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Minimization of peak stresses with the shape derivative.
Philos Trans A Math Phys Eng Sci
August 2024
Institut für Analysis und Scientific Computing Wiedner Hauptstraße 8-10, Wien 1040, Austria.
This article is concerned with the minimization of peak stresses occurring in linear elasticity. We propose to minimize the maximal von Mises stress of the elastic body. This leads to a non-smooth shape functional.
View Article and Find Full Text PDFHard interfaces with microstructure: the cases of strain gradient elasticity and micropolar elasticity.
Philos Trans A Math Phys Eng Sci
August 2024
Aix Marseille Univ, CNRS, Centrale Marseille, LMA, 4 impasse Nikola Tesla, Marseille Cedex 13453, France.
As the size of a layered structure scales down, the adhesive layer thickness correspondingly decreases from macro- to micro-scale. The influence of the material microstructure of the adhesive becomes more pronounced, and possible size effect phenomena can appear. This paper describes the mechanical behaviour of composites made of two solids, bonded together by a thin layer, in the framework of strain gradient and micropolar elasticity.
View Article and Find Full Text PDFThe homogenized dynamical model of a thermoelastic composite stitched with reinforcing filaments.
Philos Trans A Math Phys Eng Sci
August 2024
Lavrentyev Institute of Hydrodynamics, Siberian Branch of the Russian Academy of Sciences, Pr. Acad. Lavrentyeva 15, Novosibirsk 630090, Russia.
The dynamical problem of linear thermoelasticity for a body with incorporated thin rectilinear inclusions is studied. It is assumed that the inclusions (i.e.
View Article and Find Full Text PDFA variational approach to frame-indifferent quasistatic viscoelasticity of rate type.
Philos Trans A Math Phys Eng Sci
August 2024
School of Mathematics, Cardiff University, Cardiff CF24 4AG, UK.
The three-dimensional dynamical model for nonlinear viscoelasticity of strain-rate type is investigated in a quasistatic setting under the assumption of higher-order regularity of the deformation, which in the literature is referred to as the case of non-simple materials. The existence of weak solutions is proven using a time-discretization technique while respecting the condition of dynamical frame indifference. Some observations on frame indifference for strain-rate-type stresses are made, and corrections are proposed for some related work in the literature.
View Article and Find Full Text PDFOn the numerical corroboration of an obstacle problem for linearly elastic flexural shells.
Philos Trans A Math Phys Eng Sci
August 2024
Department of Applied Mathematics, School of Sciences, Xi'an University of Technology, P.O.Box 1243, Yanxiang Road No. 58, Xi'an, Shaanxi 710054, People's Republic of China.
In this article, we study the numerical corroboration of a variational model governed by a fourth-order elliptic operator that describes the deformation of a linearly elastic flexural shell subjected not to cross a prescribed flat obstacle. The problem under consideration is modelled by means of a set of variational inequalities posed over a non-empty, closed and convex subset of a suitable Sobolev space and is known to admit a unique solution. Qualitative and quantitative numerical experiments corroborating the validity of the model and its asymptotic similarity with Koiter's model are also presented.
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