A space-preserving data structure for isogeometric topology optimization in B-splines space

Yang, Aodi; Wang, Zhen; Luo, Nianmeng; Xiong, Tao; Xie, Xianda

doi:10.1007/s00158-022-03358-y

Cited by 7 publications

(3 citation statements)

References 43 publications

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“…To bypass the inefficient integral procedure and redundant memory in generating solid NURBS elements stiffness matrices for MMITO, this section presents the stiffness matrix projection between Bėzier elements under scaled and rotational geometric transformations first, and then the explicit computation of NURBS element stiffness matrix is derived in terms of Bėzier extraction operator and the Bėzier stiffness matrix projection. For the details in explicit stiffness computation of B‐spline elements, the readers can refer to Reference 37.…”

Section: Explicit Computation Of Nurbs Element Stiffness Matrixmentioning

confidence: 99%

“…Xie et al applied the R‐functions to topology description functions in MMC‐based ITO, where the convergence rate is improved significantly 17 . By virtue of the equivalence between B‐spline basis space and Bernstein basis space through Bėzier extraction operator, Yang et al proposed an explicit stiffness matrix computation formula for rectangular B‐spline IGA element, by which the preprocessing and memory efficiencies related to solid B‐spline IGA elements are simultaneously improved by orders of magnitude for ITO 37 . More recently, inspired by the tensor product decomposition technique, 38 a massively efficient implicit filter for ITO is developed, 39 where the memory overhead and computing time of the filtering matrix are significantly reduced.…”

Section: Introductionmentioning

confidence: 99%

“…17 By virtue of the equivalence between B-spline basis space and Bernstein basis space through B ̇ezier extraction operator, Yang et al proposed an explicit stiffness matrix computation formula for rectangular B-spline IGA element, by which the preprocessing and memory efficiencies related to solid B-spline IGA elements are simultaneously improved by orders of magnitude for ITO. 37 More recently, inspired by the tensor product decomposition technique, 38 a massively efficient implicit filter for ITO is developed, 39 where the memory overhead and computing time of the filtering matrix are significantly reduced. Besides, Gao et al proposed a novel multi-patch ITO for cellular structures, where Nitsche's method couples the non-conforming meshes between different NURBS patches.…”

Section: Introductionmentioning

confidence: 99%

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Tensor product decomposed multi‐material isogeometric topology optimization with explicit NURBS element stiffness computation

Yang,

Wang,

Luo

et al. 2023

Numerical Meth Engineering

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Based on the explicit stiffness computation formula of NURBS (non‐uniform rational B‐splines) element and tensor product decomposed explicit filter, a novel multi‐material isogeometric topology optimization (MMITO) method is put forward to generate multi‐material structures efficiently. The explicit NURBS element stiffness computation formula is: derived from the Bėzier extraction operator under the combination of scaled and rotational geometric transformations between NURBS elements, and the stiffness matrices of NURBS elements can be computed by the stiffness matrix of a Bėzier element without resorting to the time‐consuming integral procedure. As the presented MMITO is a nested optimization framework, we apply the explicit filtering technique to update the multi‐phase design variables efficiently in combination with the tensor product decomposition method. With the decomposed weight matrices of the filter and the explicit form of the NURBS stiffness matrix, we obtain the equivalent but much simplified preprocessing procedure and sensitivity analysis for the MMITO method. A comprehensive set of multi‐material numerical examples are optimized to verify that, while improving the preprocessing efficiency and reducing the memory overhead, the present MMITO scheme is able to generate semblable two‐dimensional and three‐dimensional multi‐material structures with identical structural performance to the traditional scheme. Therefore, the proposed MMITO method is a promising approach to optimizing multi‐material structures.

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Section: Explicit Computation Of Nurbs Element Stiffness Matrixmentioning

confidence: 99%