1D_Elasticity_01_Elastostatics

1D_Elasticity_01_Elastostatics - Section 2.1 2.1...

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Section 2.1 Solid Mechanics Part II Kelly 21 2.1 One-dimensional Elastostatics Consider a bar or rod made of linearly elastic material subjected to some load. Static problems will be considered here, by which is meant it is not necessary to know how the load was applied, or how the material particles moved to reach the stressed state; it is necessary only that the load was applied slowly enough so that the accelerations are zero, or that it was applied sufficiently long ago that any vibrations have died away and movement has ceased. The equations governing the static response of the rod are: 0 = + b dx d σ Equation of Equilibrium (2.1.1a) dx du = ε Strain-Displacement Relation (2.1.1b) E = Constitutive Equation (2.1.1c) where E is the Young’s modulus, ρ is the density and b is a body force (per unit volume). The unknowns of the problem are the stress , strain and displacement u . These equations can be combined to give a second order differential equation in
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This note was uploaded on 01/20/2012 for the course ENGINEERIN 2 taught by Professor Staff during the Fall '11 term at Auckland.

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1D_Elasticity_01_Elastostatics - Section 2.1 2.1...

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