Shape optimization of concrete free-form shells considering material damage

Shape optimization is a pervasive tool for designing concrete free-form shells. However, the existing shape optimization approaches for free-form shells usually assume the material is purely elastic without considering material damage, which may produce undesired results in real-world structural applications, especially in the case of concrete structures. In this article, a framework is presented for performing the shape optimization of concrete free-form shells while considering concrete damage. In the proposed optimization algorithm, the Mazars model is coupled with finite element analysis for modelling structural responses subjected to material damage. Through a series of numerical examples, the proposed algorithm is validated and the effects of material damage on optimal results are investigated. It is demonstrated that the consideration of material damage leads to a more robust design, which highlights the importance of accounting for the material damage during the shape optimization process of concrete free-form shells.