Three-Dimensional Force Flow Paths and Reinforcement Design in Concrete via Stress-Dependent Truss-Continuum Topology Optimization

Abstract

Strut-and-tie models (STMs) are widely used by RC designers. However, selection of a viable model is a challenging task, especially in complex three-dimensional (3D) design domains with irregular cutouts, which are common in building cores and shear walls. Therefore, topology optimization has been promoted as a means of automating the development of minimum strain energy STMs, which can lead to improved structural behavior. Current drawbacks of such methods are that solutions may be difficult to construct and may fail to properly account for tensile stresses resulting from force spreading. A two-dimensional hybrid truss-continuum topology optimization scheme was recently developed to overcome these challenges with the goal of reconfiguring traditional reinforcement layouts to automatically follow principal tensile stresses, reducing cracking at service loads and increasing strength and ductility at an ultimate limit state. That work is generalized and extended herein to 3D domains and mechanics models. Stiffness is formulated such that truss elements carry only tensile forces and thus represent straight steel rebar, while the continuum elements carry only compressive forces and thus represent concrete compression load paths. The latter is achieved using a stress-dependent orthotropic material model. The algorithm is demonstrated on several benchmark design examples.