  The derivation of nonlocal strong forms for many physical problems remains
cumbersome in traditional methods. In this paper, we apply the variational
principle/weighted residual method based on nonlocal operator method for the
derivation of nonlocal forms for elasticity, thin plate, gradient elasticity,
electro-magneto-elasticity and phase field fracture method. The nonlocal
governing equations are expressed as integral form on support and dual-support.
The first example shows that the nonlocal elasticity has the same form as
dual-horizon non-ordinary state-based peridynamics. The derivation is simple
and general and it can convert efficiently many local physical models into
their corresponding nonlocal forms. In addition, a criterion based on the
instability of the nonlocal gradient is proposed for the fracture modelling in
linear elasticity. Several numerical examples are presented to validate
nonlocal elasticity and the nonlocal thin plate .
