Research on Static and Dynamic Stability for Viscoelastic Plates and Shells
|Keywords||viscoelasticity laminated plate and shell delay loss of stability transverse shear deformation matrix cracking damage snap-through creep buckling bifurcation creep buckling dynamic stability|
The mechanical behavior of nonlinear static and dynamic stability for viscoelastic composite laminated plates and cylindrical shells is systematically investigated in the dissertation. The main research contents and results are given as follow.Based on Timoshenko-Mindlin shear deformation theory and small deflection hypothesis, the creep buckling for viscoelastic laminated plates and cylindrical shells are analyzed. Laplace Transformation is employed to the governing equation to derive the critic loads in the phase space, and extremum theorems of Laplace Inversion Transformation is then used to acquire the instantaneous critic loads and durable critic loads. It is verified that the results of two types of critic loads, obtained by viscoelastic approach and quasi-elastic approach respectively, are identical. By the investigation of instantaneous critic loads and durable critic loads, the mechanism of creep buckling of boron fiber/epoxy matrix laminated plates and boron fiber/epoxy matrix cylindrical shells exhibiting viscoelastic behavior is revealed. In the case of perfect laminated plates and shells, a disturbance model is constructed to exploit the new mechanics signification for durable critic loads, and to explain the phenomena of delay loss of stability according to the time-dependent evolution of deflection.In the analysis of dynamic stability of viscoelastic plates and shells within the geometrically linear and nonlinear theory, the Boltzmann hereditary constitutive relationship is used to model the viscoelastic behavior and relaxation modulus is characterized with Prony-Dirichlet series. A general approach to determine the boundaries of unstable regions is presented by employing harmonic balance method and incremental harmonic method corresponding to linear and nonlinear dynamic stability. The general features of dynamic stability, including the shrink and downward shift of dynamic unstable region, are examined for plate and shell structures by taking into account of material viscoelastic property. To simplify the analysis procedure, a approximate approach for the application of both harmonic balance method and incremental harmonic method is proposed, and the validity of this method is examined. Based on the thin plat and shallow shell theory respectively, the linear dynamic stability of vicoelastic laminated plates and cylindrical shells is analyzed by using this approximate approach.The quasi-elastic approach is employed to investigate the behavior ofsnap-through creep buckling of viscoelastic cross-ply cylindrical panels, with the nonliear governing equations obtained within both Timenshenko-Mindlin shear deformation theory and Donnel-Karman geometrically nonlinear relationship. Effects of transverse shear deformation on the critic time of snap-through creep buckling is examined with respect to both boron fiber /epoxy matrix laminated cylindrical panels and glass fiber/epoxy matrix laminated cylindrical panels, which exhibit obvious difference on anisotropic property. By using Schapery’s viscoelastic constitutive equations coupling matrix cracking damage, the analysis of snap-through creep buckling for viscoelastic cross-ply cylindrical panels containing transverse matrix cracking is performed, also the effects of damage on the behavior of time-dependent delay loss of stability is examined corresponding to two types of materials mentioned above.The creep bifurcation buckling of viscoelastic symmetric angle-ply cylindrical shells subjected to axial compression is analyzed. Based on thin shallow shell theory and Donnel-Karman geometrically nonlinear relationship as well as Schapery’s viscoelastic constitutive equations coupling matrix cracking damage, the governing equations for pre-buckling creep deformation and bifurcation buckling are obtained according to the assumption of instantaneous elasticity occurred during the bifurcation. Combining the discretization of space variable by finite difference with Taylor’s numerical integration of convolution integral, the pre-buckling creep deformation is analyzed. By taking the separate expression of unknown functions with respect to axial and circumferential space variables, and employing the technique of finite difference, A semi-analytic solution strategy is performed to solve the governing equations of bifurcation buckling with incremental forms. Critic time of bifurcation buckling is determined by the change of sign of characteristic determinant. The effect on the behavior of bifurcation creep buckling, exerted by boundary conditions > matrix cracking evolution and the magnitude of axisymmetric imperfection as well as the ration of radius to thickness, is examined.