We analyse the sensitivity of the solution of a nonlinear obstacle plate problem, with respect to small perturbations of the middle plane of the plate. This analysis, which generalizes the results of [9, 10] for the linear case, is done by application of an abstract variational result [6], where the sensitivity of parameterized variational inequalities in Banach spaces, without uniqueness of solution, is quantified in terms of a generalized derivative, that is the proto-derivative. We prove that...
The purpose of this paper is to derive and study a new asymptotic
model for the equilibrium state of a thin anisotropic
piezoelectric plate in frictional contact with a rigid obstacle.
In the asymptotic process, the thickness of the piezoelectric
plate is driven to zero and the convergence of the unknowns is
studied. This leads to two-dimensional Kirchhoff-Love plate
equations, in which mechanical displacement and electric potential
are partly decoupled. Based on this model numerical examples are
presented...
We analyse the sensitivity of the solution of a nonlinear obstacle plate
problem, with respect to small perturbations of the middle plane
of the plate. This analysis, which generalizes the results of [9,10]
for the linear case,
is done by application of an abstract variational
result [6], where the sensitivity of parameterized variational
inequalities in Banach spaces, without uniqueness of solution,
is quantified in terms of a generalized
derivative, that is the proto-derivative. We prove that...
We prove the conical differentiability of the solution to a bone remodeling contact rod model, for given data (applied loads and rigid obstacle), with respect to small perturbations of the cross section of the rod. The proof is based on the special structure of the model, composed of a variational inequality coupled with an ordinary differential equation with respect to time. This structure enables the verification of the two following fundamental results: the polyhedricity of a modified displacement...
We prove the conical differentiability of the solution to a bone
remodeling contact rod model, for given data (applied loads and
rigid obstacle), with respect to small perturbations of the cross
section of the rod. The proof is based on the special structure of
the model, composed of a variational inequality coupled with an
ordinary differential equation with respect to time. This
structure enables the verification of the two following
fundamental results: the polyhedricity of a modified displacement
constraint...
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