties for the reinforcement insertion. All the codes are implemented with Matlab software and several comparison examples: Deep beam with opening, a pile cap, a bridge pier, and a single corbel, are presented to validate the present formulations and the results are compared with the literature