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Mechanics of Solids and Materials by Vlado Lubarda, Robert Asaro

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13 Isotropic 3D Solutions

13.1 Displacement-Based Equations of Equilibrium

Recall the Cauchy equations of equilibrium in terms of stresses

(13.1)

along with the definition of small strains

(13.2)

and the constitutive relations for isotropic thermoelastic media

(13.3)

The coefficient of thermal expansion is α, and K the elastic bulk modulus, K = E/3(1 – 2v). The temperature difference from the reference temperature is ΔT = T

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