Massively efficient filter for topology optimization based on the splitting of tensor product structure

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

doi:10.1007/s11465-022-0710-6

Cited by 3 publications

(2 citation statements)

References 58 publications

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“…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%

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: Introductionmentioning

confidence: 99%

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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“…In parallel algorithms for topology optimization, a filter based on partial differential equations is more efficient than a density filter [37]. Yang [38] proposed a massively efficient filter for topol-ogy optimization utilizing the splitting of tensor product structure. Filtering methods are also commonly employed in topology optimization for metal additive manufacturing [39].…”

Section: Introductionmentioning

confidence: 99%

A Reconstruction Approach for Concurrent Multiscale Topology Optimization Based on Direct FE2 Method

Zhao

Tan

et al. 2023

Mathematics

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The rapid development of material science is increasing the demand for the multiscale design of materials. The concurrent multiscale topology optimization based on the Direct FE2 method can greatly improve computational efficiency, but it may lead to the checkerboard problem. In order to solve the checkerboard problem and reconstruct the results of the Direct FE2 model, this paper proposes a filtering-based reconstruction method. This solution is of great significance for the practical application of multiscale topology optimization, as it not only solves the checkerboard problem but also provides the optimized full model based on interpolation. The filtering method effectively eliminates the checkerboard pattern in the results by smoothing the element densities. The reconstruction method restores the smoothness of the optimized structure by interpolating between the filtered densities. This method is highly effective in solving the checkerboard problem, as demonstrated in our numerical examples. The results show that the proposed algorithm produces feasible and stable results.

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Topology optimization using immersed isogeometric analysis and its software implementation

Xie,

Wang,

Xie

et al. 2024

Computer Methods in Applied Mechanics and Engineering

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Massively efficient filter for topology optimization based on the splitting of tensor product structure

Cited by 3 publications

References 58 publications

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

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

A Reconstruction Approach for Concurrent Multiscale Topology Optimization Based on Direct FE2 Method

Topology optimization using immersed isogeometric analysis and its software implementation

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