Question: Develop the compatibility relations for couple-stress theory given by (15.4.12). Next, using the constitutive relations, eliminate the strains and rotations, and express these relations in

Develop the compatibility relations for couple-stress theory given by (15.4.12). Next, using the constitutive relations, eliminate the strains and rotations, and express these relations in terms of the stresses, thus verifying equations (15.4.13).

Equation 15.4.12

2ex, dey 2   + 02z  ,  Jexy  2- 2z

Equation 15.4.13

120x 12ay  ax + - vv(ax+y) mxz  mxz myz = - 2  = -(txy +Tyx) amyz   (txy + Tyx)  21%y[ox - "(7x + ,)]   = :

2ex, ey 2 + 02z , Jexy 2- 2z

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