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Displaying 61 –
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434
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 provide a sensitivity result for the solutions to the following finite-dimensional quasi-variational inequality when both the operator and the convex are perturbed. In particular, we prove the Hölder continuity of the solution sets of the problems perturbed around the original problem. All the results may be extended to infinite-dimensional (QVI).
Simulation completed with perturbation analysis provides a new approach for the optimal control of queuing network type systems. The objective of this paper is to calculate the sensitivity range of finite zero-order perturbation, that is, to determine the maximum and minimum size of perturbation within which zero-order propagation rules can be applied. By the introduction of the concept of virtual queue and first and second level no-input and full-output matrices, an algorithm is provided which...
In a typical moving contaminating source identification problem, after some type of biological or chemical contamination has occurred, there is a developing cloud of dangerous or toxic material. In order to detect and localize the contamination source, a sensor network can be used. Up to now, however, approaches aiming at guaranteeing a dense region coverage or satisfactory network connectivity have dominated this line of research and abstracted away from the mathematical description of the physical...
Let be a family of bounded Lipschitz continuous vector fields on . In this paper we prove that if is a set of finite -perimeter then his -perimeter is the limit of the -perimeters of a sequence of euclidean polyhedra approximating in -norm. This extends to Carnot-Carathéodory geometry a classical theorem of E. De Giorgi.
The framework for shape and topology sensitivity analysis in geometrical domains with cracks is established for elastic bodies in two spatial dimensions. The equilibrium problem for the elastic body with cracks is considered. Inequality type boundary conditions are prescribed at the crack faces providing a non-penetration between the crack faces. Modelling of such problems in two spatial dimensions is presented with all necessary details for further applications in shape optimization in structural...
The goal of this paper is to study the so-called worst-case or robust optimal design problem for minimal compliance. In the context of linear elasticity we seek an optimal shape which minimizes the largest, or worst, compliance when the loads are subject to some unknown perturbations. We first prove that, for a fixed shape, there exists indeed a worst perturbation (possibly non unique) that we characterize as the maximizer of a nonlinear energy. We also propose a stable algorithm to compute it....
The goal of this paper is to study the so-called worst-case or robust
optimal design problem for minimal compliance. In the context of linear
elasticity we seek an optimal shape which minimizes the largest, or worst,
compliance when the loads are subject to some unknown perturbations.
We first prove that, for a fixed shape, there exists indeed a worst
perturbation (possibly non unique) that we characterize as the maximizer
of a nonlinear energy. We also propose a stable algorithm to
compute...
The goal of this paper is to compute the shape Hessian for a generalized Oseen problem with nonhomogeneous Dirichlet boundary condition by the velocity method. The incompressibility will be treated by penalty approach. The structure of the shape gradient and shape Hessian with respect to the shape of the variable domain for a given cost functional are established by an application of the Lagrangian method with function space embedding technique.
Currently displaying 61 –
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434