2-D Green's functions for semi-infinite orthotropic piezothermoelastic plane

Area of Science:

• Solid Mechanics
• Materials Science
• Electromagnetism

Background:

• Green's functions are crucial for electroelastic analyses in piezoelectric media.
• Existing research primarily addresses uniform temperature conditions, limiting applicability.
• Piezothermoelectric materials exhibit coupled electrical, thermal, and mechanical behaviors.

Purpose of the Study:

• To derive a 2-D Green's function for a semi-infinite piezothermoelectric plane subjected to a steady line heat source.
• To extend electroelastic analysis to non-uniform temperature fields.
• To provide a computationally convenient solution for coupled field components.

Main Methods:

• Utilized a compact 2-D general solution for orthotropic piezothermoelectric materials expressed in harmonic functions.
• Employed a trial-and-error method to determine the Green's function.
• Introduced four new harmonic functions to represent the Green's function.
• Expressed all coupled field components using elementary functions.

Main Results:

• Successfully derived the 2-D Green's function for the specified boundary conditions.
• The derived Green's function is applicable to semi-infinite piezothermoelectric planes.
• All electroelastic field components are presented in a simplified, elementary function form.
• Numerical results were visualized using contour plots.

Conclusions:

• The presented Green's function offers a significant advancement for analyzing piezothermoelectric materials under thermal gradients.
• The use of elementary functions enhances the practicality and ease of application in engineering problems.
• This work provides a valuable tool for understanding coupled fields in advanced materials.