Overview
Classical formulations of models for static or dynamic behavior of systems and components made of thermoelastic materials involve partial differential equations (PDEs). Such models arise in engineering and natural systems in which the temperature is nonuniform and changing, such as in engines, thermistors, brakes, MEMS, solidifying lava, etc. In these models, the mechanical and thermal quantities are assumed to be smooth. However, the mathematical analysis of such models is difficult, and many of the modern abstract tools of functional analysis cannot be used easily. Variational formulations of such models are usually related to the energy and dissipation considerations in the system, and involve the transformation of the systems of PDEs into integral expressions. This procedure makes the models easier to analyze mathematically using modern abstract tools of functional analysis to establish the existence and...
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Shillor, M. (2014). Thermoelastic Stresses, Variational Methods. In: Hetnarski, R.B. (eds) Encyclopedia of Thermal Stresses. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2739-7_931
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DOI: https://doi.org/10.1007/978-94-007-2739-7_931
Publisher Name: Springer, Dordrecht
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