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The thermodynamics of deformation
Deformations with change of temperature
Equilibrium of an elastic medium bounded by a plane
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adiabatic arbitrary axes axis Azzzz bending biharmonic biharmonic equation boundary conditions centre clamped coefficient components constant corresponding cross-section crystal crystallite curl curvature deflection denote derivatives Determine the deformation displacement vector edge elastic wave equations of equilibrium equations of motion expression external forces fluid force F forces acting forces applied formula free energy frequency function given gives grad Hence hydrostatic compression integral internal stresses isotropic body Let us consider longitudinal waves medium moduli of elasticity modulus neutral surface non-zero perpendicular plane plate quadratic quantities radius region of contact relation respect result rotation satisfies scalar shear shell small compared solution strain tensor stress tensor stretching Substituting suffixes symmetry temperature theory of elasticity thermal conduction thermodynamic thin transverse waves two-dimensional undeformed unit volume values velocity of propagation vibrations wave vector Young's modulus z-axis zero