CONTINUUM MECHANICS (STRESS DISTRIBUTION)

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CONTINUUM MECHANICS(STRESS DISTRIBUTION)
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Stress vector
State of stress
Stress distribution
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GGO theorem
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On the body surface stress vector has to be
balanced by the traction vector
Stress on the body surface
Coordinates of vector normal to the surface
This equation states statics boundary conditions
to comply with the solution of the equation
This equation (Navier equation) reflects internal
equilibrium and has to be fulfilled in any point
of the body (structure).
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Navier equation
in coordintes reads
We have to deal with the set of 3 linear partial
differential equations.
There are 6 unknown functions which have to
fulfil static boundary conditions (SBC)
We need more equations to determine all 6
functions of stress distribution. To attain it we
have to consider deformation of the body.
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Comments

• Equation is
  derived from one of two
• equilibrium equations, i.e. that the sum of
  forces acting over the body has to vanish.

1. The other equilibrium equation sum of the
   moments equals zero yield already assumed
   symmetry of stress matrix, sij sji

1. Navier equation is the special case of the motion
   equation i.e. uniform motion (no inertia forces
   involved). The inertia effects can be included by
   adding dAlambert forces to the right hand side
   of Navier equation.

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• stop