The meshless Petrov-Galerkin (MLPG) method is developed to analyse 2-D problems for flexoelectricity and thermoelectricity. Both problems are multiphysical and scale dependent. The size-effect is considered by the strain- and electric field-gradients in the flexoelecricity and higher-grade heat flux in the thermoelectricity. The variational principle is applied to de-rive the governing equations considered constitutive equations. The order of derivatives in governing equations is higher than in equations obtained from classical theory. The coupled governing partial differential equations (PDE) are satisfied in a local weak-form on small fic-titious subdomains with a simple test function. Physical fields are approximated by the mov-ing least-squares (MLS) scheme. Applying the spatial approximations in local integral equa-tions a system of algebraic is obtained for the nodal unknowns.
The Meshless Analysis of Scale Dependent Problems for Coupled Fields