Branching behavior in the nonlinear response of sandwich panels with a transversely flexible core

A branching behavior of sandwich panels with a transversely ¯exible (``softʹʹ) core subjected to longitudinal external forces is investigated using a geometrically nonlinear analysis. The study is based on a closed form high- order theory that allows for a general analysis without resort to the classical mode decoupling approach. The governing equations and the associated boundary conditions are presented, and the appropriate boundary conditions resulting from using edge beams are derived. An ecient path-following algorithm based on the quasi- Newton global framework has been developed. It provides a powerful numerical tool for determining the branching behavior which consists of a sequence of equilibrium states of the sandwich panel as a function of the external loading factor. Application of the general numerical analysis to the ``softʹʹ core sandwich panels reveals that they possess a complicated branching behavior with limit points and secondary bifurcations. It is shown that the wrinkling of the face sheets does not necessarily identify the buckling of the panel as a whole and in many cases it is a result of the nonlinear response. The localized buckling modes are found in some cases to be the critical ones rather than the usual sinusoidal buckling patterns. It is further shown that variations in the geometry, boundary conditions and mechanical properties of the panel constituents can lead to a qualitative shift in its nonlinear response from an imperfection-sensitive, ``shell-wiseʹʹ response, to an imperfection-nonsensitive, ``plate-wiseʹʹ one. 7