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XFEM schemes for level set based structural optimization
Li LI, Michael Yu WANG, Peng WEI
Front Mech Eng. 2012, 7 (4): 335-356.
https://doi.org/10.1007/s11465-012-0351-2
In this paper, some elegant extended finite element method (XFEM) schemes for level set method structural optimization are proposed. Firstly, two- dimension (2D) and three-dimension (3D) XFEM schemes with partition integral method are developed and numerical examples are employed to evaluate their accuracy, which indicate that an accurate analysis result can be obtained on the structural boundary. Furthermore, the methods for improving the computational accuracy and efficiency of XFEM are studied, which include the XFEM integral scheme without quadrature sub-cells and higher order element XFEM scheme. Numerical examples show that the XFEM scheme without quadrature sub-cells can yield similar accuracy of structural analysis while prominently reducing the time cost and that higher order XFEM elements can improve the computational accuracy of structural analysis in the boundary elements, but the time cost is increasing. Therefore, the balance of time cost between FE system scale and the order of element needs to be discussed. Finally, the reliability and advantages of the proposed XFEM schemes are illustrated with several 2D and 3D mean compliance minimization examples that are widely used in the recent literature of structural topology optimization. All numerical results demonstrate that the proposed XFEM is a promising structural analysis approach for structural optimization with the level set method.
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Investigations on color variations of Morpho rhetenor butterfly wing scales
Guanglan LIAO, Haibo ZUO, Xuan JIANG, Xuefeng YANG, Tielin SHI
Front Mech Eng. 2012, 7 (4): 394-400.
https://doi.org/10.1007/s11465-012-0347-y
Experiments and simulations are carried out to investigate the optical properties of Morpho rhetenor butterfly wing scales. The upper surface of a male Morpho rhetenor butterfly wing presents a single-layer of scales, the microstructures of which are responsible for the brilliant blue color. The color varies from cyan blue to yellow green and soon afterwards returns back to cyan blue when some ethanol is dropped on the upper surface. At the start of the ethanol volatilization process, the reflection spectrum remains stable. As the ethanol further volatilizes, the peak reflectance decreases slightly, then increases dramatically. Meanwhile, the peak wavelength keeps approximately constant, then decreases, and keeps almost stable at the end of the process. Therefore, the optical properties depend strongly on the varying ambient conditions, including the refractive index and the thickness of the packing medium. Moreover, the possible causes for the scales in dark green region after several dropping ethanol experiments are clarified. This research benefits our understanding of the color variation mechanisms of the wing scales, and provides inspiration for further studies and applications.
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