In this thesis, isogeometric degenerated Reissner-Mindlin shell element including both geometric and material nonlinearities is formulated for the analysis of reinforced concrete plate and shell structures under monotonic loading. A Total Lagrangian approach is used to consider the effect of geometrical nonlinearity due to the change in geometry of structure. The formulation is based on large translations, and rotations and small strains.
A layered degenerated RM shell element with equivalent smeared steel layers is employed to represent reinforced concrete through the thickness. Material properties can be varied through the thickness and the surface of a shell element. Perfect bond is also assumed between concrete and steel reinforcement. For material nonlinearities, tensile cracking, tension stiffening between cracks, the nonlinear response of uncracked or cracked concrete in compression and shear transfer due to aggregate interlock and dowel action are considered. The concrete model is based on plasticity theory for a biaxial stress state. The steel reinforcement is assumed to be in a uniaxial stress state, and it is modeled as a bilinear elasto-plastic model.
For numerical integration, the mid-point rule integration scheme is adopted for each layer through the thickness and classical Gaussian quadrature rules with full integration is also used for surface of shell element because the locking phenomena such as shear or/and membrane locking can be overcome easily by only using the refinement of IGA. Arc-length method is also employed as numerical solution to solve RC problems with snap-back and snap-through phenomena.
Finally, a series of linear and nonlinear benchmark tests are performed to verify the ability of developed isogeometric degenerated shell element, followed by the nonlinear analysis for concrete structures such as concrete panels, RC panels, Vecchio and Collins panels, Mcneice slab, Duddeck slab and RC cylinder shell. The numerical results have a good agreement with experimental result available.