Effect of Boundary Constraints in the Formulation of the Partition of Unity Method: One-dimensional Setting

Abstract

The paper examines an effect of boundary constraints applied to the enhanced degrees of freedom of partition of unity based discontinuous elements. To highlight the present issue the problem is studied in a one-dimensional setting. In particular, an example of a one-dimensional bar element crossed by a set of discontinuities having a finite elastic stiffness clearly shows a need for proper approximation of the displacement field within a discontinuous element in order to correctly represent the structural response. While the discontinuous elements with boundary constraints applied to the enhanced degrees of freedom display an unrealistic dependence of the global response on the locations of the discontinuities, the discontinuous elements with complete approximation of the discontinuous part of the displacement field provide the expected global response independent of the locations of the discontinuities.