CONTINUUM MECHANICS ( STRESS DISTRIBUTION ). Stress vector. State of stress. Stress distribution. Surface traction (loading). Volume V Surface S. Stress ve c tor. x 3. Volume V 0 Surface S 0. Volumetric force. x 2. x 1. GGO theorem.
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State of stress
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).
Navier equation traction vector
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.
Comments traction vector
equilibrium equations, i.e. that the sum of forces acting over the body has to vanish.
stop traction vector