Stress constrained shape and topology optimization with fixed mesh: A B-spline finite cell method combined with level set function

Shape optimization of Dirichlet boundaries based on weighted B-spline finite cell method and level-set function

“…It vanishes whenever free boundaries are only concerned with d i , as studied in our previous work [15].…”

“…This benchmark was originally from a free boundary shape optimization problem and greatly investigated [3,5,15]. As is shown in Fig.…”

“…(15). In this section, typical Dirichlet boundaries associated with a point and a curved segment are presented for the sake of completeness.…”

“…This means that Dirichlet boundary shapes are described by implicit representations with continuous design variables independent of the mesh discretization. Meanwhile, the FCM developed previously [15,[27][28][29][30][31] is implemented to use a fixed grid over the whole optimization process no matter how the structural shape changes. As is seen, this method will provide a great flexibility of generating the discrete mesh independently of the physical domain of a structure so that discrete nodes are not necessarily located on the structural boundaries.…”

“…In most existing works [1][2][3][4][5]15], the standard shape optimization only concerned free boundaries of a structure while Dirichlet boundaries are assumed to be unchangeable. In fact, the design of structural supports constitutes a long-term motivating research topic involved in many structural engineering fields such as building constructions, workpiece machining fixture, welding, fastener connections or rivet joints of aircraft structures.…”