[en] This paper proposes to investigate topology optimization with density-dependent body forces and especially self-weight loading. Surprisingly the solution of such problems cannot be based on a direct extension of the solution procedure used for minimum-compliance topology optimization with fixed external loads. At first the particular difficulties arising in the considered topology problems are pointed out: non-monotonous behaviour of the compliance, possible unconstrained character of the optimum and the parasitic effect for low densities when using the power model (SIMP). To get rid of the last problem requires the modification of the power law model for low densities. The other problems require that the solution procedure and the selection of appropriate structural approximations be revisited. Numerical applications compare the efficiency of different approximation schemes of the MMA family. It is shown that important improvements are achieved when the solution is carried out using the gradient-based method of moving asymptotes (GBMMA) approximations. Criteria for selecting the approximations are suggested. In addition, the applications also provide the opportunity to illustrate the strong influence of the ratio between the applied loads and the structural weight on the optimal structural topology.
scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.
Bibliography
Bendsøe M, Sigmund O (2003) Topology optimization: theory, methods, and applications. Springer, Berlin Heidelberg New York
Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1:193-202
Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71:197-224
Bruyneel M, Duysinx P (2001) Topology optimization with selfweight loading: unexpected problems and solutions. In: Bendsøe M, Olhoff N, Rasmussen J (eds.) Second Max Planck Workshop on Engineering Design Optimization, Nyborg, Denmark, pp124-127
Bruyneel M, Duysinx P, Fleury C (2002) A family of MMA approximations for structural optimization. Struct Multidisc Optim 24:263-276
Duysinx P (1997) Layout optimization: a mathematical programming approach. Danish Center for Applied Mathematics and Mechanics, DCAMM Report No. 540
Duysinx P, Bendsøe M (1998) Control of local stresses in topology optimization of continuum structures. Int J Numer Methods Eng 43:1453-1478
Duysinx P, Zhang W, Fleury C, Nguyen V, Haubruge S (1995) A new separable approximation scheme for topological problems and optimization problems characterized by a large number of design variables. In: Rozvany G, Olhoff N (eds.) First World Congress of Structural and Multidisciplinary Optimization. Pergamon, New York, pp1-8
Eschenauer H, Olhoff N (2001) Topology optimization of continuum structures: a review. ASME Appl Mech Rev 54(4):331-390
Fleury C (1993) Mathematical programming methods for constrained optimization: dual methods, Vol. 150 of Progress in astronautics and aeronautics, AIAA, Chap. 7, pp123-150
Fleury C, Braibant V (1986) Structural optimization: A new dual method using mixed variables. Int J Numer Methods Eng 23:409-428
Imam M (1998) Shape optimization of umbrella-shaped concrete shells subjected to serf-weight as the dominant load. Comput Struct 69:513-524
Karihaloo BL, Kanagasundaram S (1987) Optimum design of statically indeterminate beams under multiple loads. Comput Struct 26(3):521-538
Kwak D-Y, Jeong J-H, Cheon J-S, Im Y-T (1997) Optimal design of composite hood with reinforcing ribs through stiffness analysis. Composite Struct 38(1-4):351-359
Park K, Chang S, Youn S (2003) Topology optimization of the primary mirror of a multi-spectral camera. Struct Multidisc Optim 25(1):46-53
Pedersen N (2000) Maximization of eigenvalues using topology optimization. Struct Multidisc Optim 20:2-11
Pedersen N (2001) On topology optimization of plates with prestres. Int J Numer Methods Eng 51:225-239
Rozvany G (1977) Optimal plastic design: allowance for selfweight. J Eng Mech Div ASCE 103:1165-1170
Rozvany G (1989) Structural design via optimality criteria. Kluwer, Dordrecht
Rozvany G, Nakanamura H, Kuhnell B (1980) Optimal archgrids: allowance for selfweight. Comput Methods Appl Mech Eng 24:287-304
Rozvany G, Yep K, Ong T, Karihaloo B (1988) Optimal design of elastic beams under multiple design constraints. Int J Solids Struct 24(4):331-349
Sigmund O (1997) On the design of compliant mechanisms using topology optimization. Mech Struct Mach 25(4):493-526
Sigmund O (2001) Design of multiphysics actuators using topology optimization - Part I: One-material structures - Part II: Two-material structures. Comput Methods Appl Mech Eng 190(49-50):6577-6627
Stolpe M, Svanberg K (2001) An alternative interpolation model for minimum compliance topology optimization. Struct Multidisc Optim 22:116-124
Svanberg K (1987) The method of moving asymptotes - a new method for structural optimization. Int J Numer Methods Eng 24:359-373
Svanberg K (1995) A globally convergent version of MMA without linesearch. In: Rozvany G and Olhoff N (eds.), First World Congress of Structural and Multidisciplinary Optimization. Pergamon, New York, pp9-16
Turteltaub S, Washabaugh P (1999) Optimal distribution of material properties for an elastic continuum with structure-dependent body force. Int J Solids Struct 36:4587-4608
Wang C, Rozvany G (1983) On plane Prager - structure - non-parallel external loads and allowance for selfweight. Int J Mech Sci 25:529-541
Zhou M, Rozvany G (1991) The COC algorithm, part II: topological, geometry and generalized shape optimization. Comput Methods Appl Mech Eng 89:309-336
Similar publications
Sorry the service is unavailable at the moment. Please try again later.
This website uses cookies to improve user experience. Read more
Save & Close
Accept all
Decline all
Show detailsHide details
Cookie declaration
About cookies
Strictly necessary
Performance
Strictly necessary cookies allow core website functionality such as user login and account management. The website cannot be used properly without strictly necessary cookies.
This cookie is used by Cookie-Script.com service to remember visitor cookie consent preferences. It is necessary for Cookie-Script.com cookie banner to work properly.
Performance cookies are used to see how visitors use the website, eg. analytics cookies. Those cookies cannot be used to directly identify a certain visitor.
Used to store the attribution information, the referrer initially used to visit the website
Cookies are small text files that are placed on your computer by websites that you visit. Websites use cookies to help users navigate efficiently and perform certain functions. Cookies that are required for the website to operate properly are allowed to be set without your permission. All other cookies need to be approved before they can be set in the browser.
You can change your consent to cookie usage at any time on our Privacy Policy page.