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- W1987165089 abstract "A comprehensive treatment of the topological derivative for anisotropic elasticity is presented, with both the background material and the trial small inhomogeneity assumed to have arbitrary anisotropic elastic properties. A formula for the topological derivative of any cost functional defined in terms of regular volume or surface densities depending on the displacement is established, by combining small-inhomogeneity asymptotics and the adjoint solution approach. The latter feature makes the proposed result simple to implement and computationally efficient. Both three-dimensional and plane-strain settings are treated; they differ mostly on details in the elastic moment tensor (EMT). Moreover, the main properties of the EMT, a critical component of the topological derivative, are studied for the fully anisotropic case. Then, the topological derivative of strain energy-based quadratic cost functionals is derived, which requires a distinct treatment. Finally, numerical experiments on the numerical evaluation of the EMT and the topological derivative of the compliance cost functional are reported." @default.
- W1987165089 created "2016-06-24" @default.
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- W1987165089 date "2013-10-22" @default.
- W1987165089 modified "2023-10-13" @default.
- W1987165089 title "The topological derivative in anisotropic elasticity" @default.
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- W1987165089 doi "https://doi.org/10.1093/qjmam/hbt018" @default.
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