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we address the well-posedness of the planar linearized equilibrium problem for homogenized pantographic lattices. To do so: (i) we introduce a class of subsets of anisotropic Sobolev’s space as the most suitable energy space E relative to assigned boundary conditions; (ii) we prove that the considered strain energy density is coercive and positive definite in E ; (iii) we prove that the set of placements for which the strain...
Pantographic metamaterials: an example of mathematically driven design and of its technological challenges
In this paper, we account for the research efforts that have been started, for some among us, already since 2003, and aimed to the design of a class of exotic architectured, optimized (meta) materials. At the first stage of these efforts, as it often happens, the research was based on the results of mathematical investigations. The problem to be solved was stated as follows: determine the material (micro)structure governed by those...
Comparison of anti-plane surface waves in strain-gradient materials and materials with surface stresses
Here we discuss the similarities and differences in anti-plane surface wave propagation in an elastic half-space within the framework of the theories of Gurtin–Murdoch surface elasticity and Toupin–Mindlin strain-gradient elasticity. The qualitative behaviour of the dispersion curves and the decay of the obtained solutions are quite similar. On the other hand, we show that the solutions relating to the surface elasticity model...
Uzyskane stopnie/tytuły naukowe
Nadanie stopnia naukowegodr hab. Matematyka (Dziedzina nauk matematycznych)Higher Attestation Commission of Russia
Nadanie stopnia naukowegodr Mechanika (Dziedzina nauk technicznych)Rostov State University
wyświetlono 340 razy