Question

A unit cube of a transversely isotropic solid is subjected to uniform surface tractions resulting in the strain, , where  is a constant. The symmetry axis of the solid is on the -plane and is inclined at angle to -axis.

(a) Calculate the applied tractions in terms of the elastic constants and .

(b) Compare results with those for an isotropic solid.

 

 

 

 

 

 

Answer 1

Below is the diagram with answer:

(b) Above we saw two additive decompositions of an arbitrary tensor A. Of com- parable significance in continuum mechanics are the multiplicative decompo- sitions afforded by the polar decomposition theorem.