Thesis (Ph.D.) - Cairo University - Faculty of Science - Department of Mathematics

Anumericalsolutionispresentedforfournonlinear, one-dimensionalboundary- value problems of thermoelasticity with variable volume force and heat supply inaslaborhalf-spaceofananisotropicelasticmaterial. Onesurfaceofthebody is subjected to a given periodic displacement and Robin thermal condition, while the other surface is kept {uFB01}xed and at zero temperature. The volume force and bulk heating simulate the e{uFB00}ect of a beam of hot particles in{uFB01}ltrating the medium and coming to rest in a layer adjacent to the boundary. Particular forms for the bulk force and heating functions are considered for de{uFB01}niteness, but other choices may be treated equally well. No phase transition is considered and the domain of the solution excludes any shock wave formation. The basic {uFB01}eld equations used in this thesis have been derived elsewhere (cf. [18]) on the basis of rigorous thermodynamics and are formulated in material coordinates, making them adequate for dealing with moving boundaries. As to the used numerical scheme, it {uFB01}nds its origin in [15,23{u2013}25] and was readapted in [62]. This is a three-level, iterative {uFB01}nite-di{uFB00}erence scheme. It has been shown to exhibit unconditional stability for the case of only one dis- placement component in [62]. This result was extended in the present Thesis to include the case of three displacement components. Based on the obtained results, the used numerical method reproduces correctly the di{uFB00}erent aspects of the process of coupled thermo-mechanical wave propagation.

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