Harmonic shapes are known to minimize stress disturbance when introduced into an
elastic body as either holes or inclusions. This paper is concerned with the
design of harmonic shapes in an isotropic laminated plate. Specifically, we
require that the harmonic shape does not disturb the sum of the two normal
membrane stress resultants and that of the two normal bending moments when
inserted into a uniformly loaded laminated plate. Using complex variable
methods, we demonstrate how a single harmonic shape (hole or rigid inclusion)
and two interacting harmonic shapes can be successfully designed to meet
our requirements. In our discussion, the two interacting harmonic shapes
include (i) two interacting harmonic holes, (ii) two interacting harmonic rigid
inclusions, and (iii) one harmonic hole interacting with another harmonic rigid
inclusion.