Combined steady-state nonlinear heat transfer/thermal postbuckling computations in unstiffened and stiffened laminated composite plates and shells

Abstract

A computational scheme for the solution of the decoupled (i.e. applied stepwise sequentially) nonlinear steady-state heat transfer and geometrically nonlinear thermoelastic problem is presented for unstiffened and stiffened multilayered composite plates and shells. More specifically, a two-step formulation is conceived; first, the nonuniform temperature field resulting from applied heat fluxes is estimated by considering the three modes of heat transfer, namely nonlinear conduction, convection and radiation; second, the resulting temperatures are used as input to a stress analysis code which performs geometrically nonlinear analysis of composite panels with emphasis on thermal postbuckling computations. Two triangular elements are used for the computational experiments. For the solution of the heat transfer problem a 3-node triangular shell element is adopted which estimates the temperatures based on a first-order thermal lamination theory by employing primarily Cartesian notation. The element uses exact integrations for all nonlinear conduction, convection and radiation matrices [1,2] and accomplishes this by using extensive symbolic algebra techniques. The nonlinear stress analysis problem is solved using a shallow shell multilayered triangular element of varying and adaptable curvature which can accomodate the dependence of the material properties on temperature and also utilizes only exact integrations [5] made possible by employing once again symbolic computation; the latter element is developed using the principles of the natural mode method. The algorithms used for the solution of the two-stage problem are discussed. Numerical examples are presented which show the efficiency of the formulation and the interest of the thermophysical problem in hand.