Numerical analysis perspective in structural shape optimization: A review post 2000

This review presents developments in structural shape optimization post 2000 from perspective of numerical analysis techniques. Traditional shape optimization with FEM has undergone considerable transformation as developments in CAD, numerical analysis techniques and optimization algorithms have contributed significantly in improving it. Mesh dependency and inconsistent description of the geometry for design and analysis models remained major challenges in traditional FEM based shape optimization. To improve mesh based shape optimization, in-plane regularization and out-of plane filtering, vertex morphing, traction method in node based shape optimization, mesh morphing and adaptive mesh refinement techniques are discussed. Alternative numerical techniques have also been discussed briefly from shape optimization perspectives which includes modified versions of FEM like eXtended FEM (XFEM) with level sets, Fixed Grid (FG) FEM/Eulerian approach, interface enriched generalized FEM (IGFEM) and finite cell method (FCM), isogeometric analysis (IGA) and its variants like eXtended IGA (XIGA) and IGABEM and meshless methods (MMs) like element free Galerkin (EFG) and reproducing Kernal particle method (RKPM). These numerical techniques have different mathematical background and hence possess different capabilities and limitations. The present work highlights these differences and compares them in context of shape optimization. Critical observations and future research recommendations are presented before concluding remarks.