scholarly journals Carleman estimate for a 1D linear elastic problem involving interfaces: Application to an inverse problem

2021 ◽  
Author(s):  
Bochra Méjri
Keyword(s):  
Inverse Problem ◽  
Elastic Problem ◽  
Carleman Estimate ◽  
Linear Elastic

scholarly journals Membrane analogy for multi-material bars under torsion

2019 ◽  
Vol 475 (2225) ◽  
pp. 20190124 ◽  
Author(s):  
Laura Galuppi ◽  
Gianni Royer-Carfagni
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Cross Sections ◽  
Three Dimensional ◽  
Element Model ◽  
Elastic Problem ◽  
Two Dimensional ◽  
Torsion Problem ◽  
Linear Elastic ◽  
Physical Apparatus

Prandtl's membrane analogy for the torsion problem of prismatic homogeneous bars is extended to multi-material cross sections. The linear elastic problem is governed by the same equations describing the deformation of an inflated membrane, differently tensioned in regions that correspond to the domains hosting different materials in the bar cross section, in a way proportional to the inverse of the material shear modulus. Multi-connected cross sections correspond to materials with vanishing stiffness inside the holes, implying infinite tension in the corresponding portions of the membrane. To define the interface constrains that allow to apply such a state of prestress to the membrane, a physical apparatus is proposed, which can be numerically modelled with a two-dimensional mesh implementable in commercial finite-element model codes. This approach presents noteworthy advantages with respect to the three-dimensional modelling of the twisted bar.

scholarly journals Inverse parabolic problems of determining functions with one spatial-component independence by Carleman estimate

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Oleg Y. Imanuvilov ◽  
Yavar Kian ◽  
Masahiro Yamamoto
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Boundary Data ◽  
Stability Estimate ◽  
Carleman Estimate ◽  
Parabolic Problems ◽  
Conditional Stability ◽  
Inverse Source Problem ◽  
Lateral Boundary ◽  
Spatial Component

Abstract For a parabolic equation in the spatial variable x = ( x 1 , … , x n ) {x=(x_{1},\ldots,x_{n})} and time t, we consider an inverse problem of determining a coefficient which is independent of one spatial component x n {x_{n}} by lateral boundary data. We apply a Carleman estimate to prove a conditional stability estimate for the inverse problem. Also, we prove similar results for the corresponding inverse source problem.

scholarly journals Global Carleman estimate on a network for the wave equation and application to an inverse problem

2011 ◽  
Vol 1 (3) ◽  
pp. 307-330 ◽  
Author(s):  
Lucie Baudouin ◽  
◽  
Emmanuelle Crépeau ◽  
Julie Valein ◽  
◽  
...  
Keyword(s):  
Inverse Problem ◽  
Wave Equation ◽  
Carleman Estimate ◽  
Global Carleman Estimate

Moving Morphable Inclusion Approach: An Explicit Framework to Solve Inverse Problem in Elasticity

2020 ◽  
Vol 88 (4) ◽  
Author(s):  
Yue Mei ◽  
Zongliang Du ◽  
Dongmei Zhao ◽  
Weisheng Zhang ◽  
Chang Liu ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Shear Modulus ◽  
New Paradigm ◽  
Elastic Solids ◽  
Shear Moduli ◽  
Numerical Examples ◽  
Linear Elastic ◽  
Inverse Approach ◽  
Optimization Parameters ◽  
Very High

Abstract In this work, we present a novel inverse approach to characterize the nonhomogeneous mechanical behavior of linear elastic solids. In this approach, we optimize the geometric parameters and shear modulus values of the predefined moving morphable inclusions (MMIs) to solve the inverse problem. Thereby, the total number of the optimization parameters is remarkably reduced compared with the conventional iterative inverse algorithms to identify the nonhomogeneous shear modulus distribution of solids. The proposed inverse approach is tested by multiple numerical examples, and we observe that this approach is capable of preserving the shape and the shear moduli of the inclusions well. In particular, this inverse approach performs well even without any regularization when the noise level is not very high. Overall, the proposed approach provides a new paradigm to solve the inverse problem in elasticity and has potential of addressing the issue of computational inefficacy existing in the conventional inverse approaches.

scholarly journals On the determination of the principal coefficient from boundary measurements in a KdV equation

2014 ◽  
Vol 22 (6) ◽  
Author(s):  
Lucie Baudouin ◽  
Eduardo Cerpa ◽  
Emmanuelle Crépeau ◽  
Alberto Mercado
Keyword(s):  
Inverse Problem ◽  
Kdv Equation ◽  
Carleman Estimate ◽  
Lipschitz Stability ◽  
Single Solution ◽  
De Vries ◽  
Boundary Measurements ◽  
Global Carleman Estimate

AbstractThis paper concerns the inverse problem of retrieving the principal coefficient in a Korteweg–de Vries (KdV) equation from boundary measurements of a single solution. The Lipschitz stability of this inverse problem is obtained using a new global Carleman estimate for the linearized KdV equation. The proof is based on the Bukhgeĭm–Klibanov method.

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