  In this work, we present a compactly supported radial basis function (CSRBF)
based meshfree method to analyse geometrically nonlinear flexoelectric
nanostructures considering surface effects. Flexoelectricity is the
polarization of dielectric materials due to the gradient of strain, which is
different from piezoelectricity in which polarization is dependent linearly on
strain. The surface effects gain prominence as the size of the structure tends
to nanoscale and so their consideration is inevitable when flexoelectric
nanostructures are analysed. First, the proposed meshfree formulation is
validated and the influence of nonlinear strain terms on the energy conversion
ability of flexoelectric beams made of a non-piezoelectric material like cubic
Strontium Titanate is studied. Subsequently, the meshfree formulation for
nonlinear flexoelectricity is extended to include nonlinear surface effects. It
is determined that the surface effects can have notable influence on the output
flexoelectric voltage of nano-sized cantilever structures in the nonlinear
regime.
