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It is also necessary that the stress function <p must not only satisfy the equilibrium conditions of the problem but must also satisfy the compatibility relationships, i.e. eqn. 8.76. For the two-dimensional case these reduce to:

d2Vxy 92£x dxdy dy2

yy dx2

This equation can be written in terms of stress using the appropriate constitutive (stress-strain) relations. To illustrate the procedure the plane strain case will be considered. In this the relevant equations are:

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