Interfacial shear stress optimization in sandwich beams with polymeric core using non-uniform distribution of reinforcing ingredients

Core shearing and core/face debonding are two common failure states of sandwich beams which
are mainly the result of excessive shear stresses in the core. Generally, the core made of
homogeneous Fiber Reinforced Polymer (FRP) shows better shear resistance in comparison with
that made of pure polymer. Usually, this enhancement is however somewhat limited. This paper
proposes a methodology to decrease interfacial stresses by presenting the optimal distribution of
reinforcing ingredients in the polymeric matrix. For this purpose, a Non-Uniform Rational Bspline
(NURBS) based reinforcement distribution optimizer is developed. This technique aims at
the local stress minimization within any arbitrary zone of the design domain. In our
methodology, optimization and model analysis (calculation of the objective function and the
design constraints) have common data sets. The quadratic NURBS basis functions smoothly
define the reinforcement distribution function as a NURBS surface. The core and face sheets are
modeled as multi-patches and compatibility in the displacement field is enforced by the penalty
method. An adjoint sensitivity method is devised to minimize the objective function within areas
of interest defined over arbitrary regions in the design domain. It is also used for efficient
updating of design variables through optimization iterations. The method is verified by several
examples.