A G space theory and a weakened weak (W² ) form for a unified formulation of compatible and incompatible methods: Part I theory

This paper introduces a G space theory and a weakened weak form (W 2 ) using the generalized gradient smoothing technique for a unified formulation of a wide class of compatible and incompatible methods. The W 2 formulation works for both finite element method settings and mesh‐free settings, and W 2 models can have special properties including softened behavior, upper bounds and ultra accuracy. Part I of this paper focuses on the theory and...