A Study On Isogeometric Analysis Of Laminated Composite Structures

The requirements for higher stifness-to-weight ratio, greater wear resistance and better designable property over conventional materials have resulted in wide applications of composite laminates in the areas of aerospace, automotive, underwater and architecture structures. Therefore, the accurate numerical analysis of composite laminates has become an important research topic in computational structural mechanics. Although the finite element method is one of the most powerful techniques in numerical analysis, it has many inherent disadvantages, for example, the mesh generation process is time consuming and may create inaccuracies, and most finite element analyses are still performed with low-order elements, which are based on the C0-continuity Lagrange basis functions.Isogeometric analysis is a novel concept in computational mechanics, and aims at linking the gap between computer aided design (CAD) and finite element analysis (FEA). The basic idea here is to use non-uniform rational B-splines (NURBS), which are commonly used in CAD systems to describe geometries, as the interpolation functions for analysis rather than the traditional Lagrange polynomial functions. Exact geometries are determined at the coarsest level of discretization and during the mesh refinement process. Furthermore, isogeometric analysis provides flexible ways to perform mesh refinement, therefore high order NURBS elements can be obtained easily and directly.In this dissertation, isogeometric analysis is applied for static, free vibration, buckling and transient analysis of laminated composite structures based on several frequently-used theories of plates and shells. The accuracy and stability of the present method are demonstrated through comparing the obtained numerical results with analytical solutions, experiment values and results of other available numerical methods.In the first part of this dissertation, isogeometric analysis is applied for static, free vibration and buckling analysis of laminated composite plates based on the classical plate theory (CPT). CPT requires C1-continuity of generalized displacements while NURBS basis functions are well-suited for this requirement. The convergence rates of NURBS elements with various orders are studied in the static analysis. Moreover, frequency outlier is observed in the free vibration analysis and the outlier frequencies are eliminated by linear parameterization method. Furthermore, the influences of shapes, boundary conditions and ply angles are also studied in the vibration and buckling analysis.The thickness of a plate is ignored in the CPT and thus both transver normal and transver shear effects are neglected, therefore the CPT is only suitable for the analysis of thin plates. In the second part of this dissertation, isogeometric analysis is applied for geometric nonliear analysis of laminated composite plates based on the first order shear deformation theory (FSDT). Total Lagrangian formulation is employed to describe the nonlinear behaviour of plates under large deformations and the Newton-Raphson method is applied to solve the nonlinear equations. The effects of various mesh refinement strategies on the accuracy of numerical results are studied. The influences of thickness, boundary conditions, lamination schemes and loads on the nonlinear behavior of laminated composite plates are also investigated.FSDT assumes that the transverse shear strains are constant along the thickness direction thus a shear correction factor (SCF) has to be considered, therefore it can only be applied for moderately thick and thin plates. To overcome the limitations of CPT and FSDT, a more accurate high order shear deformation theory, termed as the third order shear deformation theory (TSDT), is applied in the static and free vibration analysis of composite lamanited plates. TSDT introduces the quadratic variation of the strains along the thickness direction such that the SCF does not need to be calculated. Isogeometric analysis satisfies the C1-continuity requirement of the TSDT and more accurate deflections and inter-laminar stress distributions are yield in both thick and thin plates. Due to the non-interpolatory nature of NURBS basis functions, a penalty method is applied to enforce the essential boundary conditions. High order NURBS elements are applied to improve the numerical results, and the shear locking phenomenon is significantly alleviated in the meantime. Free vibration analyses of plates with complicated shapes are also conducted.Finally, the isogeometric analysis module of LS-DYNA is applied in the static, free vibration and transient analysis of shells based on the Reissner-Mindlin shell theory. Isogeometric analysis assures the exact geometries and excellent numerical results are obtained in the analysis of shell structures, which are significantly sensitive to geometric imperfections. The shear locking phenomenon is effectively alleviated by high order NURBS elements.