Solve the Stress Tensor Problem Now

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SUMMARY

The discussion addresses the solution to the Stress Tensor Problem, focusing on the calculation of the stress vector and stress scalar. The key method involves multiplying the stress matrix by the normal vector to the tangent plane. The normal vector can be derived from a radius vector originating from the point where y = z = 0, which makes specific angles with the axes: 30 degrees with the y-axis and 60 degrees with the z-axis. A diagram is recommended for visual clarity.

PREREQUISITES
  • Understanding of stress matrices in continuum mechanics
  • Knowledge of vector mathematics and normal vectors
  • Familiarity with cylindrical coordinates
  • Ability to interpret geometric diagrams
NEXT STEPS
  • Research methods for calculating normal vectors in three-dimensional space
  • Study the application of stress matrices in engineering problems
  • Learn about the geometric interpretation of vectors in cylindrical coordinates
  • Explore visual tools for diagramming stress tensor problems
USEFUL FOR

This discussion is beneficial for mechanical engineers, materials scientists, and students studying continuum mechanics who are looking to solve stress tensor problems effectively.

rahooma
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So what you really need is the vector normal to that "tangent plane."
If you multiply your stress matrix by that normal vector, then that gives you the desired result (stress vector).
If you pre and post multiply by that normal vector then you have your answer to the second part of the problem (stress scalar).

The only issue is how to obtain that normal vector, and you're on your own there (google).
 
Draw a diagram. You will see that a radius vector from y = z = 0 at any x value is normal to the cylinder. The radius vector makes an angle of 30 degrees with the y axis, and 60 degrees with the z axis.

Chet
 

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