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A meshless Fragile Points Method (FPM) is presented for analyzing 2Dflexoelectric problems. Local, simple, polynomial and discontinuous trial andtest functions are generated with the help of a local meshless differentialquadrature approximation of the first three derivatives. Interior PenaltyNumerical Fluxes are employed to ensure the consistency of the method. Based ona Galerkin weak-form formulation, the present FPM leads to symmetric and sparsematrices, and avoids the difficulties of numerical integration in the previousmeshfree methods. Numerical examples including isotropic and anisotropicmaterials with flexoelectric and piezoelectric effects are provided asvalidations. The present method is much simpler than the Finite Element Method,or the Element-Free Galerkin (EFG) and Meshless Local Petrov-Galerkin (MLPG)methods, and the numerical integration of the weak form is trivially simple.

A New Meshless "Fragile Points Method (FPM)" Based on A Galerkin Weak-Form for 2D Flexoelectric Analysis