A MULTILAYER COMPOSITE TRIANGULAR ELEMENT FOR STEADY-STATE CONDUCTION CONVECTION RADIATION HEAT-TRANSFER IN COMPLEX SHELLS

Our latest study presents the theoretical formulation and computer implementation of a three-node six degrees of freedom multilayer flat triangular element intended for the study of the temperature fields in complex multilayer composite shells. Inherent in the formulation, in this first introductory and self-consistent systematic study, are the three modes of heat transfer, namely conduction, convection and radiation, the latter introducing in our theoretical model strong nonlinear effects. In the present discourse, all nonlinear terms are strictly due to radiation; the material properties are assumed independent of temperature but this in no way restricts the generality of the basic theory. The formulation is based on a first-order thermal lamination theory which assumes a linear through-the-thickness temperature variation. The following features are uniquely implemented in the computer model: (1) Exact integration of all matrices including the highly nonlinear radiation matrix (2) Exact integration of all derivative (Jacobian) matrices for efficient nonlinear analysis (3) Geometrical generality achieved by an arbitrarily oriented inexpensive flat shell element (4) Compatibility with structural elements (5) Computational efficiency and simplicity A predictor-corrector scheme in the form of the Newton-Raphson method is adopted for the solution of the steady-state nonlinear problem. Numerical examples, ranging from simple panels to complex anisotropic shells substantiate the theoretical formulation and show the potential of the present laminated triangular element in the computer simulation of temperature effects in complex geometries.