Topological control for 2D minimum compliance topology optimization using SIMP method

Wang, Qianglong; Han, Haitao; Wang, Chong; Liu, Zhenyu

doi:10.1007/s00158-021-03124-6

Cited by 19 publications

(6 citation statements)

References 31 publications

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“…However, it is worth noting that previous studies such as [5, 9-11, 14, and 21] have observed that mesh failure is dependent on the size of the sharp angles formed at the edges and vertices, irrespective of type of geometrical shape such as the honeycomb. By increasing the sharpness of the angles in a geometry, the meshing algorithm in many numerical modelling packages automatically finds it increasingly difficult to identify the best possible arrangement of elements [9][10]. The elements generated in the corner regions of the HC model showed low connectivity.…”

Section: Methodsmentioning

confidence: 99%

“…To determine the location, to create and shape voids in thin wall sections is very difficult when using the SIMP method for many software packages of TO. This is because such structures have a delicate structural connectivity, and by creating voids to optimise the wall sections, further structural discontinuities can easily occur [9][10]17]. Such voids can also lead to impractical designs because of the limitation of low Member with applied load…”

Section: The To Analysismentioning

confidence: 99%

“…These fewer effective iterations can lead to inaccurate changes of shape for the HC model. This inaccuracy is usually noted when the HC model has lower densities at the vertices and edges than other HC parts after TO [9][10][11]. Topology optimisation gives rise to models with changes of shape at their boundaries.…”

Section: Introductionmentioning

confidence: 99%

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REDUCED ORDER TOPOLOGY OPTIMISATION OF A PLANAR HONEYCOMB DEFINED BY A LINEAR ELASTIC Ti6Al4V (ELI) MATERIAL MODEL

Chibinyani

Dzogbewu²,

Maringa³

et al. 2022

SAJIE

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Combined numerical modelling and topology optimisation methods are useful in the design and analysis of engineering structures. The two tools are used to predict and optimise the mechanical properties of structures. Numerical modelling and optimisation of three-dimensional honeycomb structures is challenged by the sharp angles in its geometry. This reduces effective iterations in topology optimisation at the vertices and edges. The alternative – generating effective iterations at the vertices and edges in planar honeycombs of Ti6Al4V (ELI) – is presented in this paper. Mesh convergence tests with varying mesh densities were conducted on planar unit hexagonal cells at the start. The results obtained from planar unit hexagonal cells under out-of-plane compression loads before and after topology optimisation were compared. This was followed by shape optimisation and numerical analysis, and the results were compared with the numerical analysis before topology optimisation. The same procedure was followed for a planar honeycomb model. Acceptable predictions were obtained for the planar numerical models. Material reductions of 30% and 8% for the planar unit hexagon cell and for the honeycomb model respectively were obtained in topology optimisation. The maximum stresses in these numerical models after shape optimisation reduced by 58% and 4% respectively.

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Section: Methodsmentioning

confidence: 99%

Section: The To Analysismentioning

confidence: 99%

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REDUCED ORDER TOPOLOGY OPTIMISATION OF A PLANAR HONEYCOMB DEFINED BY A LINEAR ELASTIC Ti6Al4V (ELI) MATERIAL MODEL

Chibinyani

Dzogbewu²,

Maringa³

et al. 2022

SAJIE

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“…One is geometric boundary representation-based methods [7][8][9]. The other is material representation-based methods [10][11][12], in which structural topology is defined by 0-1 distribution of material and evolved by making a material trade-off. Among them, the solid isotropic material with penalization (SIMP) is the most classic method based on variable density theory with the advantages of simple program implementation and stable solution.…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Parallel Strategy for Isogeometric Topology Optimization via CPU/GPU Heterogeneous Computing

Xia,

Gao,

et al. 2024

CMES

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This paper aims to solve large-scale and complex isogeometric topology optimization problems that consume significant computational resources. A novel isogeometric topology optimization method with a hybrid parallel strategy of CPU/GPU is proposed, while the hybrid parallel strategies for stiffness matrix assembly, equation solving, sensitivity analysis, and design variable update are discussed in detail. To ensure the high efficiency of CPU/GPU computing, a workload balancing strategy is presented for optimally distributing the workload between CPU and GPU. To illustrate the advantages of the proposed method, three benchmark examples are tested to verify the hybrid parallel strategy in this paper. The results show that the efficiency of the hybrid method is faster than serial CPU and parallel GPU, while the speedups can be up to two orders of magnitude.

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“…It establishes the relationship between density and elastic modulus, takes the material density as the topological optimization design variable, and obtains the optimal distribution of structural materials through the presence or absence of materials. Compared with the homogenization method, the variable density method can directly obtain the relationship between the unit density and the elastic modulus without solving it again, which greatly reduces the variables of optimization design, simplifies the optimization solution process, and improves the calculation efficiency [8][9][10][11][12]. The evolutionary ESO method realizes structural topology optimization by imitating the biological evolution process and gradually deleting invalid or inefficient materials.…”

Section: Introductionmentioning

confidence: 99%

Topology Optimization Design of an Active Deformable Mirror Based on Discrete Orthogonal Zernike Polynomials

et al. 2022

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In order to design an active deformation mirror for projection objective aberration imaging quality control, a topology optimization design method of active deformation mirrors based on discrete orthogonal Zernike polynomials is proposed in this paper. Firstly, in order to solve the problem that continuous Zernike polynomials do not have orthogonality on the discrete coordinates inside the unit circle, which causes the instability of topology optimization results, discrete orthogonal Zernike polynomials are used to characterize the active deformation mirror wave aberrations. Then, the optical and structural deformations are combined to establish an optical-mechanical coupling topology optimization model with the help of the variable density method to derive the sensitivity of the mathematical model. Finally, a wave aberration corrected deformation mirror in an optical machine system is used as an arithmetic example for topology optimization, and the results show that the absolute value of the Zernike coefficient Z4 after optimization is improved by nearly one order of magnitude compared with the value before optimization, and the vibration characteristics of the optimized structure meet the design requirements. The optimization effect is significant, which improves the optical performance of the deformed mirror and provides a new scheme for the design of the deformed mirror structure which has a certain practical value for engineering.

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Topological control for 2D minimum compliance topology optimization using SIMP method

Cited by 19 publications

References 31 publications

REDUCED ORDER TOPOLOGY OPTIMISATION OF A PLANAR HONEYCOMB DEFINED BY A LINEAR ELASTIC Ti6Al4V (ELI) MATERIAL MODEL

REDUCED ORDER TOPOLOGY OPTIMISATION OF A PLANAR HONEYCOMB DEFINED BY A LINEAR ELASTIC Ti6Al4V (ELI) MATERIAL MODEL

A Hybrid Parallel Strategy for Isogeometric Topology Optimization via CPU/GPU Heterogeneous Computing

Topology Optimization Design of an Active Deformable Mirror Based on Discrete Orthogonal Zernike Polynomials

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