×

zbMATH — the first resource for mathematics

Volume preserving nonlinear density filter based on Heaviside functions. (English) Zbl 1274.74419
Summary: To prevent numerical instabilities and ensure manufacturability, restrictions should be applied in topology optimization. In this paper, a volume preserving density filter based on Heaviside functions is presented. Different from earlier Heaviside density filters, this filter is volume preserving, which ensures efficiency and stability in optimization. The new filter is compared with four other filters through a compliance minimization problem.

MSC:
74P15 Topological methods for optimization problems in solid mechanics
74P05 Compliance or weight optimization in solid mechanics
65K05 Numerical mathematical programming methods
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Allaire G, Jouve F, Toader AM (2004) Structural optimization using sensitivity analysis and a level-set method. J Comput Phys 194(1):363–393 · Zbl 1136.74368
[2] Ambrosio L, Buttazzo G (1993) An optimal design problem with perimeter penalization. Calc Var Partial Differ Equ 1(1):55–69 · Zbl 0794.49040
[3] Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Multidiscipl Optim 1(4):193–202
[4] Bendsøe MP (1995) Optimization of structural topology, shape and material. Springer, New York · Zbl 0822.73001
[5] Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in optimal design using a homogenization method. Comput Methods Appl Mech Eng 71(2):197–224 · Zbl 0671.73065
[6] Borrvall T (2001) Topology optimization of elastic continua using restriction. Arch Comput Methods Eng 8(4):351–385 · Zbl 1141.74356
[7] Bourdin B (2001) Filters in topology optimization. Int J Numer Methods Eng 50(9):2143–2158 · Zbl 0971.74062
[8] Bourdin B, Chambolle A (2003) Design-dependent loads in topology optimization. ESAIM, Control Optim Calc Var 9:19–48 · Zbl 1066.49029
[9] Bruns TE, Tortorelli DA (2001) Topology optimization of non-linear elastic structures and compliant mechanisms. Comput Methods Appl Mech Eng 190(26-27):3443–3459 · Zbl 1014.74057
[10] Cheng KT, Olhoff N (1981) An investigation concerning optimal design of solid elastic plates. Int J Solids Struct 17(3):305–323 · Zbl 0457.73079
[11] Guest JK, Prévost JH, Belytschko T (2004) Achieving minimum length scale in topology optimization using nodal design variables and projection functions. Int J Numer Methods Eng 61(2):238–254 · Zbl 1079.74599
[12] Guo X, Gu YX (2004) A new density-stiffness interpolation scheme for topology optimization of continuum structures. Eng Comput 21(1):9–22 · Zbl 1063.74079
[13] Haber RB, Jog CS, Bendsøe MP (1996) A new approach to variable-topology shape design using a constraint on perimeter. Struct Multidiscipl Optim 11(1–2):1–12
[14] Kim YY, Yoon GH (2000) Multi-resolution multi-scale topology optimization–a new paradigm. Int J Solids Struct 37(39):5529–5559 · Zbl 0981.74044
[15] Niordson F (1983) Optimal design of plates with a constraint on the slope of the thickness function. Int J Solids Struct 19(2):141–151 · Zbl 0502.73074
[16] Petersson J, Sigmund O (1998) Slope constrained topology optimization. Int J Numer Methods Eng 41(8):1417–1434 · Zbl 0907.73044
[17] Poulsen TA (2002) Topology optimization in wavelet space. Int J Numer Methods Eng 53(3):567–582 · Zbl 1112.74464
[18] Sethian JA, Wiegmann A (2000) Structural boundary design via level set and immersed interface methods. J Comput Phys 163(2):489–528 · Zbl 0994.74082
[19] Sigmund O (1994) Design of material structures using topology optimization. Phd thesis, Department of Solid Mechanics, Technical University of Denmark
[20] Sigmund O (2001) Design of multiphysics actuators using topology optimization–part ii: two-material structures. Comput Methods Appl Mech Eng 190(49-50):6605–6627 · Zbl 1116.74407
[21] Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidiscipl Optim 33(4–5):401–424
[22] Sigmund O, Petersson J (1998) Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct Multidiscipl Optim 16(1):68–75
[23] Svanberg K (1987) The method of moving asymptotes–a new method for structural optimization. Int J Numer Methods Eng 24:359–373 · Zbl 0602.73091
[24] Wang MY, Wang S (2005) Bilateral filtering for structural topology optimization. Int J Numer Methods Eng 63(13):1911–1938 · Zbl 1138.74379
[25] Wang MY, Zhou S (2004) Phase field: a variational method for structural topology optimization. Comput Model Eng Sci 6(6):547–566 · Zbl 1152.74382
[26] Wang MY, Wang X, Guo D (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Eng 192(1–2):227–246 · Zbl 1083.74573
[27] Zhou M, Shyy YK, Thomas HL (2001) Checkerboard and minimum member size control in topology optimization. Struct Multidiscipl Optim 21(2):152–158
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.