Three-dimensional analysis for functionally graded piezoelectric semiconductors

This article presents numerical analyses of functionally graded piezoelectric beam with piezoelectric semiconducting material properties using meshless method. Unlike piezoelectric dielectric materials, electron density and electric current are additionally considered in constitutive equations for piezoelectric semiconductors. Mutual coupling of elastic displacements, electric potentials, and electron density increases the complexity of the analyzed problem. For the solution of the set of partial differential equations with non-constant coefficients, the local radial basis function collocation method is proposed in this work. Approximating the spatial variations of all physical fields in the partial differential equations by the multiquadric radial basis function entails an ensuing system for time-dependent problems solved by the Houbolt finite-difference scheme as a time-stepping method. The presented local radial basis function collocation method is verified using the corresponding results obtained using the finite element method. The influence of material parameter gradation and initial electron density is then investigated, along with transient analyses.