The coupling resulting from the mutual influence of material thermal and mechanical parameters is examined in the thermal stress analysis of a long, hollow, multilayered, isotropic composite cylinder subjected to sudden axisymmetric external and internal temperature. The method of complex frequency response functions together with the Fourier transform technique is utilized. Because coupling parameters for some composite materials, such as carbon-carbon, are very small, the effect of coupling is neglected in the orthotropic thermal stress analysis. The stress distributions in long, hollow, multilayered orthotropic cylinders subjected to sudden axisymmetric temperature loading combined with dynamic pressure as well as asymmetric temperature loading are also obtained. The method of Fourier series together with Laplace transform is utilized in solving the heat conduction equation and thermal stress analysis. The inertial term is considered and the perturbation technique is applied to cylinders subjected to dynamic pressure loading. For brittle materials, like carbon-carbon composite, the strength variability is represented by two or three parameter Weibull distributions. The “weakest link" principle which takes into consideration both the applied stresses and the effected volume of material is used in the reliability analyses for both the isotropic and orthotropic carbon-carbon composite cylinders. The complex frequency response analysis is performed on a long hollow multilayed orthotropic cylinder under asymmetrical thermal load. Both deterministic and random thermal stress and reliability analyses can be based on the results of this frequency response analysis. The stress and displacement distributions and reliability of rocket motors under static or dynamic line loads are analyzed by an elasticity approach. Rocket motors are modeled as long hollow multilayered cylinders with an air core, a thick isotropic propellant inner layer and a thin orthotropic kevlar-epoxy case. The case is treated as a single orthotropic layer or a ten layered orthotropic structure. Five material properties and the load are treated as random variables with normal distributions when the reliability of the rocket motor is analyzed by the first-order, second-moment method (FOSM). / Ph. D. / incomplete_metadata