Name
Title | ||
|---|---|---|
The topological derivative of stress-based cost functionals in anisotropic elasticity |
Abstract | ||
|---|---|---|
The topological derivative of cost functionals J that depend on the stress (through the displacement gradient, assuming a linearly elastic material behavior) is considered in a quite general 3D setting where both the background and the inhomogeneity may have arbitrary anisotropic elastic properties. The topological derivative D J ( z ) of J quantifies the asymptotic behavior of J induced by the nucleation in the background elastic medium of a small anisotropic inhomogeneity of characteristic radius a at a specified location z . The fact that the strain perturbation inside an elastic inhomogeneity remains finite for arbitrarily small a makes the small-inhomogeneity asymptotics of stress-based cost functionals quite different than that of the more usual displacement-based functionals.The asymptotic perturbation of J is shown to be of order O ( a 3 ) for a wide class of stress-based cost functionals having smooth densities. The topological derivative of J , i.e. the coefficient of the O ( a 3 ) perturbation, is established, and computational procedures then discussed. The resulting small-inhomogeneity expansion of J is mathematically justified (i.e. its remainder is proved to be of order o ( a 3 ) ). Several 2D and 3D numerical examples are presented, in particular demonstrating the proposed formulation of D J on cases involving anisotropic elasticity and non-quadratic cost functionals. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1016/j.camwa.2015.03.010 | Computers & Mathematics with Applications |
Keywords | Field | DocType |
stress-based criteria,topological derivative,topology optimization | Mathematical optimization,Anisotropy,Nucleation,Topological derivative,Mathematical analysis,Remainder,Topology optimization,Elasticity (economics),Asymptotic analysis,Mathematics,Perturbation (astronomy) | Journal |
Volume | Issue | ISSN |
69 | 10 | 0898-1221 |
Citations | PageRank | References |
0 | 0.34 | 5 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Gabriel Delgado | 1 | 0 | 0.34 |
| Marc Bonnet | 2 | 3 | 2.65 |