In a two-dimensional plane problem of the theory elasticity in polar coordinates for nonhomogeneous body, it is possible to obtain analytical or numerical-analytical solutions only one-dimensional nonuniformity [1 - 3]. As rule, this when all unknown functions depend on radius. These tasks correspond majority ring and cylindrical structures exposed axisymmetric effects temperature, radiation, h...

A variational limit defined on the space of bi-dimensional gradient Young measures is obtained from three-dimensional elasticity via dimension reduction. The obtained limit problem uniquely determines the energy density of the thin film. Our result might be used to compute the microstructure in membranes made of phase transforming material.

Composite material properties are dependent on their microstructure. To adequately model these microstructural effects, a formulation of elasticity that accounts for effects must be considered. Size-dependent behaviour is an inherent property such materials, resulting in need non-classical continuum theories adequate characterization. A three-dimensional exponentially graded composite with deve...

In this work, we propose appealing bounding techniques that enable to derive accurate and strict error bounds on outputs of interest computed from numerical approximation methods such as the finite element method. These techniques are based on Saint-Venant’s principle and exploit specific homotheticity properties in order to improve the quality of the bounds computed from the classical bounding...

In this study, stress and displacement functions of the three-dimensional theory of elasticity for homogeneous isotropic bodies are derived from first principles from the differential equations of equilibrium, the generalized stress – strain laws and the geometric relations of strain and displacement. It is found that the stress and displacement functions must be biharmonic functions. The deriv...

The problem of determining the shape an object from knowledge far-field a single incident wave in two-dimensional elasticity was considered. We applied iterative hybrid method to tackle this problem. An advantage is that it does not need forward solver, and therefore, exact boundary condition essential. By deriving Fréchet derivatives two operators, we established reconstruction algorithms for ...

Abstract. We model the coupled system formed by an incompressible, irrotational fluid and a nonlinear elastic body. We work with large displacement, small deformation elasticity (or St Venant elasticity), which makes the problem very interesting from the physical point of view. The elastic body is three-dimensional Ω ∈ R, and thus it can not be reduced to its boundary Γ (like in the case of a m...