Since 1963
ARTICLE
A mathematical programming method for the topology optimization of a truss-like continuum
1
College of Civil Engineering, Huaqiao University, Xiamen, China
Submission date: 2018-11-03
Acceptance date: 2019-04-04
Online publication date: 2019-07-15
Publication date: 2019-07-15
Journal of Theoretical and Applied Mechanics 2019;57(3):751-763
KEYWORDS
ABSTRACT
A mathematical programming method to optimize the distribution field of a truss-like ma-
terial is presented. The densities and angles of members are optimized in two separate
procedures in each iteration. An explicit sub-problem in a variable separation form is es-
tablished at every iteration procedure. At each sub-problem, the stress constraint function
is expanded into a trigonometric series of the member angles. According to the extreme
condition, the optimal orientations of members are determined. The member densities are
optimized using the method of moving asymptotes (MMA). Two examples demonstrate that
the optimal truss-like structures are very close to analytic solutions.
REFERENCES (44)
1.
Allaire G., Jouve, F., 2008, Minimum stress optimal design with the level set method, Engineering Analysis with Boundary Elements, 32, 11, 909-918.
2.
Amstutz S., Novotny A.A., 2010, Topological optimization of structures subject to von Mises stress constraints, Structural and Multidisciplinary Optimization, 41, 3, 407-420.
3.
Baratta A., Corbi I., 2014, Topology optimization for reinforcement of no-tension structures, Acta Mechanica, 225, 3, 663-678.
4.
Bendsøe M.P., 1989, Optimal shape design as a material distribution problem, Structural Optimization, 1, 4, 193-202.
5.
Bendsøe M.P., Kikuchi N., 1988, Generating optimal topologies in structural design using a homogenization method, Computer Methods in Applied Mechanics and Engineering, 71, 2, 197-224.
6.
Bendsøe M.P., Lund E., Olhoff N., Sigmund O., 2005, Topology optimization broadening the areas of application, Control and Cybernetics, 34, 1, 7-35.
7.
Bruggi M., 2008, On an alternative approach to stress constraints relaxation in topology optimization, Structural and Multidisciplinary Optimization, 36, 125-141.
8.
Bruggi M., Venini P., 2008, A mixed FEM approach to stress-constrained topology optimization, International Journal for Numerical Methods in Engineering, 73, 1693-1714.
9.
Cai S.Y., Zhang W.H., 2015, Stress constrained topology optimization with free-form design domains, Computer Methods in Applied Mechanics and Engineering, 289, 267-290.
10.
Cai S.Y., Zhang W.H., Zhu J.H., Gao T., 2014, Stress constrained shape and topology optimization with fixed mesh: a B-spline finite cell method combined with level set function, Computer Methods in Applied Mechanics and Engineering, 278, 361-387.
11.
Cheng K.T., Olhoff N., 1981, An investigation concerning optimal design of solid elastic plates, International Journal of Solids and Structures, 17, 3, 305-323.
12.
Deaton J.D., Grandhi R.V., 2014, A Survey of Structural and Multidisciplinary Continuum Topology Optimization: Post 2000, Structural and Multidisciplinary Optimization, 49, 1, 1-38
13.
Duysinx P., Bendsøe M.P., 1998, Topology optimization of continuum structures with local stress constraints, International Journal for Numerical Methods in Engineering, 43, 8, 1453-1478.
14.
Emmendoerfer H., Fancello E.A., 2016, Topology optimization with local stress constraint based on level set evolution via reaction-diffusion, Computer Methods in Applied Mechanics and Engineering, 305, 62-88.
15.
Eschenauer H.A., Olhoff N., 2001, Topology optimization of continuum structures: a review, Applied Mechanics Reviews, 54, 4, 331-390
16.
Guo X., Zhang W., Zhong W., 2014, Doing topology optimization explicitly and geometrically: a new moving morphable components based framework, Journal of Applied Mechanics, 81, 8, 081009.
17.
Guo X., Cheng G.D., 2010, Recent development in structural design and optimization, Acta Mechanica Sinica, 26, 6, 807-823.
18.
Guo X., Zhang W.S., Wang M.Y., Wei P., 2011, Stress-related topology optimization via level set approach, Computer Methods in Applied Mechanics and Engineering, 200, 47, 3439-3452.
19.
Guo X., Zhang W., Zhong W., 2014, Stress-related topology optimization of continuum structures involving multi-phase materials, Computer Methods in Applied Mechanics and Engineering, 268, 1, 632-655.
21.
Holmberg E., Torstenfelt B., Klarbring A., 2013, Stress constrained topology optimization, Structural and Multidisciplinary Optimization, 48, 33-47.
22.
Kennedy G.J., Hicken J.E., 2015, Improved constraint-aggregation methods, Computer Methods in Applied Mechanics and Engineering, 289, 332-354.
23.
Kiyono C.Y., Vatanabe S.L., Silva E.C.N., Reddy J.N., 2016, A new multi-p-norm, formulation approach for stress-based topology optimization design, Composite Structures, 156, 10-19.
24.
Le C., Norato J., Bruns T., Ha C., Tortorelli D., 2010, Stress-based topology optimization for continua, Structural and Multidisciplinary Optimization, 41, 605-620.
25.
Michell A.G.M., Melbourne M.C.E., 1904, The limits of economy of material in frame-structure, Philosophical Magazine, 8, 6, 589-597.
26.
París J., Navarrina F., Colominas I., Casteleiro M., 2009, Topology optimization of continuum structures with local and global stress constraints, Structural and Multidisciplinary Optimization, 39, 419-437.
27.
Parvizian J., Düster A., Rank E., 2012, Topology optimization using the finite cell method, Optimization and Engineering, 13, 1, 57-78.
28.
Pereira J.T., Fancello E.A., Barcellos C.S., 2004, Topology optimization of continuum structures with material failure constraints, Structural and Multidisciplinary Optimization, 26, 50-66.
29.
Picelli R., Townsend S., Brampton C., Norato J., Kim H.A., 2018, Stress-based shape and topology optimization with the level set method, Computer Methods in Applied Mechanics and Engineering, 329, 1-23.
30.
Prager W., Rozvany G.I.N., 1977, Optimal layout of grillages, Journal of Structural Mechanics, 5, 1, 1-18.
31.
Rozvany G.I.N., Zhou M., Birker T., 1992, Generalized shape optimization without homogenization, Structural Optimization, 4, 3-4, 250-252.
32.
Sigmund O., Maute K., 2013, Topology optimization approaches, Structural and Multidisciplinary Optimization, 48, 6, 1031-1055.
33.
Suresh K., Takalloozadeh M., 2013, Stress-constrained topology optimization: a topological level-set approach, Structural and Multidisciplinary Optimization, 48, 2, 295-309.
34.
Svanberg K., 1987, The method of moving asymptotes – a new method for structural optimization, International Journal for Numerical Methods in Engineering, 24, 2, 359-373.
35.
Wang M.Y., Li L., 2013, Shape equilibrium constraint: a strategy for stress-constrained structural topology optimization, Structural and Multidisciplinary Optimization, 47, 3, 335-352.
36.
Wang M.Y., Wang X.M., Guo D.M., 2003, A level set method for structural topology optimization, Computer Methods in Applied Mechanics and Engineering, 192, 1-2, 227-246.
37.
Xia Q., Shi T., Liu S., Wang M.Y., 2012, A level set solution to the stress-based structural shape and topology optimization, Computers and Structures, 90-91, 1, 55-64.
38.
Xie Y.M., Steven G.P., 1993, A simple evolutionary procedure for structural optimization, Computers and Structures, 49, 5, 885-896.
39.
Zhang W.S., Guo X., Wang M.Y., Wei P., 2013, Optimal topology design of continuum structures with stress concentration alleviation via level set method, International Journal for Numerical Methods in Engineering, 93, 9, 942-959.
40.
Zhang W.S., Yang W.Y., Zhou J., Guo X., Li D., 2017, Structural topology optimization through explicit boundary evolution, Journal of Applied Mechanics, 84, 1, 011011.
41.
Zhou K., Li J.F., 2005, Forming Michell truss in three-dimensions by finite element method, Applied Mathematics and Mechanics, English Edition, 26, 3, 381-388.
42.
Zhou K., Li X., 2006, Topology optimization of structures under multiple load cases using fiber-reinforced composite material model, Computational Mechanics, 38, 2, 163-170.
43.
Zhou K., Li X., 2011, Topology optimization of truss-like continua with three member model under stress constraints, Structural and Multidisciplinary Optimization, 43, 4, 487-493.
44.
Zhou M., Rozvany G.I.N., 1991, The COC algorithm, Part II: Topological, geometrical and generalized shape optimization, Computer Methods in Applied Mechanics and Engineering, 89, 309-336.
| eISSN: | 2543-6309 |
| ISSN: | 1429-2955 |
We process personal data collected when visiting the website. The function of obtaining information about users and their behavior is carried out by voluntarily entered information in forms and saving cookies in end devices. Data, including cookies, are used to provide services, improve the user experience and to analyze the traffic in accordance with the Privacy policy. Data are also collected and processed by Google Analytics tool (more).
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
