1,243 research outputs found
Asymptotic behavior of Structures made of Plates
The aim of this work is to study the asymptotic behavior of a structure made
of plates of thickness when . This study is carried on
within the frame of linear elasticity by using the unfolding method. It is
based on several decompositions of the structure displacements and on the
passing to the limit in fixed domains. We begin with studying the displacements
of a plate. We show that any displacement is the sum of an elementary
displacement concerning the normal lines on the middle surface of the plate and
a residual displacement linked to these normal lines deformations. An
elementary displacement is linear with respect to the variable 3. It is
written where U is a displacement of the mid-surface of
the plate. We show a priori estimates and convergence results when . We characterize the limits of the unfolded displacements of a plate as well
as the limits of the unfolded of the strained tensor. Then we extend these
results to the structures made of plates. We show that any displacement of a
structure is the sum of an elementary displacement of each plate and of a
residual displacement. The elementary displacements of the structure (e.d.p.s.)
coincide with elementary rods displacements in the junctions. Any e.d.p.s. is
given by two functions belonging to where S is the skeleton of the
structure (the plates mid-surfaces set). One of these functions : U is the
skeleton displacement. We show that U is the sum of an extensional displacement
and of an inextensional one. The first one characterizes the membrane
displacements and the second one is a rigid displacement in the direction of
the plates and it characterizes the plates flexion. Eventually we pass to the
limit as in the linearized elasticity system, on the one hand we
obtain a variational problem that is satisfied by the limit extensional
displacement, and on the other hand, a variational problem satisfied by the
limit of inextensional displacements
Continuum Electromechanical Modeling of Protein-Membrane Interaction
A continuum electromechanical model is proposed to describe the membrane
curvature induced by electrostatic interactions in a solvated protein-membrane
system. The model couples the macroscopic strain energy of membrane and the
electrostatic solvation energy of the system, and equilibrium membrane
deformation is obtained by minimizing the electro-elastic energy functional
with respect to the dielectric interface. The model is illustrated with the
systems with increasing geometry complexity and captures the sensitivity of
membrane curvature to the permanent and mobile charge distributions.Comment: 5 pages, 12 figure
A dual weighted residual method applied to complex periodic gratings
An extension of the dual weighted residual (DWR) method to the analysis of electromagnetic waves in a periodic diffraction grating is presented. Using the α,0-quasi-periodic transformation, an upper bound for the a posteriori error estimate is derived. This is then used to solve adaptively the associated Helmholtz problem. The goal is to achieve an acceptable accuracy in the computed diffraction efficiency while keeping the computational mesh relatively coarse. Numerical results are presented to illustrate the advantage of using DWR over the global a posteriori error estimate approach. The application of the method in biomimetic, to address the complex diffraction geometry of the Morpho butterfly wing is also discussed
Existence theorems in the geometrically non-linear 6-parametric theory of elastic plates
In this paper we show the existence of global minimizers for the
geometrically exact, non-linear equations of elastic plates, in the framework
of the general 6-parametric shell theory. A characteristic feature of this
model for shells is the appearance of two independent kinematic fields: the
translation vector field and the rotation tensor field (representing in total 6
independent scalar kinematic variables). For isotropic plates, we prove the
existence theorem by applying the direct methods of the calculus of variations.
Then, we generalize our existence result to the case of anisotropic plates. We
also present a detailed comparison with a previously established Cosserat plate
model.Comment: 19 pages, 1 figur
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On the numerical approximation of p-biharmonic and ∞-biharmonic functions
In [KP16] (arXiv:1605.07880) the authors introduced a second-order variational problem in L∞. The associated equation, coined the ∞-Bilaplacian, is a \emph{third order} fully nonlinear PDE given by Δ2∞u:=(Δu)3|D(Δu)|2=0. In this work we build a numerical method aimed at quantifying the nature of solutions to this problem which we call ∞-Biharmonic functions. For fixed p we design a mixed finite element scheme for the pre-limiting equation, the p-Bilaplacian Δ2pu:=Δ(|Δu|p−2Δu)=0. We prove convergence of the numerical solution to the weak solution of Δ2pu=0 and show that we are able to pass to the limit p→∞. We perform various tests aimed at understanding the nature of solutions of Δ2∞u and in 1-d we prove convergence of our discretisation to an appropriate weak solution concept of this problem, that of -solutions
Rate of Convergence of Space Time Approximations for stochastic evolution equations
Stochastic evolution equations in Banach spaces with unbounded nonlinear
drift and diffusion operators driven by a finite dimensional Brownian motion
are considered. Under some regularity condition assumed for the solution, the
rate of convergence of various numerical approximations are estimated under
strong monotonicity and Lipschitz conditions. The abstract setting involves
general consistency conditions and is then applied to a class of quasilinear
stochastic PDEs of parabolic type.Comment: 33 page
Real time plasma equilibrium reconstruction in a Tokamak
The problem of equilibrium of a plasma in a Tokamak is a free boundary
problemdescribed by the Grad-Shafranov equation in axisymmetric configurations.
The right hand side of this equation is a non linear source, which represents
the toroidal component of the plasma current density. This paper deals with the
real time identification of this non linear source from experimental
measurements. The proposed method is based on a fixed point algorithm, a finite
element resolution, a reduced basis method and a least-square optimization
formulation
Identification of nonlinearity in conductivity equation via Dirichlet-to-Neumann map
We prove that the linear term and quadratic nonlinear term entering a
nonlinear elliptic equation of divergence type can be uniquely identified by
the Dirichlet to Neuman map. The unique identifiability is proved using the
complex geometrical optics solutions and singular solutions
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