An Analytical Strip Method (ASM) for the analysis of stiffened and non-stiffened antisymmetric laminated composite plates is derived by considering the bending-extension coupling effect for bending, free vibration and buckling. A system of three equations of equilibrium, governing the general response of arbitrarily laminated composite plates, is reduced to a single eighth order partial differential equation in terms of a displacement function. The displacement function is solved in a single series form to determine the displacement, fundamental frequency, and buckling load of antisymmetric cross-ply and angle-ply laminated composite plates. The solution is applicable to rectangular plates with two opposite edges simply supported, while the other edges are simply supported, clamped, free, beam supported, or any combinations of these boundary conditions. This method overcomes the limitations of other analytical methods (Navier’s and Lévy’s), and provides an alternative to numerical, semi-numerical, and approximate methods of analysis. Numerical examples of bending, free vibration, and buckling of antisymmetric laminated composite plates are presented in tabular and graphical form. Whenever possible, the results of the present study are compared with those published in the literature and/or ANSYS solutions. The comparison firmly establishes that this method could be used for the analysis of antisymmetric laminated composite plates. Future research needs are identified for the aspects that have not been reached by the present study and others.

For the next generation of aircraft, the use of fibre-reinforced polymer composites and the design of

<p>Buckling and postbuckling of plates and stiffened panels are considered. Computational models for direct calculation of the response are developed using large deflection plate theory and energy principles. Deflections are represented by trigonometric functions. All combinations of biaxial in-plane compression or tension, shear, and lateral pressure are included in the formulations. The procedure is semi-analytical in the sense that the incremental equilibrium equations are derived analytically, while a numerical method is used for solving the equation systems, and for incrementation of the solution.</p><p>Unstiffened plate models are developed both for the simply supported case and for the clamped case. For the simply supported case the material types considered are isotropic elastic, orthotropic elastic, and elastic-plastic. Two models are developed for analysis of local buckling of stiffened plates, one for open profiles and one for closed profiles. A global buckling model for stiffened panels is developed by considering the panel as a plate with general anisotropic stiffness. The stiffness coefficients are input from the local analysis. Two models are developed for combined local and global buckling, in order to account for interaction between local and global deflection. The first is for a single stiffened plate, and uses a column approach. The second is for a stiffened panel with several stiffeners.</p><p>Numerical results are calculated for a variety of plate and stiffener geometries for verification of the proposed model, and comparison is made with nonlinear finite element methods. Some examples are presented. For all models, the response in the elastic region is well predicted compared with the finite element method results. Also, the efficiency of the calculations is very high. Estimates of ultimate strength are found using first yield as a collapse criterion. In most cases, this leads to conservative results compared to predictions from finite element calculations. </p>

Because of their high strength to weight ratio, stiffened steel plates are often used in light structures where plates are placed into compression. The stability of steel plates stiffened with longitudinal tee-shaped stiffeners and subjected to uniaxial compression or combined axial compression and out-of-plane bending formed the basis for this research project. The research was conducted to develop a simple approach to assess the post-buckling behaviour of stiffened steel plates and provide a limit states design procedure that accounts for the post-buckling stability in the assessment of the resistance factor. The behaviour of stiffened plates was investigated using a finite element model that had been validated through comparison with test results. An exhaustive parametric study, including 1440 finite element analyses, was conducted to investigate the strength and behaviour of stiffened steel plates. A virtual work model was developed to explain the effect of the formation of a plastic hinge mechanism on the post-buckling strength and behaviour. Combined with the numerical results, the theoretical model confirms that the plastic hinge mechanism can cause a sudden loss of capacity. The required lateral deflection for a plastic hinge development can be calculated using the virtual work model for prediction of the unstable behaviour. Based on a better understanding of the behaviour of stiffened steel plates, a set of design equations were developed to calculate the strength of stiffened steel plate subjected to compression in the direction of the stiffener and out-of-plane bending. The proposed design equations were compared with current design guidelines through a comparison of the design approaches with the finite element analysis results. The proposed method showed much better accuracy than the current design approaches. A reliability analysis was conducted to provide appropriate resistance factors for limit states design. Due to the complexity of the design formulas, the Monte Carlo simulation technique was used to generate the statistical distributions of the predicted strength. The second-moment method was used to calculate the resistance factors for different values of safety index. The resistance factor varied from 0.90 to 0.65 for values of safety index from 2.5 to 4.5, respectively. / Structural Engineering

Buckling and postbuckling of plates and stiffened panels are considered. Computational models for direct calculation of the response are developed using large deflection plate theory and energy principles. Deflections are represented by trigonometric functions. All combinations of biaxial in-plane compression or tension, shear, and lateral pressure are included in the formulations. The procedure is semi-analytical in the sense that the incremental equilibrium equations are derived analytically, while a numerical method is used for solving the equation systems, and for incrementation of the solution. Unstiffened plate models are developed both for the simply supported case and for the clamped case. For the simply supported case the material types considered are isotropic elastic, orthotropic elastic, and elastic-plastic. Two models are developed for analysis of local buckling of stiffened plates, one for open profiles and one for closed profiles. A global buckling model for stiffened panels is developed by considering the panel as a plate with general anisotropic stiffness. The stiffness coefficients are input from the local analysis. Two models are developed for combined local and global buckling, in order to account for interaction between local and global deflection. The first is for a single stiffened plate, and uses a column approach. The second is for a stiffened panel with several stiffeners. Numerical results are calculated for a variety of plate and stiffener geometries for verification of the proposed model, and comparison is made with nonlinear finite element methods. Some examples are presented. For all models, the response in the elastic region is well predicted compared with the finite element method results. Also, the efficiency of the calculations is very high. Estimates of ultimate strength are found using first yield as a collapse criterion. In most cases, this leads to conservative results compared to predictions from finite element calculations.

In this study a methodology is developed for the fatigue and fracture analysis of helicopter fuselage structures, which are considered as the stiffened panels. The damage tolerance behavior of the stiffened panels multiaxially loaded is investigated by implementing virtual crack closure technique (VCCT). Validation of VCCT is done through comparison between numerical analysis and the studies from literature, which consists of stiffened panels uniaxially loaded and the panel with an inclined crack. A program based on Fortran programming language is developed to automate the crack growth analysis under mixed mode conditions. The program integrates the prediction of the change in crack propagation direction by maximum circumferential stress criterion and the computation of energy release rate by VCCT. It allows reducing the computation time for damage tolerance evaluation for mixed mode cases through finite element analysis and runs the procedure file of MSC.Marc/Mentat for numerical analysis and the program generated by Patran Command Language (PCL) of MSC.Patran for remeshing. The developed code is verified by comparing the crack growth trajectories obtained by numerical analysis with the experimental studies from literature. A submodeling technique is utilized to analyze a particular fuselage portion of helicopter tail boom. Effects of different skin/stringer configurations of the helicopter fuselage structure on stress intensity factor are studied by means of the developed program. Fatigue crack growth analysis is performed by using stress intensity factors obtained from numerical analysis and fatigue propagation models proposed in literature.

The aim of the project presented in this thesis is to demonstrate a modelling method for predicting the variability in the ultimate load of stiffened panel under axial compression due to manufacturing variability. Bulking is sensitive to imperfections. In the case of a post-buckled panel, manu-facturing variability produces a scatter in the ultimate load. Thus, reasonable leeway for imperfections and inherent variability must be allowed in their design. Firstly, a finite element model of a particular stiffened panel was developed, and all nonlinearities within the material, boundary condition and geometry were considered. Verification and validation were performed to examine the accuracy of the buckling behaviour prediction, especially ultimate load. Experiments on 5 identical panels in design were performed to determine the level of panel-panel variation in geometry and collapse load. A data reduction programme based on the practical geometry scanning was developed, in addi-tion to which, the procedure of importing measured imperfection into Finite Ele-ment model was introduced. To identify and apply representative imperfections to the panel model, a double Fourier series representation of the random geometric distributions is attempt-ed, and was used thereby to derive a series of shapes representing random ge-ometry scatters. With these newly generated geometric imperfections, the variation in collapse load was determined, using the validated FE analysis. And also, the probability of these predicted loads was generalized.

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Design of thermoelastic structures can be highly counterintuitive due to design-dependent loading and impact of geometric nonlinearity on the structural response. Thermal loading generates in-plane stresses in a restrained panel, but the presence of geometric nonlinearity creates an extension-bending coupling that results in considerable transverse displacement and variation in stiffness characteristics, and these affects are enhanced in post-bucking regimes. Herein a methodology for structural sizing of thermally stressed post-buckled stiffened panels is proposed and applied for optimization of the blade and hat stiffeners using a gradient-based optimizer. The stiffened panels are subjected to uniform thermal loading and optimized for minimum mass while satisfying stress and stability constraints. The stress constraints are used to avoid yielding of the structure, whereas the stability constraints are used to ensure static stability. Corrugation of the hat stiffeners is also studied through variation of its magnitude and position. A continuation solver has been validated to tackle the highly nonlinear nature of the thermoelastic problem, and formulations for the stability constraints have been derived and imposed to satisfy the static stability of the structure. The study confirms that geometric nonlinearity is an important aspect of sizing optimization and is needed for an accurate modeling of the structural behavior. The results also show that modeling of geometric nonlinearity adds extra complexity to the thermoelastic problem and requires a path-tracking solver. Finally, this work supports that corrugation enhances the stability features of the panel but requires a blending function to reduce stresses at the panel boundaries.