Abstract
• An efficient iteration approach is proposed to analyze boundary value problems in 2D PSCs. • By analyzing a plane problem, the proposed approach is verified with finite element method . • By analyzing an elliptical hole problem, the stress concentration phenomenon of the edge of elliptical hole is studied. • When an elliptical hole existing in PSCs is narrow enough, the mechanical-electric properties in PSCs remain unchanged. • The coupling effect among the mechanical field, electric field and electric current field is proved. Based on initial nonlinear constitutive equations, we establish the extended displacement and traction boundary integral equations for a piezoelectric medium with a volume electric charge, along with electron and electric current density boundary integral equations for a conductor with a volume electric current. Then, an iterative approach is proposed for investigation of boundary value problems in two-dimensional piezoelectric semiconductors (PSCs). Compared with extended displacements obtained by finite element analysis, this approach is validated via a rectangular PSC under extended external loads. Furthermore, as a numerical example, extended displacements across an elliptical hole in a rectangular PSC are investigated. It is shown that there is a stress concentration near the elliptical hole, which is closely dependent on its shape.
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