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- W3204410243 abstract "Purpose The object of the paper is to illustrate how to obtain the topological derivative as a semidifferential in a general and practical mathematical setting for d -dimensional perturbations of a bounded open domain in the n -dimensional Euclidean space. Design/methodology/approach The underlying methodology uses mathematical notions and powerful tools with ready to check assumptions and ready to use formulas via theorems on the one-sided derivative of parametrized minima and minimax. Findings The theory and the examples indicate that the methodology applies to a wide range of problems: (1) compliance and (2) state constrained objective functions where the coupled state/adjoint state equations appear without a posteriori substitution of the adjoint state. Research limitations/implications Direct approach that considerably simplifies the analysis and computations. Originality/value It was known that the shape derivative was a differential. But the topological derivative is only a semidifferential, that is, a one-sided directional derivative, which is not linear with respect to the direction, and the directions are d -dimensional bounded measures." @default.
- W3204410243 created "2021-10-11" @default.
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- W3204410243 date "2021-09-28" @default.
- W3204410243 modified "2023-10-18" @default.
- W3204410243 title "Topological derivatives via one-sided derivative of parametrized minima and minimax" @default.
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- W3204410243 doi "https://doi.org/10.1108/ec-06-2021-0318" @default.
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