Introduction to Elasticity/Sample quiz5

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  • An infinite body has a uniform state stress of pure hydrostatic pressure . This stress state is perturbed by a spherical void of radius which leads to a new stress state
What do you expect the values of , , and to be? What is the stress concentration factor at the void?
  • What are the displacement conditions for antiplane strain in rectangular co- ordinates? Give an example of a problem that can be approximated by antiplane strain.
  • What are the strain conditions for plane strain in rectangular co-ordinates? Give an example of a problem that can be approximated by plane strain. What is the difference between plane strain and generalized plane strain?
  • What are the stress conditions for plane stress in rectangular co-ordinates? Give an example of a problem that can be approximated by plane stress.
  • Can the Airy stress function be used for three-dimensional problems? Write down the relation between the Airy stress function and stress in rectangular co-ordinates. How does this relation change when you solve problems that involve a body force? What additional restriction on the Airy stress function must be checked to see if compatibility is satisfied?
  • In the absence of body forces, the displacements (plane strain/stress) can be expressed as
What is and what are the restrictions on it?