A finite difference formulation is developed for the stress analyses in orthotropic
three-layer composite beams with mono-symmetrical cross-sections under various
force boundary and loading conditions. Four interfacial shear and peeling stress fields
at material interfaces are assumed as unknown functions. Based on shear stress flow
equilibrium conditions, three groups of stress fields including transverse shear,
transverse normal and longitudinal normal stresses in the beam, the plate and the
adhesive layer are expressed in terms of the unknown functions. A set of
compatibility equations and corresponding boundary conditions are then derived
from a variational principle of complementary strain energy and solved by a finite
difference technique. The present theory eliminates kinematic assumptions of equal
curvatures for the beam and the plate, it satisfies the infinitesimal stress
equilibrium conditions of the interfacial shear and peeling stresses at material
interfaces, and it captures the longitudinal normal stresses in the adhesive. By
comparing to numerical and analytical solutions, the present theory is a
solution for the prediction of concentrated transverse shear and transverse
normal (peeling) in the adhesive occurring near the plate ends. Based on the
present theory, a parametric study is conducted to quantify the effects of
the strengthening length, thickness, and elasticity moduli of the FRP plate
and adhesive layer on the peak values of the interfacial shear and peeling
stresses.
