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Homework help: anisotropic elasticity equations

  • #1

Homework Statement


Hello, I'm studying anisotropic elasticity. One of the books I'm using is Lekhnitskii's. The book presents the general equations of the theory of elasticity for an orthotropic body as follows:

Homework Equations


upload_2018-7-13_9-56-33.png


The Attempt at a Solution


However, when I combine the strain-displacement equations and the Hook's Law and then replace them into the equilibrium equations I cannot get the same expression. My reasoning looks like this (for example, the first equation of the system):

A11.Uxx + A12.Vyx + A13.Wzx + A66.(Uyy + Vyx) + A55.(Wzx + Uzz) = 0

Obviously, I'm doing something wrong. What is my mistake?

Many thanks for your kind help.
 

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Answers and Replies

  • #2
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Maybe they are able to eliminate the cross derivatives by combining the equations with the continuity equation.
 

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