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Recent research studies have confirmed that curved I-girders are capable of developing substantial shear postbuckling resistance due to tension field action and have demonstrated that the AASHTO LRFD equations for the tension field resistance in straight I-girders may be applied to curved I-girders within specific limits. However, the corresponding demands on intermediate transverse stiffeners in curved I-girders are still largely unknown. Furthermore, a number of prior research studies have demonstrated that transverse stiffeners in straight I-girders are loaded predominantly by bending induced by their restraint of web lateral deflections at the shear strength limit state, not by in-plane tension field forces. This is at odds with present Specification approaches for the design of transverse stiffeners, which are based on (1) providing sufficient stiffener bending rigidity only to develop the shear buckling strength of the web and (2) providing sufficient stiffener area to resist the in-plane tension field forces. In this research, the behavior of one- and two-sided intermediate transverse stiffeners in straight and horizontally curved steel I-girders is investigated by refined full nonlinear finite element analysis. Variations in stiffener rigidity, panel aspect ratio, panel slenderness, and stiffener type are considered. New recommendations for design of transverse stiffeners in straight and curved I-girder bridges are developed by combining the solutions from the above FEA studies with the results from prior research.

A computationally efficient analysis capability for the geometrically non-linear response of compressively loaded prismatic plate structures was developed. Both a "full" finite strip solution procedure and a "reduced" solution procedure were implemented in a FORTRAN 90 computer code, and comparisons were made with results available in the technical literature. Both the full and reduced solution procedures were demonstrated to provide accurate results for displacement and strain quantities through moderately large post-buckling loads. The full method is a non-linear finite strip analysis of the semi-analytical, multi-term type. Individual finite strips are modeled as balanced and symmetric laminated composite materials which are assumed to behave orthotropically in bending, and the structure is loaded in uniaxial or biaxial compression. The loaded ends of the structure are assumed to be simply supported, and geometric shape imperfections may be modeled. The reduced solution method makes use of a reduced basis technique in conjunction with the full finite strip analysis. Here, the potentially large set of non-linear algebraic equations produced by the finite strip method are replaced by a small set of system equations. In the present implementation, the basis vectors consist of successive derivatives of the non-linear solution vector with respect to a loading parameter. Depending on the nature of the problem, the reduced solution procedure is capable of computational savings of up to 60%+ compared to the full finite strip method. The reduced method is most effective in reducing the computational cost of the full method when the most significant portion of the cost of the full method is factorization of the assembled system matrices. The robustness and efficiency of the reduced solution procedure was found to be sensitive to the user specified error norm which is used during the reduced solution procedure to determine when to generate new sets of basis vectors. In parallel with this effort, a new method for performing global/local design optimization of large complex structures (such as aircraft wings or fuselages) was developed. A simple and flexible interface between the global and local design levels was constructed using response surface methodology. The interface is constructed so as to minimize the changes required in either the global design code or the local design codes(s). Proper coupling is maintained between the global and local design levels via a "weight constraint" and the transfer of global stiffness information to the local level. The method was verified using a simple isotropic global wing model and the local panel design code PASCO. / Ph. D.

Curved panels constructed of laminated graphite-epoxy composite material are of potential interest in airframe fuselage applications. An understanding of structural response at elevated temperatures is required for anticipated future high speed aircraft applications. This study concentrates on the response of unstiffened, curved composite panels subjected to combinations of thermal and mechanical loading conditions. Mechanical loading is due to compressive end-shortening and thermal loading is due to a uniform temperature increase. Thermal stresses, which are induced by mechanical restraints against thermal expansions or contractions, cause buckling and postbuckling panel responses. Panels with three different lamination sequences are considered, including a quasi-isotropic laminate, an axially soft laminate, and an axially stiff laminate. These panels were chosen because they exhibit a range of stiffnesses and a wide variation in laminate coefficients of thermal expansion. The panels have dimensions of 10 in. by 10 in. with a base radius of 60 in. The base boundary conditions are clamped along the curved ends, and simply supported along the straight edges. Three methods are employed to study the panel response, including a geometrically nonlinear Rayleigh-Ritz solution, a finite element solution using the commercially available code STAGS, and an experimental program. The effects of inplane boundary conditions and radius of curvature are studied analytically, along with consideration of order of application in combined loading. A substantial difference is noted in the nonlinear load vs. axial strain responses of panels loaded in end-shortening and panels loaded with uniform temperature change, depending on the specific lamination sequence, boundary conditions, and radius of curvature. Experiments are conducted and results are presented for both room temperature end-shortening tests and elevated temperature tests with accompanying end-shortening. The base finite element model is modified to include measured panel thicknesses, boundary conditions representative of the experimental apparatus, measured initial geometric imperfections, and measured temperature gradients. With these modifications, and including an inherent end displacement of the panel present during thermal loading, good correlation is obtained between the experimental and numerically predicted load vs. axial strain responses from initial loading through postbuckling. / Ph. D.

The European Commission 6th Framework Project COCOMAT (Improved MATerial Exploitation at Safe Design of COmposite Airframe Structures by Accurate Simulation of COllapse) was a four and a half year project (2004 to mid-2008) aimed at exploiting the large reserve of strength in composite structures through more accurate prediction of collapse. In the experimental work packages, significant statistical variation in buckling behaviour and ultimate loading were encountered. The variations observed in the experimental results were not predicted in the finite element analyses that were done in the early stages of the project. The work undertaken in this thesis to support the COCOMAT project was initiated when it was recognised that there was a gap in knowledge about the effect of initial defects and variations in the input variables of both the experimental and simulated panels. The work involved the development of stochastic algorithms to relate variations in boundary conditions, material properties and geometries to the variation in buckling modes and loads up to first failure. It was proposed in this thesis that any future design had to focus on the dominant parameters affecting the statistical scatter in the results to achieve lower sensitivity to variation. A methodology was developed for designing stiffened composite panels with improved robustness. Several panels tested in the COCOMAT project were redesigned using this approach to demonstrate its applicability. The original contributions from this thesis are therefore the development of a stochastic methodology to identify the impact of variation in input parameters on the response of stiffened composite panels and the development of Robust Indices to support the design of new panels. The stochastic analysis included the generation of metamodels that allow quantification of the impact that the inputs have on the response using two first order variables, Influence and Sensitivity. These variables are then used to derive the Robust Indices. A significant outcome of this thesis was the recognition in the final report for COCOMAT that the development of a validated robust index should be a focus of any future design of postbuckling stiffened panels.

The European Commission 6th Framework Project COCOMAT (Improved MATerial Exploitation at Safe Design of COmposite Airframe Structures by Accurate Simulation of COllapse) was a four and a half year project (2004 to mid-2008) aimed at exploiting the large reserve of strength in composite structures through more accurate prediction of collapse. In the experimental work packages, significant statistical variation in buckling behaviour and ultimate loading were encountered. The variations observed in the experimental results were not predicted in the finite element analyses that were done in the early stages of the project. The work undertaken in this thesis to support the COCOMAT project was initiated when it was recognised that there was a gap in knowledge about the effect of initial defects and variations in the input variables of both the experimental and simulated panels. The work involved the development of stochastic algorithms to relate variations in boundary conditions, material properties and geometries to the variation in buckling modes and loads up to first failure. It was proposed in this thesis that any future design had to focus on the dominant parameters affecting the statistical scatter in the results to achieve lower sensitivity to variation. A methodology was developed for designing stiffened composite panels with improved robustness. Several panels tested in the COCOMAT project were redesigned using this approach to demonstrate its applicability. The original contributions from this thesis are therefore the development of a stochastic methodology to identify the impact of variation in input parameters on the response of stiffened composite panels and the development of Robust Indices to support the design of new panels. The stochastic analysis included the generation of metamodels that allow quantification of the impact that the inputs have on the response using two first order variables, Influence and Sensitivity. These variables are then used to derive the Robust Indices. A significant outcome of this thesis was the recognition in the final report for COCOMAT that the development of a validated robust index should be a focus of any future design of postbuckling stiffened panels.

The use of composite materials in vehicle structures could reduce the weight and thereby the fuel consumption of vehicles. As the road safety of the vehicles must be ensured, it is vital that the energy absorbing capability of the composite materials are similar to or better than the commonly used steel structures. The high specific bending stiffness of sandwich structures can with advantage be used in vehicles, provided that the structural behaviour during a crash situation is well understood and possible to predict. The purpose of this thesis is to identify and if possible to describe the failure initiation and progression in in-plane compression loaded sandwich panels. An experimental study on in-plane compression loaded sandwich panels with two different material concepts was conducted. Digital speckle photography (DSP) was used to record the displacement field of one outer face-sheet surface during compression. The sandwich panels with glass fibre preimpregnated face-sheets and a polymer foam core failed due to disintegration of the face-sheets from the core, whereas the sandwich panels with sheet molding compound face-sheets and a balsa core failed in progressive end-crushing. A simple semi-empirical model was developed to describe the structural response before and after initial failure. The postfailure behaviour of in-plane compression loaded sandwich panels was studied by considering the structural behaviour of sandwich panels with edge debonds. A parametrical finite element model was used to determine the influence of different material and geometrical properties on the buckling and postbuckling failure loads. The postbuckling failure modes studied were debond crack propagation and face-sheet failure. It could be concluded that the postbuckling failure modes were mainly determined by the ratio between the fracture toughness of the face-core interface and the bending stiffness of the face-sheets. / QC 20101111

Discussed is a numerical and experimental characterization of the response of small-scale fiber-reinforced composite cylinders constructed to represent a fuselage design whereby the crown and keel consist of one laminate stacking sequence and the two sides consist of another laminate stacking sequence. This construction is referred to as a segmented cylinder. The response to uniform axial endshortening is discussed. Numerical solutions for the nonlinear prebuckling, buckling, and postbuckling responses are compared to experimental results. Focus is directed at the investigation of two specific cylinder configurations, referred to as axially-stiff and circumferentially-stiff cylinders. Small-scale cylinders, each having a nominal radius of 5 in., were fabricated on a mandrel by splicing adjacent segments together to form 0.5 in. overlaps. Finite-element models of both cylinder configurations, including the overlap regions, are developed using the STAGS finite-element code. Perfectly circular cylinder models are considered, as are models which include the measured geometry of the specimens as an imperfection. Prebuckling predictions show that the segmented cylinder response is characterized by the existence of circumferential displacement, and an axial boundary layer accompanied by circumferential gradients in radial displacement. Experimental measurements, taken with strain gages and displacement transducers, confirm these numerical findings. As the endshortening approaches the critical, or buckling, values, the response of the cylinders is characterized by wrinkling in the axial direction. In the axially-stiff cylinder, the crown and keel segments wrinkle, while in the circumferentially-stiff cylinder the side segments wrinkle. Experimental images taken from Moire interferometry show this response in the circumferentially-stiff cylinder. Four methods are used to predict the buckling values of endshortening and load for both cylinders, and the four values are in good agreement. The experimentally-measured buckling conditions, however, show that the models overpredict buckling values. For the axially-stiff cylinder, the difference could be due to the fact material failure not included in the model plays a role in the cylinder response. For the circumferentially-stiff cylinder, the difference is definitely due to material failure characteristics not included in the model. The predicted postbuckling response of the segmented cylinders is shown to be dominated by the existence of inward dimples in some or all of the segments. For the axially-stiff cylinder, the as-predicted dimpled crown and keel configuration is observed in the experiment but at a load 12 percent below predicted values. For the circumferentially-stiff cylinder material failure in the linear prebuckling range of response triggered buckling that resembled the predicted circumferential rings of dimples, but at a load 31 percent below predictions. Finally, it is shown that the effect of including the measured imperfections in the model has little observable effect on the circumferentially-stiff cylinder. For the axially-stiff cylinder the inclusion of the imperfections is found to effect the transition from buckling to postbuckling, but ultimately has little effect on postbuckling deformations. / Ph. D.

Sandwich structures constitute basic components of advanced supersonic/hypersonic flight and launch vehicles. These advanced flight vehicles operate in hostile environments consisting of high temperature, moisture, and pressure fields. As a result, these structures are exposed to large lateral pressures, large compressive edge loads, and high temperature gradients which can create large stresses and strains within the structure and can produce the instability of the structure. This creates the need for a better understanding of the behavior of these structures under these complex loading conditions. Moreover, a better understanding of the load carrying capacity of sandwich structures constitutes an essential step towards a more rational design and exploitation of these constructions. In order to address these issues, a comprehensive geometrically non-linear theory of doubly curved sandwich structures constructed of anisotropic laminated face sheets with an orthotropic core under various loadings for simply supported edge conditions is developed. The effects of the radii of curvature, initial geometric imperfections, pressure, uniaxial compressive edge loads, biaxial edge loading consisting of compressive/tensile edge loads, and thermal loads will be analyzed. The effect of the structural tailoring of the facesheets upon the load carrying capacity of the structure under these various loading conditions are analyzed. In addition, the movability/immovability of the unloaded edges and the end-shortening are examined. To pursue this study, two different formulations of the theory are developed. One of these formulations is referred to as the mixed formulation, While the second formulation is referred to as the displacement formulation. Several results are presented encompassing buckling, postbuckling, and stress/strain analysis in conjunction with the application of the structural tailoring technique. The great effects of this technique are explored. Moreover, comparisons with the available theoretical and experimental results are presented and good agreements are reported. / Ph. D.

To advance structural tailoring methods in composite structures, an experimental and numerical investigation of the prebuckling and postbuckling responses of flat rectangular graphite-epoxy composite panels with a centrally located I-shaped stiffener subjected to a uniform end shortening is presented. Axial-shear stiffness coupling is introduced by rotating the stiffener and/or prescribing skin laminates with membrane and bending stiffness coupling. A panel’s axial-shear coupling response is defined as the ratio of the panel’s shear load to its compression load when a simple end shortening is applied. Experimental results are reported for five panels. The baseline test panel has an unrotated stiffener and a [±45/∓45/0₃/90]_s skin laminate. Two panels have either the stiffener or the entire skin laminate rotated 20°, and the remaining two panels have both the stiffener and the skin laminate rotated by 20°, either in the same direction, or in opposite directions. Extensive experimental data are obtained electronically during quasi-static tests. Finite element models are defined which accurately represent the conditions in the experiment, and geometrically nonlinear analyses are conducted. Measured and predicted responses are compared to verify the numerical models. The panels’ stiffness, buckling parameters, load vs. end shortening relations, out-of-plane deformations, and axial-shear coupling responses are reported. The finite element analyses, based on two-dimensional plate elements, are utilized to address failure due to skin-stiffener separation by estimating the skin-stiffener attachment forces and moments at failure. The results of a parametric study which isolates the mechanisms which contribute to axial-shear stiffness coupling are reported. It is found that rotating the stiffener or introducing skin anisotropy typically reduces the axial stiffness and buckling loads. The axial shear coupling response due to rotating the stiffener is constant in prebuckling and increases after skin buckling, and the magnitude of the response can be adjusted by varying the stiffener rotation and rigidity. Skin membrane stiffness coupling creates axial-shear coupling responses that are constant in prebuckling and decrease in magnitude after skin buckling. Skin bending stiffness coupling creates axial-shear coupling responses that are zero in prebuckling and increase in magnitude after skin buckling. Examples are presented which demonstrate how different mechanisms can be tailored independently and then superimposed to effectively tailor a stiffened panel’s axial-shear coupling response in the pre buckling and postbuckling load ranges. / Ph. D.