## Theory of Elasticity |

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### Contents

FUNDAMENTAL EQUATIONS 1 The strain tensor | 1 |

2 The stress tensor | 4 |

3 The thermodynamics of deformation | 8 |

Copyright | |

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### Common terms and phrases

adiabatic arbitrary axis bending biharmonic biharmonic equation boundary conditions centre clamped coefficient components constant corresponding cross-section crystal crystallite curl curvature damping deflection denote derivatives Determine the deformation direction displacement vector dissipative dxdy 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 div Hence hydrostatic compression integral internal stresses isotropic body Let us consider longitudinal waves medium moduli of elasticity modulus neutral surface non-zero perpendicular plane 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 transverse waves two-dimensional undeformed unit volume values velocity of propagation vibrations viscosity wave vector Young's modulus z-axis zero