Topology optimization - broadening the areas of application

• Autorzy: Bendsoe M. P. , Lund E. , Olhoff N. , Sigmund O.
• Języki publikacji: EN

Abstrakty

EN

This paper deals with recent, developments of topology optimization techniques for application in some new types of design problems. The emphasis is on recent work of the Danish research groups at Aalborg University and at the Technical University of Denmark and focus is on the central role that the choice of objective functions and design parameterization plays for a successful extension of the material distribution approach to new design settings and to new types of physics models. The applications that will be outlined encompass design of laminated composite structures, design for pressure loads, design in fluids, design in acoustics, and design in photonics. A short outline of other design optimization activities is also given.

Słowa kluczowe

EN

topology optimization; laminates; pressure loads; multiphysics; fluids

PL

optymalizacja topologiczna; laminat; płyn

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2005
• Tom: Vol. 34, no 1
• Strony: 7--35
• Opis fizyczny: Bibliogr. 59 poz., rys., wykr.

Twórcy

autor

Bendsoe M. P.

• Department of Mathematics, Technical University of Denmark DK-2800 Lyngby, Denmark

autor

Lund E.

• Department of Mechanical Engineering, Aalborg University DK-9220 Aalborg Ø, Denmark

autor

Olhoff N.

• Department of Mechanical Engineering, Aalborg University DK-9220 Aalborg Ø, Denmark

autor

Sigmund O.

• Department of Mechanical Engineering, Technical University of Denmark DK-2800 Lyngby, Denmark

Bibliografia

• Allaire, G., Jouve, F. and Toader, A.-M. (2004) Structural optimization using sensitivity analysis and a level-set method. Journal of Computational Physics 194 (1), 363–393.
• Bendsøe, M.P. and Sigmund, O. (2003) Topology Optimization - Theory, Methods and Applications. Springer Verlag, Berlin Heidelberg. Borel, P., Harpøth, A., Frandsen, L.H., Kristensen, M., Shi, J.S.J.P. and Sigmund, O. (2004) Topology optimization and fabrication of photonic crystal structures. Optics Express 12 (9), 1996–2001.
• Borrvall, T. and Petersson, J. (2003) Topology optimization of fluids in Stokes flow. International Journal for Numerical Methods in Fluids 41, 77–107.
• Bourdin, B. and Chambolle, A. (2003) Design-dependent loads in topology optimization. ESAIM: Control, Optimisation and Calculus of Variations 9, 19–48.
• Bruns, T.E., Sigmund, O. and Tortorelli, D.A. (2002) Numericalmethods for the topology optimization of structures that exhibit snap-through. International Journal for Numerical Methods in Engineering 55, 1215–1237.
• Buhl, T. (2002) Simultaneous topology optimization of structure and supports. Structural and Multidisciplinary Optimization 23 (5), 336–346.
• Bywater, R., Poulsen, T.A., Røgen, P. and Hjorth, P.G. (2004) De novo generation of molecular structures using optimization to select graphs on a given lattice. Journal of Chemical Information Theory and Computer Science 44 (3), 856–86.
• Chellappa, S., Diaz, A.R. and Bendsøe, M.P. (2004) Layout optimization of structures with finite-sized features using multiresolution analysis. Structural and Multidisciplinary Optimization 26 (1), 77–91.
• Chen, B.-C. and Kikuchi, N. (2001) Topology optimization with design-dependent loads. Finite Element in Analysis and Design 37, 57–70.
• Du, J. and Olhoff, N. (2004a) Topological optimization of continuum structures with design-dependent surface loading - Part I: new computational approach for 2D problems. Structural and Multidisciplinary Optimization 27 (3), 151–165.
• Du, J. and Olhoff, N. (2004b) Topological optimization of continuum structures with design-dependent surface loading - Part II: algorithm and examples for 3D problems. Structural and Multidisciplinary Optimization 27 (3), 166–177.
• Eschenauer, H.A. and Olhoff, N. (2001) Topology optimization of continuum structures: A review. Appl. Mech. Rev. 54 (4), 331–390.
• Foldager, J., Hansen, J.S. and Olhoff, N. (1998) A general approach forcing convexity of ply angle optimization in composite laminates. Structural Optimization 16 (2), 201–211.
• Foldager, J.P., Hansen, J.S. and Olhoff, N. (2001) Optimization of the buckling load for composite structures taking thermal effects into account. Structural and Multidisciplinary Optimization 21 (1), 14–31.
• Fuchs, M.B. and Moses, E. (2000) Optimal structural topologies with transmissible loads. Structural and Multidisciplinary Optimization 19, 263–273.
• Gartling, D., Hickox, C. and Givler, R. (1996) Simulation of coupled viscous and porous flow problems. Compu. Fluid. Dyn. 7, 23–48.
• Gersborg-Hansen, A., Sigmund, O. and Haber, R.B. (2004) Topology optimization of channel flow problems. Structural and Multidisciplinary Optimization, to appear.
• Gibiansky, L.V. and Sigmund, O. (2000)Multiphase elastic composites with extremal bulk modulus. Journal of the Mechanics and Physics of Solids 48 (3), 461–498.
• Guedes, J.M., Rodrigues, H.C. and Bendsøe, M.P. (2003) A material optimization model to approximate energy bounds for cellular materials under multiload conditions. Structural and Multidisciplinary Optimization, 25, 446-452.
• Hammer, V. B., Bendsøe, M.P., Lipton, R. and Pedersen, P. (1997) Parametrization in laminate design for optimal compliance. International Journal of Solids and Structures 34 (4), 415–434.
• Hammer, V.B. and Olhoff, N. (1999) Topology optimization with design dependent loads. In: C.L. Bloebaum, ed., Proc. WCSMO-3, Third World Congress of Structural and Multidisciplinary Optimization, CD-Rom.
• Hammer, V.B. and Olhoff, N. (2000) Topology optimization of continuum structures subjected to pressure loading. Structural and Multidisciplinary Optimization 19, 85–92.
• Hammer, V.B. and Olhoff, N. (2001) Topology optimization of 3D structures with design dependent loads. In: G.D. Cheng, Y. Gu, S. Liu and Y. Wang, eds., Proc. Second World Congress of Structural and Multidisciplinary Optimization, Liaoning Electronic Press, Dalian, CD-rom.
• Jensen, J.S. (2003) Phononic band gaps and vibrations in one- and twodimensional mass-spring structures. Journal of Sound and Vibration 266 (5), 1053–1078.
• Jensen, J.S. and Pedersen, N.L. (2005) On separation of eigenfrequencies in two-material structures using topology optimization: The 1D and 2D scalar cases. J. Sound and Vibration, to appear.
• Jensen, J.S. and Sigmund, O. (2004) Systematic design of photonic crystal structures using topology optimization: Low-loss waveguide bends. Applied Physics Letters 84 (12), 2022–2024.
• Jensen, J.S. and Sigmund, O. (2005) Topology optimization of photonic crystal structures using active sets: Design of a T-juntion waveguide. J. Opt. Soc. Am. B, to appear.
• Jonsmann, J., Sigmund, O. and Bouwstra, S. (1999)Multi degrees of freedom electro-thermal microactuators. In: ‘TRANSDUCERS’99’, 1372–1375.
• Kawamoto, A., Bendsøe, M.P. and Sigmund, O. (2004) Articulated mechanism design with a degree of freedom constraint. International Journal for Numerical Methods in Engineering 61 (9), 1520–1545.
• Landau, L.D. and Lifshitz, E.M. (1975) The Classical Theory of Fields, 4th ed. Pergamon Press, Oxford.
• Langthjem, M. and Olhoff, N. (2004a) A numerical study of flow-induced noise in a two-dimensional centrifugal pump. Part I. Hydrodynamics. Journal of Fluids and Structures 19 (3), 349–368.
• Langthjem, M. and Olhoff, N. (2004b) A numerical study of flow-induced noise in a two-dimensional centrifugal pump. Part II. Hydroacoustics. Journal of Fluids and Structures 19 (3), 369–386.
• Lund, E., Møller, H. and Jakobsen, L. (2003) Shape design optimization of stationary fluid-structure interaction problems with large displacements and turbulence. Structural and Multidisciplinary Optimization 25 (5-6), 383–392.
• Lund, E., Møller, H. and Jakobsen, L.A. (2002) Shape optimization of fluid-structure interaction problems using two-equation turbulence models. In: Proc. 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, 22 - 25 April 2002, Denver, Colorado, AIAA, CD-ROM.
• Lund, E. and Stegmann, J. (2005) On structural optimization of composite shell structures using a discrete constitutive parameterization. Wind Enrgy 8 (1), 109–124.
• Neves, M.M., Sigmund, O. and Bendsøe, M.P. (2002) Topology optimization of periodic microstructures with a penalization of highly localized buckling modes. International Journal for Numerical Methods on Engineering 54 (6), 809–834.
• Norato, J., Haber, R., Tortorelli, D. and Bendsøe, M.P. (2004) A geometry projection method for shape optimization. International Journal for Numerical Methods in Engineering 60 (14), 2289–2312.
• Olhoff, N. and Du, J. (2004) Topology optimization of vibrating structures with hydrodynamic surface pressure loading. In: Proc. 21st International Congress of Theoretical and Applied Mechanics, Warsaw, Poland, August 15-21, 2004, Institute of Fundamental Technological Research, Warsaw, Poland, CD-Rom.
• Pedersen, C.B.W. (2003) Topology optimization for crashworthiness of frame structures. International Journal of Crashworthiness 8 (1), 29–40.
• Pedersen, C.B.W. (2004) Crashworthiness design of transient frame structures using topology optimization. Computer Methods in Applied Mechanics and Engineering 193 (6-8), 653–678.
• Pedersen, N. L. and Pedersen, P. (2003) Shape, position and orientational design of holes for plates with optimized eigenfrequencies. Materials Science Forum 440-441, 321–328.
• Pedersen, P. (2003) A note on design of fiber-nets for maximum stiffness. Journal of Elasticity 73 (3), 127–145.
• Pironneau, O. (1973) On optimal profiles in Stokes flow. Journal of Fluid Mechanics 59, 117–128.
• Poulsen, T.A. (2002a) A simple scheme to prevent checkerboard patterns and one-node connected hinges in topology optimization. Structural and Multidisciplinary Optimization 24 (5), 396–399.
• Poulsen, T.A. (2002b) Topology optimization in wavelet space. International Journal for Numerical Methods in Engineering 53, 567–582.
• Poulsen, T.A. (2003) A new scheme for imposing a minimum length scale in topology optimization. International Journal for Numerical Methods in Engineering 57 (6), 741–760.
• Rodrigues, H.C., Guedes, J.M. and Bendsøe, M.P. (2002) Hierarchical optimization of material and structure. Structural and Multidisciplinary Optimization 24 (1), 1–10.
• Sigmund, O. (2001) A 99 line topology optimization code written in MATLAB. Structural and Multidisciplinary Optimization 21, 120–127.
• Sigmund, O. and Jensen, J.S. (2003) Systematic design of phononic band gap materials and structures by topology optimization. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 361, 1001–1019.
• Sigmund, O. and Jensen, J.S. (2005) Systematic design of acoustic devices using topology optimization. Under preparation.
• Sigmund, O. and Petersson, J. (1998) Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, meshdependencies and local minima. Structural Optimization 16 (1), 68–75.
• Sigmund, O. and Torquato, S. (1997) Design of materials with extreme thermal expansion using a three-phase topology optimization method. Journal of the Mechanics and Physics of Solids 45 (6), 1037–1067.
• Stegmann, J. and Lund, E. (2005) Discrete material optimization of general composite shell structures. International Journal for Numerical Methods in Engineering 62 (14), 2009–2027.
• Stolpe, M. and Kawamoto, A. (2005) Design of planar articulated mechanisms using branch and bound. Mathematical Programming B, published on-line, April 2005.
• Svanberg, K. (1987) The method of moving asymptotes - A new method for structural optimization. International Journal for Numerical Methods in Engineering 24, 359–373.
• Svanberg, K. (2002) A class of globally convergent optimization methods based on conservative convex separable approximation. SIAM Journal on Optimization 12 (2), 555–557.
• Wang, X., Wang, M.Y. and Guo, D. (2004) Structural shape and topology optimization in a level-set-based framework of region representation. Structural and Multidisciplinary Optimization 27 (1-2), 1–19.
• Yoon, G.H., Kim, Y.Y., Bendsøe, M.P. and Sigmund, O. (2004) Hingefree topology optimization with embedded translation-invariant differentiable wavelet shrinkage. Structural and Multidisciplinary Optimization 27 (3), 139–150.