A note on the uniqueness of 2D elastostatic problems formulated by different types of potential functions

Abstract

New additional conditions required for the uniqueness of the 2D elastostatic problems formulated in terms of potential functions for the derived Papkovich-Neuber representations, are studied. Two cases are considered, each of them formulated by the scalar potential function plus one of the rectangular non-zero components of the vector potential function. For these formulations, in addition to the original (physical) boundary conditions, two new additional conditions are required. In addition, for the complete Papkovich-Neuber formulation, expressed by the scalar potential plus two components of the vector potential, the additional conditions established previously for the three-dimensional case in z-convex domain can be applied. To show the usefulness of these new conditions in a numerical scheme two applications are numerically solved by the network method for the three cases of potential formulations.

Keywords

• papkovich-neuber representation
• uniqueness solution
• network simulation method
• linear elasticity
• classical linear elasticity
• 02.30.em
• 02.60.lj
• 02.70.-c
• 04.20.ex
• 46.25.-y