An asymptotic study of a plate problem by a rearrangement method. Application to the mechanical impedance
An asymptotically optimal model for isotropic heterogeneous linearly elastic plates
In this paper, we derive and analyze a Reissner-Mindlin-like model for isotropic heterogeneous linearly elastic plates. The modeling procedure is based on a Hellinger-Reissner principle, which we modify to derive consistent models. Due to the material heterogeneity, the classical polynomial profiles for the plate shear stress are replaced by more sophisticated choices, that are asymptotically correct. In the homogeneous case we recover a Reissner-Mindlin model with as shear correction factor....
An asymptotically optimal model for isotropic heterogeneous linearly elastic plates
In this paper, we derive and analyze a Reissner-Mindlin-like model for isotropic heterogeneous linearly elastic plates. The modeling procedure is based on a Hellinger-Reissner principle, which we modify to derive consistent models. Due to the material heterogeneity, the classical polynomial profiles for the plate shear stress are replaced by more sophisticated choices, that are asymptotically correct. In the homogeneous case we recover a Reissner-Mindlin model with 5/6 as shear correction...
An augmented mixed finite element method for linear elasticity with non-homogeneous Dirichlet conditions.
An elastic membrane with an attached non-linear thermoelastic rod
We study a thermo-mechanical system consisting of an elastic membrane to which a shape-memory rod is glued. The slow movements of the membrane are controlled by the motions of the attached rods. A quasi-static model is used. We include the elastic feedback of the membrane on the rods. This results in investigating an elliptic boundary value problem in a domain Ω ⊂ R^2 with a cut, coupled with non-linear equations for the vertical motions of the rod and the temperature on the rod. We prove the existence...
An elastohydrodynamic coupled problem between a piezoviscous Reynolds equation and a hinged plate model
An elasto-plastic contact problem
An elementary theory of the oblique impact of rods
An extension is proposed of a classical approximate method for estimating the stress state in an elastic rod obliquely colliding against a rigid wall.
An energy-preserving Discrete Element Method for elastodynamics∗
We develop a Discrete Element Method (DEM) for elastodynamics using polyhedral elements. We show that for a given choice of forces and torques, we recover the equations of linear elastodynamics in small deformations. Furthermore, the torques and forces derive from a potential energy, and thus the global equation is an Hamiltonian dynamics. The use of an explicit symplectic time integration scheme allows us to recover conservation of energy, and thus stability over long time simulations. These theoretical...
An energy-preserving Discrete Element Method for elastodynamics∗
We develop a Discrete Element Method (DEM) for elastodynamics using polyhedral elements. We show that for a given choice of forces and torques, we recover the equations of linear elastodynamics in small deformations. Furthermore, the torques and forces derive from a potential energy, and thus the global equation is an Hamiltonian dynamics. The use of an explicit symplectic time integration scheme allows us to recover conservation of energy, and thus stability over long time simulations. These theoretical...
An entropy satisfying scheme for two-layer shallow water equations with uncoupled treatment
We consider the system of partial differential equations governing the one-dimensional flow of two superposed immiscible layers of shallow water. The difficulty in this system comes from the coupling terms involving some derivatives of the unknowns that make the system nonconservative, and eventually nonhyperbolic. Due to these terms, a numerical scheme obtained by performing an arbitrary scheme to each layer, and using time-splitting or other similar techniques leads to instabilities in...
An equilibrium finite element method in three-dimensional elasticity
The tetrahedral stress element is introduced and two different types of a finite piecewise linear approximation of the dual elasticity problem are investigated on a polyhedral domain. Fot both types a priori error estimates in -norm and in -norm are established, provided the solution is smooth enough. These estimates are based on the fact that for any polyhedron there exists a strongly regular family of decomprositions into tetrahedra, which is proved in the paper, too.
An estimate for deviations from the exact solution of the Reissner-Mindlin plate problem.
An example in the gradient theory of phase transitions
We prove by giving an example that when the asymptotic behavior of functionals is quite different with respect to the planar case. In particular we show that the one-dimensional ansatz due to Aviles and Giga in the planar case (see [2]) is no longer true in higher dimensions.
An example in the gradient theory of phase transitions
We prove by giving an example that when n ≥ 3 the asymptotic behavior of functionals is quite different with respect to the planar case. In particular we show that the one-dimensional ansatz due to Aviles and Giga in the planar case (see [2]) is no longer true in higher dimensions.
An expression of classical dynamics
An extension of small-strain models to the large-strain range based on an additive decomposition of a logarithmic strain
This paper describes model combining elasticity and plasticity coupled to isotropic damage. However, the conventional theory fails after the loss of ellipticity of the governing differential equation. From the numerical point of view, loss of ellipticity is manifested by the pathological dependence of the results on the size and orientation of the finite elements. To avoid this undesired behavior, the model is regularized by an implicit gradient formulation. Finally, the constitutive model is extended...
An inverse eigenvalue problem for an arbitrary multiply connected bounded region in .
An inverse problem for biharmonic equation.
An inverse quadratic eigenvalue problem for damped structural systems.