Nonlocal strong forms of thin plate, gradient elasticity, magneto-electro-elasticity and phase-field fracture by nonlocal operator method

Abstract 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 operator elasticity, thin plate, gradient electro-magneto-elasticity and phase-field fracture method. governing equations are expressed as an integral form support dual-support. first example shows that elasticity has same dual-horizon non-ordinary state-based peridynamics. is simple general it can convert efficiently local models into their corresponding forms. addition, a criterion instability proposed modelling linear elasticity. Several numerical examples presented to validate plate.