[en] The so-called bi-value coding parameterization (BCP) method is developed for the simultaneous optimization of layout design and discrete fiber orientations of laminated structures related to the compliance minimization and natural frequency maximization. Both kinds of problems are transformed into a discrete material selection problem that is then solved as a continuous topology optimization
problem with multiphase materials. A new form of the volume constraint is introduced in accordance with the BCP to control the material usage and material removal in the corresponding problem formulation. The BCP scheme assigning the integer value of +1 or -1 to each design variable for the unique “coding” is efficiently used to interpolate discrete fiber orientations and to identify the presence and removal of materials. Meanwhile, a general set-up strategy is proposed by assigning “uniform” weight values in BCP to ensure the feasibility of the initial starting point. Numerical tests illustrate that the BCP is efficient in dealing with both kinds of design problems including the volume constraint.
Disciplines :
Aerospace & aeronautics engineering
Author, co-author :
TONG, Gao; North Western Polytechnic University
ZHANG, Weihong; North Western Polytechnic University
Duysinx, Pierre ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Ingénierie des véhicules terrestres
Language :
English
Title :
Simultaneous design of structural layout and discrete fiber orientation using bi-value coding parameterization and volume constraint
Alternative titles :
[fr] Conception simultanée de la disposition et de l'orientation discrète des fibres utilisant la paramétrisation en codage binaire et une contrainte de volume
Bendsøe, M.P., Sigmund, O., Material interpolation schemes in topology optimization (1999) Arch Appl Mech, 69, pp. 635-654. , 10.1007/s004190050248
Blasques, J., Stolpe, M., Maximum stiffness and minimum weight optimization of laminated composite beams using continuous fiber angles (2011) Struct Multidiscip Optim, 43, pp. 573-588. , 10.1007/s00158-010-0592-9
Bruyneel, M., SFP - A new parameterization based on shape functions for optimal material selection: Application to conventional composite plies (2011) Struct Multidiscip Optim, 43, pp. 17-27. , 10.1007/s00158-010-0548-0
Bruyneel, M., Duysinx, P., Fleury, C., Gao, T., Extensions of the shape functions with penalization parameterization for composite-ply optimization (2011) AIAA J, 49, pp. 2325-2329. , 10.2514/1.J051225
Cheng, H.C., Kikuchi, N., Ma, Z.D., An improved approach for determining the optimal orientation of orthotropic material (1994) Struct Multidiscip Optim, 8, pp. 101-112
Díaz, A.R., Bendsøe, M.P., Shape optimization of structures for multiple loading conditions using a homogenization method (1992) Struct Multidiscip Optim, 4, pp. 17-22
Fleury, C., Braibant, V., Structural optimization: A new dual method using mixed variables (1986) Int J Numer Methods Eng, 23, pp. 409-428. , 833188 10.1002/nme.1620230307
Gao, T., Zhang, W., A mass constraint formulation for structural topology optimization with multiphase materials (2011) Int J Numer Methods Eng, 88, pp. 774-796. , 10.1002/nme.3197
Gao, T., Zhang, W., Duysinx, P., A bi-value coding parameterization scheme for the discrete optimal orientation design of the composite laminate (2012) Int J Numer Methods Eng, 91, pp. 98-114. , 10.1002/nme.4270
Gea, H.C., Luo, J.H., On the stress-based and strain-based methods for predicting optimal orientation of orthotropic materials (2004) Struct Multidiscip Optim, 26, pp. 229-234. , 10.1007/s00158-003-0348-x
Hvejsel, C., Lund, E., Material interpolation schemes for unified topology and multi-material optimization (2011) Struct Multidiscip Optim, 43, pp. 1-15. , 10.1007/s00158-011-0625-z
Kennedy, J., Eberhart, R.C., Particle swarm optimization (1995) Proceedings of the IEEE International Conference on Neural Networks, pp. 1942-1948. , Perth, Wa
Kitayama, S., Arakawa, M., Yamazaki, K., Penalty function approach for the mixed discrete nonlinear problems by particle swarm optimization (2006) Struct Multidiscip Optim, 32, pp. 191-202. , 2252744 10.1007/s00158-006-0021-2
Le Riche, R., Haftka, R.T., Optimization of laminate stacking sequence for buckling load maximization by genetic algorithm (1993) AIAA J, 31, pp. 951-956. , 10.2514/3.11710
Le Riche, R., Haftka, R.T., Improved genetic algorithm for minimum thickness composite laminate design (1995) Compos Eng, 5, pp. 143-161. , 10.1016/0961-9526(95)90710-S
Lund, E., Buckling topology optimization of laminated multi-material composite shell structures (2009) Compos Struct, 91, pp. 158-167. , 10.1016/j.compstruct.2009.04.046
Omkar, S., Mudigere, D., Naik, G., Gopalakrishnan, S., Vector evaluated particle swarm optimization (VEPSO) for multi-objective design optimization of composite structures (2008) Comput Struct, 86, pp. 1-14. , 10.1016/j.compstruc.2007.06.004
Pedersen, P., On optimal orientation of orthotropic materials (1989) Struct Multidiscip Optim, 1, pp. 101-106
Pedersen, P., Bounds on elastic energy in solids of orthotropic materials (1990) Struct Multidiscip Optim, 2, pp. 55-63
Pedersen, P., On thickness and orientational design with orthotropic materials (1991) Struct Multidiscip Optim, 3, pp. 69-78
Sigmund, O., Design of multiphysics actuators using topology optimization - Part II: Two-material structures (2001) Comput Methods Appl Mech Eng, 190, pp. 6605-6627. , 10.1016/S0045-7825(01)00252-3
Sigmund, O., Torquato, S., Design of materials with extreme thermal expansion using a three-phase topology optimization method (1997) J Mech Phys Solids, 45, pp. 1037-1067. , 1456086 10.1016/S0022-5096(96)00114-7
Stegmann, J., Lund, E., Discrete material optimization of general composite shell structures (2005) Int J Numer Methods Eng, 62, pp. 2009-2027. , 10.1002/nme.1259
Stegmann, J., Lund, E., On discrete material optimization of laminated composites using global and local criteria (2006) IUTAM Symposium on Topological Design Optimization of Structures. Machines and Materials, pp. 89-98. , M. Bendsøe N. Olhoff O. Sigmund (eds) Springer Netherlands 10.1007/1-4020-4752-5-9
Stolpe, M., Stegmann, J., A Newton method for solving continuous multiple material minimum compliance problems (2008) Struct Multidiscip Optim, 35, pp. 93-106. , 2383005 10.1007/s00158-007-0131-5
Svanberg, K., (1995) A Globally Convergent Version of MMA Without Line Search. In: First World Congress of Structural and Multidisciplinary Optimization, pp. 9-16. , Pergamon Press Goslar
Zhang, W.H., Fleury, C., A modification of convex approximation methods for structural optimization (1997) Comput Struct, 64, pp. 89-95. , 1464993 10.1016/S0045-7949(96)00147-2