In the present study, we propose a computational model for the linear and nonlinear analysis of shell structures. We consider a tensor-based finite element formulation which describes the mathematical shell model in a natural and simple way by using curvilinear coordinates. To avoid membrane and shear locking we develop a family of high-order elements with Lagrangian interpolations. The approach is first applied to linear deformations based on a novel and consistent third-order shear deformation shell theory for bending of composite shells. No simplification other than the assumption of linear elastic material is made in the computation of stress resultants and material stiffness coefficients. They are integrated numerically without any approximation in the shifter. Therefore, the formulation is valid for thin and thick shells. A conforming high-order element was derived with 0 C continuity across the element boundaries. Next, we extend the formulation for the geometrically nonlinear analysis of multilayered composites and functionally graded shells. Again, Lagrangian elements with high-order interpolation polynomials are employed. The flexibility of these elements mitigates any locking problems. A first-order shell theory with seven parameters is derived with exact nonlinear deformations and under the framework of the Lagrangian description. This approach takes into account thickness changes and, therefore, 3D constitutive equations are utilized. Finally, extensive numerical simulations and comparisons of the present results with those found in the literature for typical benchmark problems involving isotropic and laminated composites, as well as functionally graded shells, are found to be excellent and show the validity of the developed finite element model. Moreover, the simplicity of this approach makes it attractive for future applications in different topics of research, such as contact mechanics, damage propagation and viscoelastic behavior of shells.

Ceramic composites for high temperature applications must be designed with crack arrest capability to improve the resistance to flaws produced in service, such as by thermal shock. Laminated composites containing Al2O3 layers in 3mol%Y2O3-ZrO2 (TZ3Y) were fabricated by electrophoretic deposition (EPD) and pressureless sintering. The layering design (Al2O3 layer thickness and volume fraction) was varied to determine the influence on fracture behaviour. The residual stress in Al2O3 layers was measured using a fluorescence spectroscopy technique. The fracture strength of 15 different laminates, and monolithic Al2O3 and TZ3Y, was tested in 4-point bending at room temperature. Vickers indentation (10 kg load) was used to simulate natural flaws at the sample surface before testing as a measure of flaw tolerance. Fracture ranged from catastrophic failure, to multi-stage failure and complete delamination (in processing). Transitions in behaviour were found related to a geometrical parameter derived from the strain energy release rate for edge cracks. The strength of three Al2O/TZ3Y composites was compared with monolithic Al2O3 and TZ3Y for a range of indentation loads (up to 20 kg). The strength of the composites was similar to monolithic TZ3Y but the flaw tolerance was improved due to multi-stage fracture. The strength and flaw tolerance (using 10 kg indentation) of two Al2O3/TZ3Y composites and monolithic TZ3Y was measured < 1300°C. The multi-stage fracture behaviour disappeared > 25 °C, and there was no beneficial effect of the Al2O3 layers on the strength. Superplastic deformation of the TZ3Y layers at 1300°C was prevented by the constraint of the Al2O3 layers. Recommendations are made about the design of flaw tolerant ceramic laminates for high temperature use. / Thesis / Master of Engineering (ME)