Steady-state nonlinear heat transfer in stiffened composite plates and shells by an exactly integrated facet triangular element Original Research Article

The present research work expands a previously developed study which was primarily concerned with the development of a multilayered composite triangular element for the steady-state analysis of the temperature fields in laminated shells (see J. Argyris, L. Tenek and F. Oberg. A multilayer composite triangular element for steady-state conduction, convection, radiation heat transfer in complex shells, Comput. Methods Appl. Mech. Engrg. 120 (1995) 271–301). These temperature fields included the linear effects of conduction and convection and the nonlinear effects of radiation. Here we augment the basic formulation with quadratically time-dependent thermal conductivities thus achieving together with the previously included radiation effects a high degree of nonlinearity in our steady-state heat transfer formulation. A distinct characteristic of the study is the exact integration of all matrices which is accomplished by employing advanced symbolic computation techniques as well as delicate programming. Comparison is made with available analytical results for various panels of different complexity; simple flat unstiffened plates to stiffened cylindrical shells are studied. The 3-node triangular element can be applied to any geometry thus ensuring generality. As we shall show in a subsequent study it can be made also compatible with structural elements.