Download PDF by J.R. Barber: Elasticity

By J.R. Barber

ISBN-10: 1402009666

ISBN-13: 9781402009662

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Show that in a state of plane stress without body forces, the in-plane displacements must satisfy the equations 6. Show that in a state of plane strain without body forces, 7. If a material is incompressible , a state of hydrostatic stress produces no strain. One way to write the corresponding stress-strain relations is where is an unknown hydrostatic pressure which will generally vary with position. Also, the condition of incompressibility requires that the dilatation Show that the stress components and the hydrostatic pressure equations where is the body force.

For the continuous solid, the compatibility condition guarantees that (ii) is satisfied, since shape is defined by displacement derivatives and hence by strains. g. if it has a central hole — condition (ii) is not sufficient to ensure that the deformed pieces can be assembled into a coherent body. Suppose we imagine assembling the ‘deformed’ puzzle working from one piece outwards. The partially completed puzzle is simply-connected and the shape condition is sufficient to ensure the success of our assembly until we reach a piece which would convert the partial puzzle to a multiply connected body.

One way of satisfying the compatibility equations in the absence of rotation is to define the components of displacement in terms of a potential function through the relations Use the stress-strain relations to derive expressions for the stress components in terms of Hence show that the stresses will satisfy the equilibrium equations in the absence of body forces if and only if 4. Plastic deformation during a manufacturing process generates a state of residual stress in the large body If the residual stresses are functions of only and the surface is not loaded, show that the stress components must be zero everywhere.

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Elasticity by J.R. Barber

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