Composite laminated structures are prone to delamination. Rotorcraft flexbeams, apart from many other aerospace primary load carrying members are made up of composite laminated structures. A delaminated primary load carrying member can lead to catastrophic failure of the system of which it is a part. Delamination modeling and detection in composite laminated structures are challenging areas of ongoing research worldwide. Existing literature falls short of addressing effects of widthwise partial delamination on the modal characteristics of beams. To address this issue, a new partial delamination model for composite beams is proposed and implemented using the finite element method. Homogenized cross-sectional stiffness of the delaminated beam is obtained by the proposed analytical technique, including extension-bending, extension-twist and torsion-bending coupling terms, and hence can be used with an existing finite element method. A two-noded C1-type Timoshenko beam element with four degrees of freedom per node for dynamic analysis of beams is implemented. The results for different delamination scenarios and beams subjected to different boundary conditions are validated with available experimental results in the literature and/or with a 3-D finite element simulation using COMSOL. Results of the first torsional mode frequency for the partially delaminated beam are validated with the COMSOL results. The key point of the current work is that even partial delamination in long structures can be analyzed using a 1-D beam model, rather than using computationally more demanding 3-D or 2-D models. Rotor craft flexbeams are prone to delaminations, which in most realistic situations are partial along both the length and the width. However, the effect of partial delamination on the modal characteristics of the beam is not studied by researchers to the best of the author’s knowledge. Addressing this issue, a rotorcraft flexbeam is analysed here in the presence of delamination. A set of nonlinear governing equations for the rotating flexbeam are developed in hybrid basis. The flexbeam model developed has axial stretch, transverse displacement and flexural rotation in flapwise direction and twist as its degrees of freedom. The nonlinear governing differential equations are linearised and solved for eigenvalues and eigenvectors using a finite element method. The effects of angular speed and delamination size and location on the flexbeam modes are analysed. The results obtained using the proposed model are validated with the COMSOL 3-D finite element simulations. Next, the issue of delamination detection in beams is addressed. Mode shape curvature and Katz fractal dimension are used to detect the presence of partial delaminations in a beam. The effects of boundary conditions and location of delamination on the fractal dimension curve are studied. Usage of higher mode shape data for detection of delamination in beams is evaluated. Limitations of the Katz fractal dimension curve for delamination detection are enumerated. It is shown that fractal dimension measure and mode shape curvature can be used to detect the presence of partial delamination in beams. It is found that the torsional mode shape is best suited for partial delamination detection in beams. Apart from beams, Shell-and plate-like structures are also extensively used in aerospace structures. The modeling of multilayered plates is introduced herein with the intention to model delaminations in 2D. Carrera Unified Formulation(CUF)plate model, developed using variational formulations, is used to derive the stiffness matrices and to apply, the Principle of Virtual Displacement(PVD) and the Reissner Mixed Variational Theorem (RMVT). It is known that FEM implementation for plates leads to the phenomenon of numerical locking: the so-called membrane and shear locking effects. A well-known remedy for addressing locking is the use of the Mixed Interpolated Tensorial Components(MITC) technique. A strategy similar to MITC approach in the RMVT formulation is used to construct an advanced locking-free finite element to treat the multilayered plates. Composite laminated plates are prone to delamination. Implementation of delamination in the CUF frame work using nine-noded quadrilateral MITC9 elements is discussed. MITC9 elements are devoid of shear locking and membrane locking. Delaminated structures, as well as the corresponding healthy structures, are analysed for free vibration modes. The results from the present work are compared with those from available experimental or/and theoretical research articles or/and the 3-D finite element simulations. The effects of different kinds and different percentages of interfacial area of delaminations on the first three natural frequencies of the structure are discussed. The presence of the open-mode or breathing mode delamination mode shape for large delaminations within the first three natural frequencies is discussed. Also, the switching of the places between the second bending mode and the first torsional mode frequencies is discussed. Results obtained from different ordered theories are compared in the presence of delamination. Advantage of layer wise theory as compared to equivalent single layer theories for very large delaminations is stated. The effects of different kinds of delamination and its effect on the second bending and first torsional mode shapes are discussed.

Composite structures are extremely useful for aerospace, automotive, marine and civil applications due to their very high specific structural properties. These structures are subjected to severe dynamic loading in their service life. Repeated exposure to these severe loading conditions can induce structural damage which ultimately may precipitate a catastrophic failure. Therefore, an interest in the continuous inspection and maintenance of engineering structures has grown tremendously in recent years. Sensitive aerospace applications can have small design margins and any inadequacy in knowledge of the system may cause design failure. Structures made from composite materials posses complicated failure mechanism as compared to those made from conventional metallic materials. In composite structural design, it is hence very important to properly model geometric intricacies and various imperfections such as delaminations and cracks. Two important issues are addressed in this thesis: (1) structural modeling of nonlinear delamination and uncertainty propagation in nonlinear characteristics of composite plate structures and (2) development of a model based damage detection system to handle uncertainty issues. An earlier proposed shear deformable C0 composite plate finite element is modified to alleviate modeling uncertainty issues associated with a damage detection problem. Parabolic variation of transverse shear stresses across the plate thickness is incorporated into the modified formulation using mixed shear interpolation technique. Validity of the proposed modification is established through available literature. Correction of the transverse shear stress term in the formulation results in about 2 percent higher solution accuracy than the earlier model. It is found that the transverse shear effect increases with higher modes of the plate deformation. Transverse shear effects are more prominent in sandwich plates. This refined composite plate finite element is used for large deformation dynamic analysis of delaminated composite plates. The inter-laminar contact at the delaminated region in composite plates is modeled with the augmented Lagrangian approach. Numerical simulations are carried out to investigate the effect of delamination on the nonlinear transient behavior of composite plates. Results obtained from these studies show that widely used unconditionally stable β-Newmark method presents numerical instability problems in the transient simulation of delaminated composite plate structures with large deformation. To overcome this instability issue, an energy and momentum conserving composite implicit time integration scheme presented by Bathe and Baig is used for the nonlinear dynamic analysis. It is also found that a proper selection of the penalty parameter is very crucial in the simulation of contact condition. It is shown that an improper selection of penalty parameter in the augmented Lagrangian formulation may lead to erroneous prediction of dynamic response of composite delaminated plates. Uncertainties associated with the mathematical characterization of a structure can lead to unreliable damage detection. Composite structures also show considerable scatter in their structural response due to large uncertainties associated with their material properties. Probabilistic analysis is carried out to estimate material uncertainty effects in the nonlinear frequencies of composite plates. Monte Carlo Simulation with Latin Hypercube Sampling technique is used to obtain the variance of linear and nonlinear natural frequencies of the plate due to randomness in its material properties. Numerical results are obtained for composite plates with different aspect ratio, stacking sequence and oscillation amplitude ratio. It is found that the nonlinear frequencies show increasing non-Gaussian probability density function with increasing amplitude of vibration and show dual peaks at high amplitude ratios. This chaotic nature of the dispersion of nonlinear eigenvalues is also revealed in eigenvalue sensitivity analysis. For fault isolation, variations in natural frequencies, modal curvatures and curvature damage factors due to damage are investigated. Effects of various physical uncertainties like, material and geometric uncertainties on the success of damage detection is studied. A robust structural damage detection system is developed based on the statistical information available from the probabilistic analysis carried out on beam type structures. A new fault isolation technique called sliding window defuzzifier is proposed to maximize the success rate of a Fuzzy Logic System (FLS) in damage detection. Using the changes in structural measurements between the damaged and undamaged state, a fuzzy system is generated and the rule-base and membership functions are generated using probabilistic informations. The FLS is demonstrated using frequency and mode shape based measurements for various beam type structures such as uniform cantilever beam, tapered beam in single as well as in multiple damage conditions. The robustness of the FLS is demonstrated with respect to the highly uncertain input information called measurement deltas (MDs). It is said, if uncertainty level is larger than or close to the changes in damage indicator due to damage, the true information would be submerged in the noise. Then the actual damaged members may not be identified accurately and/or the healthy members may be wrongly detected as damaged giving false warning. However, this being the case, the proposed FLS with new fault isolation technique tested with these noisy data having large variation and overlaps shows excellent robustness. It is observed that the FLS accurately predicts and isolates the damage levels up-to considerable uncertainty and noise levels in single as well as multiple damage conditions. The robustness of the FLS is also demonstrated for delamination detection in composite plates having very high material property uncertainty. Effects of epistemic uncertainty on damage detection in composite plates is addressed. The effectiveness of the proposed refined Reddy type shear deformable composite plate element is demonstrated for reducing the modeling or epistemic uncertainty in delamination detection.