Question

Stress in a solid body ? stress tensor ?ij = [?11 ?12 ?13; ?21 ?22 ?23; ?31 ?32 ?33] ?ij = ?ji (Stress tensor is symmetric) Strain in a solid body ? strain tensor ?ij = 1/2 (?ui/?xj + ?uj/?xi) (Einstein summation notation) Momentum conservation (Newton's second law) ? ?"ui/?t" = ??ij/?xj + fi (F = ma) Hooke's law ?ij = 2??ij + ??kk?ij Navier equations of linear elasticity ? ?"u/?t" = ??"u + (? + ?)?(? · u) + f

          Stress in a solid body ? stress tensor
?ij = [?11 ?12 ?13; ?21 ?22 ?23; ?31 ?32 ?33] ?ij = ?ji (Stress tensor is symmetric)
Strain in a solid body ? strain tensor
?ij = 1/2 (?ui/?xj + ?uj/?xi) (Einstein summation notation)
Momentum conservation (Newton's second law)
? ?"ui/?t" = ??ij/?xj + fi (F = ma)
Hooke's law
?ij = 2??ij + ??kk?ij
Navier equations of linear elasticity
? ?"u/?t" = ??"u + (? + ?)?(? · u) + f

Stress in a solid body ? stress tensor
?ij = [?11 ?12 ?13; ?21 ?22 ?23; ?31 ?32 ?33] ?ij = ?ji (Stress tensor is symmetric)
Strain in a solid body ? strain tensor
?ij = 1/2 (?ui/?xj + ?uj/?xi) (Einstein summation notation)
Momentum conservation (Newton's second law)
? ?"ui/?t" = ??ij/?xj + fi (F = ma)
Hooke's law
?ij = 2??ij + ??kk?ij
Navier equations of linear elasticity
? ?"u/?t" = ??"u + (? + ?)?(? · u) + f

Added by Maria C.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Sri K

08/03/2023

Step 1

Stress in a solid body - stress tensor: The stress tensor is given by -2 {Tg1 Og2 Tg}, where Tg1, Og2, and Tg are components of the stress tensor. The stress tensor is symmetric, meaning Tg1 = Tg2, and Og1 = Og2. Therefore, the stress tensor can be written Show more…

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Force / stress / strain Induce 3 equations Stress in a solid body - stress tensor (Stress tensor is symmetric) Strain in a solid body - strain tensor (Einstein summation notation) Momentum conservation (Newton's second law) Hooke's law Navier equations of linear elasticity