Interface shape design of multi-material structures for delamination strength
This paper deals with interface shape optimum design of multi-material structures for the delamination strength problem. The optimum design problem is formulated as a non-parametric shape optimization problem in which the interface variation in the normal direction is considered as a design variable...
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| Published in | Mechanical Engineering Journal Vol. 3; no. 1; p. 15-00360 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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The Japan Society of Mechanical Engineers
2016
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| Subjects | |
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| Abstract | This paper deals with interface shape optimum design of multi-material structures for the delamination strength problem. The optimum design problem is formulated as a non-parametric shape optimization problem in which the interface variation in the normal direction is considered as a design variable. The maximum value of a delamination function, an index of the delamination strength, is defined as an objective function subject to a volume constraint. The shape sensitivity, called shape gradient function, is derived by using the material derivative method and the adjoint variable method, and is applied to the H1 gradient method to determine the optimal interface shape. With this method, the maximum value of the delamination function can be minimized while the smooth optimal interface shape can be obtained without any shape design parametrization. Several interface shape design examples are presented to verify the validity and practical utility of the proposed method. |
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| AbstractList | This paper deals with interface shape optimum design of multi-material structures for the delamination strength problem. The optimum design problem is formulated as a non-parametric shape optimization problem in which the interface variation in the normal direction is considered as a design variable. The maximum value of a delamination function, an index of the delamination strength, is defined as an objective function subject to a volume constraint. The shape sensitivity, called shape gradient function, is derived by using the material derivative method and the adjoint variable method, and is applied to the H1 gradient method to determine the optimal interface shape. With this method, the maximum value of the delamination function can be minimized while the smooth optimal interface shape can be obtained without any shape design parametrization. Several interface shape design examples are presented to verify the validity and practical utility of the proposed method. |
| Author | SHIMODA, Masatoshi SHIBUTANI, Yoji MATSUNAKA, Daisuke LIU, Yang |
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| Cites_doi | 10.1016/S0022-5096(99)00043-5 10.1016/j.compstruc.2014.08.003 10.1016/j.compstruc.2014.07.020 10.1007/s00158-012-0822-4 10.1088/0964-1726/8/3/308 10.1299/kikaia.60.1479 10.1142/S0219876206000709 10.1007/s00158-014-1059-1 10.1016/B978-813120376-7/50010-5 10.1007/s00158-006-0035-9 10.1177/002199838802201205 10.1080/17415977.2013.793322 10.1063/1.117961 10.1007/978-3-642-87722-3 10.1007/s00158-013-0954-1 10.1016/j.cma.2003.10.008 |
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| References_xml | – reference: Azegami, H., Fukumoto, S. and Aoyama, T., Shape optimization of continua using NURBS as basis functions, Structural and Multidisciplinary Optimization, Vol.47, No.2(2013), pp.247-258. – reference: Liu, Y. and Shimoda, M, Parameter-free optimum design method of stiffeners on thin-walled structures, Structural and Multidisciplinary Optimization, Vol.49, No.1(2014b), pp.39-47. – reference: Kreisselmeier, G. and Steinhauser, R., Systematic control design by optimizing a vector performance index, Proceedings of IFAC Symposium on Computer aided Design of Control Systems (held in Zurich, Switzerland)(1979), pp.113-117. – reference: Liu, Y. and Shimoda, M., Non-parametric shape optimization method for natural vibration design of stiffened shells, Computers and Structures, Vol.146(2015b), pp.20-31. – reference: Azegami, H., Solution to domain optimization problems, Transactions of the Japan Society of Mechanical Engineers, Series A, Vol.60, No.574(1994), pp.1479-1486. (in Japanese) – reference: Shimoda, M. and Liu, Y., A non-parametric free-form optimization method for shell structures, Structural and Multidisciplinary Optimization, Vol.50, No.3(2014), pp.409-423. – reference: Lesemann, D.-I. M. and Brockerhoff, I. M., The prospects of multi-material design for a compact-class front section, ATZ Autotechnology, Vol.8, No.7(2008), pp.16-20. – reference: Wang, M. Y. and Wang, X., “Color” level sets: a multi-phase method for structural topology optimization with multiple materials, Computer Methods in Applied Mechanics and Engineering, Vol.193, No.6 (2004), pp.469-496. – reference: Haug, E. J., Choi, K. K. and Komkov, V., Design Sensitivity Analysis of Structural Systems(1986), Academic Press, INC. – reference: Choi, K. K. and Kim, N. H., Structural Sensitivity Analysis and Optimization(2005), Springer, New York. – reference: Sinha, S. M., Mathematical Programming: Theory and Methods, Elsevier(2006), pp.94. – reference: Brewer, J. C. and Lagace, P. A., Quadratic stress criterion for initiation of delamination, Journal of Composite Materials, Vol.22, No.12(1988), pp.1141-1155. – reference: Gibiansky, L. V. and Sigmund, O., Multiphase composites with extremal bulk modulus, Journal of the Mechanics and Physics of Solids, Vol.48, No.3 (2000), pp. 461-498. – reference: Ladyzhenskaya, O. A. and Ural'tseva, N. N., Linear and quasilinear elliptic equations(1968), Academic Press, New York. – reference: Sigmund, O. and Torquato, S., Composites with extremal thermal expansion coefficients, Applied Physics Letters, Vol.69, No.21 (1996), pp.3203-3205. – reference: Liu, Y. and Shimoda, M., Two-step shape optimization methodology for designing free-form shells, Inverse Problems in Science and Engineering, Vol.23, No.1(2015a), pp.1-15. – reference: Sahr, C., Concept tools and simulation for lightweight body design, International conference proceedings of innovative developments for lightweight vehicle structures, Volkswagen Group, (2009), pp.41-50. – reference: Pironneau, O., Optimal Shape Design for Elliptic Systems(1984), Springer-Verlag, New York. – reference: Zhou, S. and Wang, M. Y., Multimaterial structural topology optimization with a generalized cahnhilliard model of multiphase transition, Structural and Multidisciplinary Optimization, Vol.33, No.2(2007), pp.89-111. – reference: Sigmund, O. and Torquato, S., Design of smart composite materials using topology optimization, Smart Materials and Structures, Vol.8, No.3 (1999), pp.365-379. – reference: Azegami, H., Kaizu, S., Shimoda, M. and Katamine, E., Irregularity of shape optimization problems and an improvement technique, Computer Aided Optimum Design of Structures, V(1997), pp.309-326. – reference: Azegami, H. and Takeuchi, K., A smoothing method for shape optimization: Traction method using the robin condition, International Journal of Computational Methods, Vol.3, No.1(2006), pp.21-33. – reference: Zhou, S. and Wang, M. Y., 3d multi-material structural topology optimization with the generalized cahn-hilliard equations, Computer Modeling in Engineering and Sciences, Vol.16, No.2 (2006), pp.83-101. – reference: Liu, Y. and Shimoda, M., A non-parametric solution to shape identification problem of free-form shells for desired deformation mode, Computers and Structures, Vol.144(2014a), pp.1-11. – ident: 2 – ident: 7 doi: 10.1016/S0022-5096(99)00043-5 – ident: 17 – ident: 15 doi: 10.1016/j.compstruc.2014.08.003 – ident: 12 doi: 10.1016/j.compstruc.2014.07.020 – ident: 4 doi: 10.1007/s00158-012-0822-4 – ident: 11 – ident: 20 doi: 10.1088/0964-1726/8/3/308 – ident: 1 doi: 10.1299/kikaia.60.1479 – ident: 10 – ident: 3 doi: 10.1142/S0219876206000709 – ident: 18 doi: 10.1007/s00158-014-1059-1 – ident: 21 doi: 10.1016/B978-813120376-7/50010-5 – ident: 24 doi: 10.1007/s00158-006-0035-9 – ident: 5 doi: 10.1177/002199838802201205 – ident: 14 doi: 10.1080/17415977.2013.793322 – ident: 19 doi: 10.1063/1.117961 – ident: 6 – ident: 9 – ident: 8 – ident: 16 doi: 10.1007/978-3-642-87722-3 – ident: 13 doi: 10.1007/s00158-013-0954-1 – ident: 22 doi: 10.1016/j.cma.2003.10.008 – ident: 23 |
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| SubjectTerms | Delamination function Interface shape Joint strength Multi-material structures Optimum design |
| Title | Interface shape design of multi-material structures for delamination strength |
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