Example from book: continuum mechanics for engineers 2 edition

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SUMMARY

The discussion centers on solving Example 3.30 from the book "Continuum Mechanics for Engineers, 2nd Edition," which involves deriving the stress tensor components σij from the symmetric tensor field φij using the equation σij = εiqkεjpmφkm,qp. A participant initially struggled with the problem but later successfully solved it by applying the determinant and Kronecker delta, concluding that εiqkεjpm equals zero in the absence of body forces, thereby satisfying the equilibrium equations.

PREREQUISITES
  • Understanding of tensor calculus and stress tensors
  • Familiarity with the Kronecker delta notation
  • Knowledge of equilibrium equations in continuum mechanics
  • Basic principles of determinants in mathematical computations
NEXT STEPS
  • Study the properties and applications of the Kronecker delta in tensor analysis
  • Explore the derivation and implications of equilibrium equations in continuum mechanics
  • Learn about the role of determinants in solving tensor equations
  • Review additional examples from "Continuum Mechanics for Engineers, 2nd Edition" for practical applications
USEFUL FOR

Students and professionals in engineering mechanics, particularly those focusing on continuum mechanics and tensor analysis, will benefit from this discussion.

maros522
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example 3.30:
Let the stress tensor components σij be derivable from the symmetric
tensor field φij by the equation σij = εiqkεjpmφkm,qp. Show that, in the
absence of body forces, the equilibrium equations are satisfied.

I don't have any idea have to solve this problem. Can someone help me?
Thank you.
 
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I apologize for bad placed post.
After some time I solve this example. Use the determinant and kronecker delta. After this I found that εiqkεjpm = 0.
 

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