Eulerian shape design sensitivity analysis and optimization with a fixed grid

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Shape optimization of 2D structures using simulated annealing (2007, methodology): “Studies on shape optimization [1–87] attest that shape changes may lead to considerable savings in weight and improvements in structural performance.”
Integrated layout design of multi-component systems using XFEM and analytical sensitivity analysis (2012, background): “[14], Kim and Chang [15] and Luo et al.”
Radial basis functions and level set method for structural topology optimization (2006, unknown): “One of the key steps in the Eulerian approach is to describe the geometry (or topology) by the nodal values of Φ(x) and shape functions to ensure that the space of achievable designs will be smooth enough in shape [31,51].”
A gradient-based shape optimization scheme using an interface-enriched generalized FEM (2015, methodology): “To perform the shape design sensitivity analysis, the boundary/interface nodes are parameterized by the shape design variables [15,35].”
Investigation and improvement of sensitivity computation using the area-fraction weighted fixed grid FEM and structural optimization (2011, background): “Furthermore, stress errors can be caused by the discontinuity of material properties between interior and intersected elements [14].”