Multi-patch isogeometric topology optimization for cellular structures with flexible designs using Nitsche’s method

Gao, Jie; Wu, Xiaomeng; Xiao, Mi; Nguyen, Vinh Phu; Gao, Liang; Rabczuk, Timon

doi:10.1016/j.cma.2023.116036

Cited by 20 publications

(1 citation statement)

References 54 publications

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“…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. 40 Motivated by the advantages of ITO, a series of multi-material ITO (MMITO) methods have been developed. Taheri proposed a new MMITO method where the complexity and the minimal lengths of the optimal design are controlled by the perimeter control technique.…”

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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An Isogeometric Topology Optimization Method for Free-Form Shell Structures Using T-splines

Gao,

Zhang,

Xiao

et al. 2024

Mechanisms and Machine Science

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IGA-based topology optimization in the design of stress-constrained compliant mechanisms

Villalba,

Gonçalves,

Dias-de-Oliveira

et al. 2023

Struct Multidisc Optim

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Topology design of compliant mechanisms has gained wide popularity among the scientific community, and their use in the mechanical engineering field is being of upmost importance. In this paper, an isogeometric analysis (IGA) formulation is used to solve the topology optimization problem of compliant mechanisms. Stress constraints are introduced in the problem to guarantee the attainment of realistic solutions. For this purpose, an overweight constraint is considered for the design process, replacing the use of local stress constraints. The material distribution in the domain is modeled with quadratic B-splines and with a uniform relative density within each element of the mesh. These strategies to define the material layout are used to compare the IGA-based formulation with the finite element (FEM) formulation. The IGA formulation provides several advantages with respect to the classical FEM-based approaches that are shown and analyzed with an input-parameters sensitivity analysis. The sensitivity analysis and the assessment of the importance of introducing of stress constraints in the problem are developed by solving two benchmark problems. Regarding the sensitivity analysis of input parameters, the results show that the ratio between the material and the springs stiffnesses is the parameter with the largest influence on the solutions of the problem. Moreover, the advantages of the IGA formulations over FEM formulations are related with the computational time, the smoothness of the structural borders, and the non-appearance of the checkerboard patterns. With respect to the stress constraints, the results show that they have to be considered in order to avoid instability and structural integrity problems.

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Multi-patch isogeometric topology optimization for cellular structures with flexible designs using Nitsche’s method

Cited by 20 publications

References 54 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

An Isogeometric Topology Optimization Method for Free-Form Shell Structures Using T-splines

IGA-based topology optimization in the design of stress-constrained compliant mechanisms

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