Geometrically nonlinear thermomechanical response of circular sandwich plates with a compliant core

The geometrically nonlinear response of a circular sandwich plate that consists of two face sheets and a compliant (“soft”) core with mechanical properties that may be either independent or dependent of temperature and subjected to both mechanical loads and thermal induced deformations, but remain elastic linear throughout the loading process, is presented. The mathematical formulation follows the principles of the high-order sandwich panel theory (HSAPT) and includes the vertical flexibility of the core in addition to the temperature dependency of the mechanical properties of the core material. The mathematical formulation outlines the set of governing partial differential equations as well the appropriate boundary conditions for a general sandwich layout. The particular case of an axisymmetric circular sandwich plate subjected to axisymmetric mechanical and thermal loads, and with axisymmetric boundary conditions is studied analytically and numerically. The numerical study includes an interaction of mechanical and thermal loads which is presented through results within the plate for various load levels of various structural quantities as well as equilibrium curves of temperatures versus these structural quantities. The results reveal that the combination of mechanical and thermal loads along with a compliant core material with mechanical properties that degrade with increasing temperatures shifts the behavior from a linear and stable (strength controlled) response into a strongly nonlinear response with limit point behavior and associated loss of stability, when large displacements and large rotations (geometrical nonlinearity) are included in the modeling.