Analytical solution of temperature in laminated beams subjected to general thermal boundary conditions

Abstract

The temperature distribution in laminated beams underging thermal boundary conditions has been investigated. The thermal boundary conditions are general and include various combinations of prescribed heat fluxes and temperatures at the edges. An analytical solution of temperature for the laminated beam is present on the basis of the heat conduction theory in this paper. The proposed method is applicable to the beams with arbitrary thickness and layer numbers. Due to the complexity of the boundary conditions, the temperature field to be determined was considered from two sources. The first part was the temperature field from the complex temperature conditions at two edges of the laminated beam. The solution for the temperature of the first part was constructed to satisfy temperature boundary conditions at two edges. The second part was the temperature field from the upper and lower surface temperatures without taking account of the thermal conditions at two edges. In this part, the exact solution for the temperature was obtained based on the heat conduction theory. The convergence of the solution was examined by analyzing terms of Fourier series. The validity and feasibility of the proposed method was verified by comparing theoretical results with numerical results due to the equivalent single layer approach and the finite element method (FEM). The influences of surface temperatures, beam thicknesses, layer numbers and material properties with respects to the solution of the temperature field of the beam were investigated via a series of parametric studies.

Keywords

temperature field / laminated beam / transfer matrix / general temperature boundary

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