Viscoelastic analysis of multilayered composite structures based on higher-order zigzag theory

Abstract

This dissertation investigates the viscoelastic behaviors of multilayered composite structures based on efficient higher-order zigzag theory. In addition, the coupling hygrothermal-mechanical problem also is analyzed considering how the viscoelastic properties of material depending on the temperature and moisture of environments. Moreover, the analysis of delamination growth in the viscoelastic laminate in the creep process is examined. The efficient higher order zigzag theory given in the thesis has their own advantages such as:<br/> (1) It is accurate for both global and local responses by superimposing linear zigzag field on a varying cubic displacement fields. <br/> (2) It requires only five number of unknown variables which is independent of layer number. Therefore, it is very potential to analyze thick laminates with hundreds of layers.<br/> (3) It can be easy to reduce to other simpler theories such as classical laminated theory, first-order shear deformation theory and third-order shear deformation theory which all are well known.<br/> In this study, the time-dependent relaxation moduli of composite materials have the form of Prony series, which can be determined by the master curve from experimental data. The constitutive equation of linear viscoelastic materials in the form of the Boltzmann superposition integral is simplified by the convolution theorem of the Laplace transform to avoid direct integration as well as to improve both computational accuracy and efficiency. By using the equivalent linear elastic stress-strain relationship in the corresponding Laplace domain, the transverse shear stress-free conditions at the top and bottom surfaces and the transverse shear stress continuity conditions at the interfaces between layers are satisfied conveniently. Thus, the structures and advantages of the EHOPT can be preserved in viscoelastic laminated composites in the Laplace domain. <br/> For finite element analysis, since the time dimension is transformed to Laplace domain, the finite element discretization is only used in the spatial domain. A nonconforming three-node triangular element is employed to implement the viscoelastic EHOPT. To pass the proper bending and shear patch tests in arbitrary mesh configurations, the modified shape function developed by Specht is applied and converted into Laplace domain. Therefore, the final numerical results, which is obtained by using inverse Laplace techniques, always converge to the corresponding analytical solutions.<br/> For coupling hygrothermal-mechanical problem, the temperature and moisture fields are also assumed in the form of efficient higher-order theory and calculated by solving continuity condition at the interface and employing the thermal and hygroscopic variation principle. <br/> In order to verify the efficiency and accuracy of the present study, some numerical examples for long-term creep and relaxation processed are performed. The present study provides a powerful tool to accurately investigate the responses of the viscoelastic or time-dependent mechanical behaviors of multilayered composite structures<br/>