Conceptual scheme of contact problems and incompressible solid scheme for volume conservation

Especially regarding shear locking-less scheme for 2D plane stress using harmonic functions

Abstract

In the previous paper, I proposed a conceptual scheme for the contact problems, which firstly move the surfaces without contacting, and then correct the surface positions conserving the volume of the overlapped domains. I will report in this paper an advance of the correcting scheme on the previous paper. To conserve the volume the incompressible scheme of the solid scheme plays an important role. I propose one of such scheme based on Helmholtz-decomposition. Especially in 2D, it is represented with the harmonic functions, in which the stream function proves perfect incompressibility. It is also shear locking-less scheme.