A normalization strategy for BESO-based structural optimization and its application to frequency response suppression

Evolutionary topology optimization approach to design multiphase soundproof systems with poroelastic media

“…with r min being a mesh independent filter radius. The historical averaging and the Min-Max normalization concepts 54 are also considered, as stated in Equations ( 78) and (79), to enhance sensitivity stabilization effects,…”

Topology optimization for enhanced dynamic fracture resistance of structures

“…The compliance C is evaluated by a separated static test with an external force F s = -100 N. Note that such compliance constraint has been used by several other authors in a dynamic topology optimization context, even though in a linear vibration regime (see e.g. [58,59]). Above, u s is the static displacement response of the undamaged structure under a test static external load F s and C 0 is the prescribed compliance upper bound; V is the target structural volume (area in 2D), which can be computed as V = Ne e=1 V e ϕ e , and V 0 = Ne e=1 V e is the total volume of the design domain, and χ denotes the target volume fraction constraint.…”

Improved fracture resistance of 3D-printed elastoplastic structures with respect to their topology and orientation of deposited layers

“…The BESO variable updating scheme for this work follows part of the basic procedure presented in [73,74]. In addition, a normalization strategy introduced previously [77] is used to improve the TO convergence.…”

“…At each design iteration, the sensitivity numbers, which denote the relative ranking of the element sensitivities, are used to determine the material removal and addition. Thus, without changing the relative ranking of the element sensitivities, a normalization strategy introduced elsewhere [77] is employed to force the element sensitivities φ e to distribute in an interval of [0, 1], i.e.,…”