Fundamental solutions of uniform loads over triangular elements in a three-dimensional piezoelectric medium

In this paper, fundamental solutions of uniform loads over triangular elements in an infinite transversely isotropic piezoelectric three-dimensional space are derived. The triangle element can be parallel or vertical to the plane of isotropy and the uniform load can be mechanical and electric types, oriented in an arbitrary orientation. The solutions are expressed simply as a linear combination of three kinds of elementary functions – linear, trigonometric and logarithm functions. Three methods of superposition are employed to verify the obtained fundamental solutions. Numerical examples are also presented for the extended displacements and stresses induced by both mechanical and electric loads on the vertical and horizontal triangles.