Stiffness maximization of concrete structures using topology optimization in static and dynamic problems

Abstract

This study highlights the generation of truss-like patterns for Strut and Tie Modeling (STM) using bidirectional evolutionary topology optimization in concrete structures. STM is an effective approach for the design of Discontinuity regions (D-regions) where standard Bernoulli’s hypothesis cannot be applied. As the conventional methods of STM generally follow a trial and error procedure, the final solution may not be unique. Topology optimization is classified under structural optimization to find the effective layout of structure based on the load path method. It is a scientific method that relies on structural mechanics; the inaccuracies related to STM can be avoided with the aid of topology optimization. In static problems, minimizing compliance leads to reasonably more stiff structures. In free vibration problems, the maximization of eigen frequency can be taken as an objective to get the maximum stiff structure. Solid Isotropic Material with Penalization (SIMP) material model assumes a constant and isotropic material properties in each discretized rectangular element. Evolutionary optimization derives the optimum structural layout by removing the ineffective elements and adding the effective elements in subsequent iterations. Method of Moving Asymptotes (MMA) developed by Svanberg (1997) is a kind of convex approximation has also been implemented in static problems.