Refined stability theory for sandwich shells with transversally stiff core. 1. Nonlinear equilibrium equations

A refined version of geometrically nonlinear relationships is proposed for the static thermoelastic response of sandwich shells with face sheets made of composite or homogeneous materials and a transversally stiff core. This theory has primary importance for studying mixed forms of buckling of the bearing sheets, which are mainly realized in the zones of a momentary stress-deformed state of the shell on the whole. An iteration procedure was developed for construction of the model. In the first step, assuming that the core is transversally soft, expressions are derived for the components of the displacement vector after integration of the three-dimensional equilibrium equations. In the second step, the tangential stresses are determined assuming a transversally stiff core to obtain the in-plane stresses and highly accurate transverse normal stresses. The proposed model admits a formal changeover to the model of a shell with a transversely soft core.Center for the Study of Dynamics and Stability. A. N. Tupolev Kazan State Technical University, Kazan, Tatarstan, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 4, pp. 513–524, July–August, 1996.