3-D Temperature Fields in Laminated Shells Subjected to Thermo-Loads

The temperature fields in the laminated shells were studied, including opencylindrical shells and cylindrical shells, according to the thermal theory. Analyticalsolution of the temperature in the shells with the known temperature on the surfaces waspresent. The thinning layer approach was introduced to simplify the three-dimensionalheat conduction equation. Firstly, the layered shell was divided into N thinner layers. Thegoverning equation was simplified by replacing the variable r by r0 in the center line ofevery thin layer. The general solutions of temperature satisfying the simplified threedimensionalgoverning equation in single-layered shell were deduced in the cylindricalcoordinate system. Then, the temperature and heat flux relationships between the surfacescould be found by transferring matrixes. According to the continuities of temperature andheat flux in the interface of the laminates, the temperature and heat flux relationships ofthe surfaces were derived. With the temperature condition on the surfaces, the unknowncoefficients in the general solution of temperature were obtained. Finally, the effects fromthe thinning layer approach were eliminated by analyzing different numbers of thin layers.The validity and accuracy of the proposal method were proved from the convergence andcomparison studies. And several numerical examples were studied to investigated thetemperature effects from surface temperatures, geometric size of the shells andcomposition of layers.