A strain-constructed point interpolation method and strain field construction schemes for solid mechanics problems using triangular mesh

This paper presents a strain-constructed point interpolation method (SC-PIM) for solid mechanics problems using three-node triangular mesh. In the SC-PIM, the point interpolation method (PIM) is used to construct both displacement and strain fields. A total of 14 schemes are proposed to construct strain fields that are equivalent to the compatible strain fields in energy norm, and therefore the strain-constructed Galerkin (SC-Galerkin) weak form can be used to form the discretized system equations. In these schemes, strains at critical points (vertices of the triangular integration cells) are first obtained using the generalized strain smoothing techniques over the node-based and/or edge-based smoothing domains, and constructed strain fields in the integration cells are then obtained using linear interpolations. A SC-PIM model using any of the 14 schemes is stable and convergent, but not necessarily to the exact solution. Standard numerical patch tests are conducted to find six linearly conforming schemes converging to the exact solution. Benchmark problems have been studied to investigate the performance and properties of the SC-PIM with all these six conforming schemes. Outstanding schemes have been identified with better accuracy and high convergence rates in terms of both displacement and energy norms.