Examples, Numerical Results, and Discussion

The details about the cylinder material are provided. A hollow cylinder with viscoelastic matrix and unidirectional fibers is considered. The use of Gamma function \(\Gamma \) and fractional exponential operators \(\Pi \) is explained. Moreover, the material constants, describing the full behaviour of the considered material and which are used in the constitutive relations are presented in this chapter. Validation of the calculation algorithm is achieved by comparison with a recent study. After the validation of the model, first the numerical results obtained for the purely elastic case are presented in tabulated form. Subsequently, the criteria for the selection of critical forces to be used in the stability loss investigation of the viscoelastic case is defined and the numerical results for the viscoelastic cylinder buckling thus obtained are illustrated both in tabulated and graphical form. The values of different parameters computed using the TDLTS for stability loss of the viscoelasticity hollow cylinder are compared against the results computed with the Kirchhoff-Love shell theory and the TORST discussed in the preceding chapter. The results obtained herein are related to the values of critical time (for viscoelastic case) and critical forces (for elastic case) computed using the initial imperfection criteria. The influence of different rheological parameters on the values of critical forces and critical times is also presented herein. Detailed discussion on the obtained results and concise conclusions are provided at the end of this chapter.