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Production of Single Tracks of Ti-6Al-4V by Directed Energy Deposition to Determine the Layer Thickness for Multilayer Deposition
Published on: March 13, 2018
On the Bövik-Benveniste methodology and related approaches for modelling thin layers
S Baranova1, S G Mogilevskaya1
1Department of Civil, Environmental and Geo-Engineering, University of Minnesota, 500 Pillsbury Drive S.E., Minneapolis MN, 55455, USA.
Abstract:
This paper reviews several leading approaches for asymptotic modelling of thin layers in elastostatics and wave propagation phenomena. The issues related to applications of the so-called 'equivalent' or 'effective' boundary conditions and their interpretations are highlighted. Comparative analysis of asymptotic models is performed for a two-dimensional elastostatic case using a novel complex variables-based modelling tool. Its implementation allows for straightforward derivations of higher order boundary conditions for problems with layers of arbitrary sufficiently smooth curvatures. Explicit expressions for the conditions up to the third order are provided. All models are tested using available benchmark solutions and the solutions for the limiting cases of the layer parameters. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'.
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