Complete Polynomial Displacement Fields for Finite Element Method

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Abstract
It is generally accepted that the displacement patterns chosen to represent the deformation of a finite element should be such that there is complete compatibility with adjacent elements. Although some writers have doubted the necessity for the complete satisfaction of compatibility away from the reference nodes, provided the displacement pattern is capable of assuming certain uniform strain states, the desirability of complete compatibility is not in question. The displacement fields suggested in this note satisfy complete compatibility.

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