A constrained discrete layer model for heat conduction in laminated composites

• Authors: M. Blanc;M. Touratier
• Venue: Computers and Structures
• Year: 2005

This paper presents a new approximated computational model for heat conduction problems in laminates and is called ''constrained discrete layer model''. The approach is based on the well known layer-wise theory in which constraints from continuity conditions on normal heat flux at interfaces of a multilayered structure are incorporated into the formulation in order to reduce the number of unknowns. The discrete layer method starts by discretizing the temperature field from Lagrange interpolations, in a manner of the finite element method along the thickness of the layer. The novelty in respect to discrete layer methods first introduced in solid mechanics, then comes from the exact satisfaction of all boundary and interface conditions for temperature and heat flux, using a standard variational method to express the corresponding boundary value method. The advantage is in reducing the number of unknown functions. In this paper, all the computations from both the discrete layer and constrained discrete layer models are achieved by using quadratic Lagrange interpolations in the thickness direction of the layers. This constitutes the only approximation made. Exact solutions known in the literature have been calculated here for reference solutions. Numerical results to several problems show the efficacy of the approach on one-dimensional and two-dimensional heat conduction problems in comparison with exact calculations. Finally, the accuracy of the proposed approach can be improved by using either interpolation of a high order, or discretizing each layer in more than one subdivision, as in a finite element method. Of course, if in-layer functions are interpolated as well, then, two and three-dimensional new solid finite elements can be constructed.