The present paper is an endeavor towards assessing the stresses which may be induced in multi-layer pressure vessels subjected to the combined effects of pressure and temperature gradients across the vessel wall thickness. Assuming different geometries of membrane shells; namely cylindrical and spherical shells, a solution based on prescribed model with radial linear temperature distribution has been attained. The solution relates the induced stresses to the shell geometry, layers properties, number of layers, wall thickness and the working conditions of pressure and temperature gradient. In the analysis each layer composing the vessel thickness is treated as a membrane shell of revolution (thin lamina). By the aid of finite element analysis (FEA) technique, different cases of pressure vessels under thermal loading are investigated.

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