A boundary element and level set based bi-directional evolutionary structural optimisation with a volume constraint

Ullah, Baseer; Trevelyan, J.; Islam, Siraj Ul

doi:10.1016/j.enganabound.2017.02.012

Cited by 11 publications

(3 citation statements)

References 32 publications

(50 reference statements)

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“…Fu et al [30,31] used the SIMP method framework to perform topological design of macroscopic structures using element volume fractions, achieving smooth boundaries of grid points. Ullah et al [32,33] integrated Bidirectional evolutionary structural optimisation (BESO), the level set method, and non-uniform rational B splines (NURBS) to obtain topologies with smooth boundaries. These above works mainly focus on the topology optimisation design of 2D and 3D macroscopic structures with maximum stiffness as the goal.…”

Section: Introductionmentioning

confidence: 99%

Design and Mechanical Properties of Maximum Bulk Modulus Microstructures Based on a Smooth Topology with Grid Point Density

Zhou,

Tao,

Liang

et al. 2024

Aerospace

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The aim of topology optimisation is to determine the optimal distribution of material phases within the periodic cells of a microstructure. In this paper, the density of grid points under element volume fraction is constructed to replace the finite elements in the traditional SIMP framework, avoiding jagged and blurry boundaries in the computational process due to grid dependence. This is then combined with homogenisation theory, a microstructure topology optimisation algorithm with maximum bulk modulus under prescribed volume constraints is proposed, which can obtain 2D and 3D topologies with smooth boundaries. In addition, a closed form expression for the two-dimensional topological concave edge structure (taking the most typical topology as an example) was derived, and a compression experiment was conducted on the topological microstructure based on 3D metal printing technology. Scanning electron microscopy showed that the powder bonded on the surface of the printed structure was not completely melted and the step effect caused the finite element analysis results to be higher than the experimental results. Overall, the finite element simulation and experimental results of the concave surface structure have good consistency, with high strength and energy absorption effects. Topologies based on grid point density obtain microstructures with smooth boundaries, and the introduction of the Heaviside smoothing function and multiple filtering steps within this algorithm leads to more robust optimisation, facilitating 3D or 4D printing of microstructures that meet specific design requirements and confirming the feasibility of the proposed topology for lightweighting studies.

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Section: Introductionmentioning

confidence: 99%

Design and Mechanical Properties of Maximum Bulk Modulus Microstructures Based on a Smooth Topology with Grid Point Density

Zhou,

Tao,

Liang

et al. 2024

Aerospace

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“…Previous work on the topic of shape optimization with the BEM by the research community has mostly considered 2D structures, [1][2][3][4][5][6][7][8][9][10][11] and to a lesser-degree 3D structures. [12][13][14][15][16][17][18] Very few previous works by the research community on the topic of shape optimization with the BEM have considered plate or shell structures.…”

Section: Introductionmentioning

confidence: 99%

Manufacturing cost and reliability‐based shape optimization of plate structures

Morse

Mallardo

Aliabadi

2022

Numerical Meth Engineering

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A novel methodology is presented for the manufacturing cost and reliability-based optimization of plate structures with the boundary element method (BEM), with the aim of improving the accuracy, robustness, and efficiency of the optimization of aircraft structures. The BEM plate formulations with respect to plate thickness are derived for the first time, and used as part of an implicit differentiation method (IDM), enabling the full shape optimization of plate structures with the BEM. These implicit derivatives are validated against derivatives obtained from the finite difference method (FDM) and from an analytical solution. Results indicate that the IDM is more robust than the FDM and in excellent agreement with the analytical solution, and more accurate than the FDM for most of the step-sizes investigated. To demonstrate the full shape optimization of plates with the newly developed IDM, a numerical example involving reliability-based design optimization and manufacturing cost optimization is presented for a plate structure. Results show that the newly developed IDM is more efficient than the FDM when performing this optimization.

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“…Most prior work on structural sensitivity analysis with the BEM amongst the research community has involved 2D structures [2][3][4][5][6][7][8][9][10][11], and 3D structures [12][13][14][15][16][17] to a smaller degree. There have only been a few prior research works on the topic of structural sensitivity analysis with the BEM that have involved plate structures, with some examples being [18,19].…”

Section: Introductionmentioning

confidence: 99%

Shape Optimisation of Assembled Plate Structures with the Boundary Element Method

2022

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A novel methodology is presented for performing sensitivity analyses of assembled plate structures using the Boundary Element Method (BEM). The main novelty of this work is that the exact implicit derivatives of the BEM formulations for assembled plate structures have been derived for the first time and incorporated into a newly developed Implicit Differentiation Method (IDM), enabling sensitivity analyses to be conducted for more complex and realistic structures in a more accurate, robust, and efficient manner than previous approaches. Three numerical examples are investigated to validate the derived exact implicit derivatives and to demonstrate how they could be used for a potential application involving the shape optimisation of a complex X-core structure from the canard of a Eurofighter Typhoon fighter jet. Results show that the newly developed IDM is more accurate, robust, and efficient when compared to alternative methodologies using derivatives obtained from methods such as the Finite Difference Method (FDM) and the Finite Element Method (FEM).

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A boundary element and level set based bi-directional evolutionary structural optimisation with a volume constraint

Cited by 11 publications

References 32 publications

Design and Mechanical Properties of Maximum Bulk Modulus Microstructures Based on a Smooth Topology with Grid Point Density

Design and Mechanical Properties of Maximum Bulk Modulus Microstructures Based on a Smooth Topology with Grid Point Density

Manufacturing cost and reliability‐based shape optimization of plate structures

Shape Optimisation of Assembled Plate Structures with the Boundary Element Method

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