Computational Methods for Some Inverse Problems in Solid Mechanics
Project Code: PN-III-P4-ID-PCE-2016-0083
Contract No.: 106/12.07.2017
Duration: 12 July 2017 - 31 December 2019
Host Institution: University of Bucharest, Research Institute of the University of Bucharest
Financially supported by the Ministry of Research and Innovation, CNCS - UEFISCDI
Principal Investigator: Prof. Liviu MARIN (Senior Researcher)
Investigators: Prof. Sanda CLEJA-ȚIGOIU (Senior Researcher)
Dr. Raisa PAȘCAN (Postdoctoral Researcher)
Ms. Andreea-Paula VOINEA-MARINESCU (Research Assistant, PhD Student)
Mr. Mihai BUCĂTARU (Mathematician, MSc Student)
Project Summary:
We are concerned with the following inverse problems (IPs) in solid mechanics:
Inverse boundary value problems (BVPs) with L2-data in steady anisotropic heat conduction: These classical IPs have been overlooked so far and this study is motivated mainly by the fact that L2-data are desirable for computations. Hence the work of Hào and Lesnic (2000) has to be revisited by assuming that the boundary on which data are available and the remaining one are disjoint and considering all possible control terms, a procedure should be provided for L2-data when the above assumption does not hold, while the fading regularisation method could be extended to IPs in anisotropic heat conduction and the 3D case.
Inverse BVPs with L2-data in anisotropic (thermo-)elastostatics: These IPs are described analogously to and represent a natural extension of item 1, while temperatures and normal heat fluxes are replaced/amended by displacements and tractions.
Coefficient identification problems in transient anisotropic heat conduction from nonstandard observations: In this case, the so-called standard observations are generally used, in the form of pointwise observations or observations in the entire domain. Herein the so-called additional nonstandard integral observations are considered to determine the time- and space-dependent anisotropic heat conduction tensor. The motivation of this study is very realistic: practical measurements are retrieved as the result of an averaging process.
Inverse source problems in transient (an)isotropic thermo-elasticity: Both the theoretical and the numerical analyses of inverse source problems in thermo-elasticity are due to the coupling of the governing PDEs. We aim at investigating the recovery of a time-dependent heat source in 1D anisotropic thermo-elasticity, as well as multi-dimensional (an)isotropic thermo-elasticity; a possible extension of this would be the reconstruction of boundary sources in (an)isotropic thermo-elasticity.
Scientific Reports: 2017 [RO] 2018 [RO] 2019 [RO]
1st Workshop on Analysis, PDEs and Mechanics, 9 November 2018