Design of novel inverse analysis methodology for exact estimation of elasticity parameters in thermoelastic stress model

Abstract

This paper presents general outlines of the research conducted in the applied mathematics field, − the theory of inverse problems, specifically utilized for the thermoelastic stress analysis model for exact estimation of thermo-elasticity parameters. We present formulation of the well posed direct mathematical model that depicts general interconnections between physically governed fields for thermally heated plate subjected to fixed constrains on the boundaries with small deformations from thermal expansion over the homogeneous multilayered medium domain. Applying elements of variational calculus, functional analysis and fractional order derivatives, we demonstrate the derivation of the conjugate problem and analytical expressions used for exact estimation of structural material thermoelastic properties. The novelty of proposed methodology lies in derivation of exact estimators that could be utilized for general homogenized thermoelastic model with finite amount of sampled temperature measurements on the domain outlets. It also opens curtains over the key issues and some important aspects aroused in the derivation procedures of exact estimators for general problem statement. There were posed and discussed necessary conditions in a form of a working hypothesizes. Results may be utilized as an experimental technique designed to obtain an essential information on the surface stress field along with the thermoelastic material properties.