M. Vatandoost - Department of Architectural Technology, Faculty of Architecture, College of Fine Arts, University of Tehran, Tehran, Iran
M. Golabchi - Department of Architectural Technology, Faculty of Architecture, College of Fine Arts, University of Tehran, Tehran, Iran
A. Ekhlassi - School of Architecture and Environmental Design, Iran University of Science and Technology, Tehran, Iran
M. Rahbar - School of Architecture and Environmental Design, Iran University of Science and Technology, Tehran, Iran

This study presents the optimized shape and thickness of thin continuous concrete shell structures, minimizing their weight, deflection, and elastic energy change while meeting the performance requirements and minimizing material usage. Unlike previous studies that focused on single-objective optimization, this research focuses on multi-objective optimization (MOO) by considering three objective functions. This combination of objective functions has not been reflected in previous research, distinguishing this study. The computational design workflow incorporates a parametric model, multiple components for measuring objective functions in the grasshopper of Rhino, and a metaheuristic algorithm, the non-dominated sorting multi-objective genetic algorithm (NSGA-II), as the search tool, which was coded in Python. This workflow allows us to perform form-finding and optimization simultaneously. To demonstrate the effectiveness of this metaheuristic algorithm in structural optimization, we applied it in a case study of a well-known shell designed using the physical prototyping hanging model technique. Interpretations of samples of optimized results indicate that although solution ۱ weighs nearly the same as solution ۲, it has less deflection and strain energy. Solution ۳, with a three-fold mass, has significantly less deflection and strain energy than solution ۱ and solution ۲, with deflection reductions of over ۵۰ and ۱۷%, respectively. Solutions ۳ and ۴ show better deflection and strain energy performance. Furthermore, a comparison of the MOO results with the Isler shell revealed that this method found a solution with less weight and deflection while being stiffer, confirming its practicality. The study found that MOO is a reliable method for form-finding and optimization, generating accurate and reasonable results.

Concrete Shell Structures, Structural Optimization, Shape Optimization, Topology optimization, Multi-Objective Optimization, Non-dominated Sorting