An efficient meshless technique for the solution of transversely isotropic two-dimensional piezoelectricity

In this paper, a new meshless technique is presented for the solution of two-dimensional piezoelectricity problem. The technique derivation is based on the solution of the corresponding analog equation by transforming the original set of differential equations into three Poisson equations with unknown right hand side terms. Boundary discretisation of the resulting integral equations is eliminated by the use of the method of fundamental solutions. The right hand side terms are represented in the solution as particular solutions expressed in terms of radial basis functions. The problem solution is then rewritten in its new form, which involves complementary solution and particular solution. The governing partial differential operator for piezoelectricity is applied on the obtained solution form and forced to be satisfied at a set of domain points, whereas the prescribed boundary conditions are satisfied at another set of boundary points. The proposed technique is implemented into computer code where several numerical examples with different boundary conditions are tested. The results demonstrated excellent agreement with those obtained from analytical and FEM solutions.