Topology optimization of non-linear elastic structures and compliant mechanisms
Citations
1,816 citations
1,305 citations
Cites background or methods from "Topology optimization of non-linear..."
...was suggested in Bruns and Tortorelli (2003); Wang and Wang (2005) for use with the density filtering (12)....
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...Density filtering was introduced by Bruns and Tortorelli (2001) and mathematically proven as a viable approach by Bourdin (2001)....
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...…1) mesh-independent filtering methods, constituting sensitivity filters (Sigmund, 1994, 1997; Sigmund and Petersson, 1998) and density filters (Bruns and Tortorelli, 2001; Bourdin, 2001); 2) constraint methods such as perimeter control (Ambrosio and Buttazzo, 1993; Haber et al, 1994), global…...
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...was suggested in Bruns and Tortorelli (2003); Wang and Wang (2005) for use with the density filtering (12). In Bruns and Tortorelli (2003) the variance is defined by σd = R/3 and in Wang and Wang (2005) by σd = R/2....
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...was suggested in Bruns and Tortorelli (2003); Wang and Wang (2005) for use with the density filtering (12). In Bruns and Tortorelli (2003) the variance is defined by σd = R/3 and in Wang and Wang (2005) by σd = R/2. In both cases, the filter is truncated at radius R. For the latter case, it means that the bell-shape curve is heavily truncated. In tests, the author did not experience any advantages of the smooth Gaussian function compared to the original linear function, however, it is possible that there is an advantage when the filtering scheme is used in connection with the element removal and re-introduction scheme suggested by Bruns and Tortorelli (2003). For completeness one may also consider a constant weighting function...
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1,052 citations
Cites background from "Topology optimization of non-linear..."
...These include the sensitivity filter (Sigmund and Petersson 1998) and the density filter (Bourdin 2001; Bruns and Tortorelli 2001), which modify either the sensitivity or the density value of an element based on the sensitivity or density of elements in a localized neighborhood....
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1,047 citations
Cites methods from "Topology optimization of non-linear..."
...Filtering techniques originally comprised sensitivity filtering (Sigmund 1997) and density filtering approaches ( Bruns and Tortorelli 2001; Bourdin 2001) and these two approaches have produced globally meshconvergent designs that in many cases are fully satisfactory for practical purposes....
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...Here the mesh independent density filtering ( Bruns and Tortorelli 2001; Bourdin 2001) is used as a basis to ensure existence of solutions....
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998 citations
Cites methods from "Topology optimization of non-linear..."
...In addition to the sensitivity filter (Sigmund, 1994, 1997), which is already implemented in the 99 line code, the new 88 line code also includes density filtering (Bruns and Tortorelli, 2001 ; Bourdin, 2001)....
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...The results obtained with the PDE filter are similar to the ones obtained by using an exponentially decaying filter kernel (Bruns and Tortorelli, 2001)....
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References
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