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This study treats a new model of nonlocal fractal thermoelasticity beam theory for nanomaterials characterized by an apparent negative thermal conductivity which occurs in shaped graded materials. The model is based on the new concept of "product-like fractal measure" introduced by Li and Ostoja-Starzewski in their formulation of fractal continuum media with fractal dimensionThe basic setups of the theory are formulated, yet, we have restricted our analysis for the static case. The effects of fractal dimension on field variables, in particular the lateral deflection and the temperature increment of the resonator were analyzed analytically and graphically. It was observed that the physics of the thin elastic nanobeam is affected by the numerical value of the fractal dimension and the characteristic lengths of the theory. Comparable scenarios observed in complex material structures are obtained and discussed.

Fractal nonlocal thermoelasticity of thin elastic nanobeam with apparent negative thermal conductivity