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For plane structures, under the small strain and small rotation hypotheses we can write the following relations between deformations and displacements:

 

                               

or in matrix form:

 

                                                 

or in a condensed form:

 

                                                             

where u and v are the components of displacements in the x and y directions. If the displacement field is represented by polynomials, the strains and stresses are one order lower than the displacements.

 

 

 

 

 

 

 

 

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