Distribution of resonances for the Neumann problem in linear elasticity outside a ball
Effective computation of restoring force vector in finite element method
We introduce a new way of computation of time dependent partial differential equations using hybrid method FEM in space and FDM in time domain and explicit computational scheme. The key idea is quick transformation of standard basis functions into new simple basis functions. This new way is used for better computational efficiency. We explain this way of computation on an example of elastodynamic equation using quadrilateral elements. However, the method can be used for more types of elements and...
Efficient application of e-invariants in finite element method for an elastodynamic equation
We introduce a new efficient way of computation of partial differential equations using a hybrid method composed from FEM in space and FDM in time domain. The overall computational scheme is explicit in time. The key idea of the suggested way is based on a transformation of standard basis functions into new basis functions. The results of this matrix transformation are e-invariants (effective invariants) with such suitable properties which save the number of arithmetical operations needed for a...
Étude spectrale du système différentiel associé à un problème d’élasticité linéaire
Exact controllability of the linear elasticity system with evolutive Ventcel conditions. (Contrôlabilité exacte d'un problème avec conditions de Ventcel évolutives pour le système linéaire de l'élasticité.)
Existence and convergence of the expansion in the asymptotic theory of elastic thin plates
Existence and uniqueness for wave propagation in inhomogeneous elastic solids
Existence Result for the Displacement Field of Elastic Body
Explicit solutions of the basic boundary value problems of statics of the elastic mixture theory for an annulus.
First boundary value problem of electroelasticity for a transversally isotropic plane with curvilinear cuts.
First-order system least squares for velocity-vorticity-pressure form of the Stokes equations, with application to linear elasticity.
Flaw identification in elastic solids: theory and experiments.
In this work the problem of identificating flaws or voids in elastic solids is addressed both from a theoretical and an experimental point of view. Following a so called inverse procedure, which is based on appropriately devised experiments and a particular bounding of the strain energy, a gap functional for flaw identification is proposed.
Formules de l'élasticité des corps amorphes que des compressions permanentes et inégales ont rendus hétérotropes.
Generalized Newton methods for the 2D-Signorini contact problem with friction in function space
The 2D-Signorini contact problem with Tresca and Coulomb friction is discussed in infinite-dimensional Hilbert spaces. First, the problem with given friction (Tresca friction) is considered. It leads to a constraint non-differentiable minimization problem. By means of the Fenchel duality theorem this problem can be transformed into a constrained minimization involving a smooth functional. A regularization technique for the dual problem motivated by augmented lagrangians allows to apply an infinite-dimensional...
Generalized Newton methods for the 2D-Signorini contact problem with friction in function space
The 2D-Signorini contact problem with Tresca and Coulomb friction is discussed in infinite-dimensional Hilbert spaces. First, the problem with given friction (Tresca friction) is considered. It leads to a constraint non-differentiable minimization problem. By means of the Fenchel duality theorem this problem can be transformed into a constrained minimization involving a smooth functional. A regularization technique for the dual problem motivated by augmented Lagrangians allows to apply an...
Global superconvergence approximations of the mixed finite element method for the Stokes problem and the linear elasticity equation
Global uniqueness for an inverse boundary problem arising in elasticity.
Global well-posedness and blow up for the nonlinear fractional beam equations
We establish the Strichartz estimates for the linear fractional beam equations in Besov spaces. Using these estimates, we obtain global well-posedness for the subcritical and critical defocusing fractional beam equations. Of course, we need to assume small initial data for the critical case. In addition, by the convexity method, we show that blow up occurs for the focusing fractional beam equations with negative energy.
Higher integrability of the gradient in linear elasticity.
Homogenization of some contact problems for the system of elasticity in perforated domains