A study aimed at determining the thermal deformation response and thermal buckling loads of rectangular grid-stiffened composite panels is presented. Two edge conditions are considered for the panel, one in which all panel edges are free to deform, and another when all the edges are restrained. In the first case panel deformations due to a uniformly distributed thermal load are analyzed. In the latter case, thermal loads causing buckling failure due to the suppressed in-plane deformations are determined. The panel is composed of a skin and a network of stiffeners, which are all made of the same graphite-epoxy composite material. Kirchhoff's Theory is used to determine the pre-buckling deformations and load distributions of the composite laminates for a panel with free to deform edges. To illustrate both the in-plane and out-of-plane deformations of plate structures under uniform thermal loads, two thermal coefficient vectors, thermal expansion and thermal bending coefficient vectors are introduced. Linear panel buckling analysis performed by assuming a linear undeformed prebuckling state. Rayleigh-Ritz Method, which utilizes minimization of the total energy of a structure to determine the buckling loads, is used to govern the buckling analysis of composite laminates forming the panel. Lagrange Multiplier Method is used along with the Rayleigh-Ritz Method to enforce the deformation continuity constraints at discrete locations along the skin and stiffener interface. As a result, graphical and numerical presentations of the effects of skin and stiffener laminate stacking sequences on the thermal deformations and on the thermal buckling load of the grid-stiffened panel are given. / Master of Science

Composite materials have been more and more used in aircraft primary structures such as wing and fuselage. The aim of this thesis is to identify an effective way to optimize composite wing structure, especially the stiffened skin panels for minimum weight subject to stiffness and strength constraints. Many design variables (geometrical dimensions, ply angle proportion and stacking sequence) are involved in the optimum design of a composite stiffened panel. Moreover, in order to meet practical design, manufacturability and maintainability requirements should be taken into account as well, which makes the optimum design problem more complicated. In this thesis, the research work consists of three steps: Firstly, attention is paid to metallic stiffened panels. Based on the study of Emero’s optimum design method and buckling analysis, a VB program IPO, which employs closed form equations to obtain buckling load, is developed to facilitate the optimization process. The IPO extends the application of Emero’s method to an optimum solution based on user defined panel dimensional range to satisfy practical design constraints. Secondly, the optimum design of a composite stiffened panel is studied. Based on the research of laminate layup effects on buckling load and case study of bucking analysis methods, a practical laminate database (PLDB) concept is presented, upon which the optimum design procedure is established. By employing the PLDB, laminate equivalent modulus and closed form equations, a VB program CPO is developed to achieve the optimum design of a composite stiffened panel. A multi-level and step-length-adjustable optimization strategy is applied in CPO, which makes the optimization process efficient and effective. Lastly, a composite outer wing box, which is related to the author’s GDP work, is optimized by CPO. Both theoretical and practical optimum solutions are obtained and the results are validated by FE analysis.

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.

A stiffened DKT shell element is formulated for the linear static analysis of stiffened plates and shells. Three-noded triangular shell elements and two-noded beam elements with 18 and 12 degrees of freedom are used respectively in the formulation. The stiffeners follow the nodal lines of the shell element. Eccentricity of the stiffener is taken into account. The dynamic and stability characteristic of the element is also investigated. With the developed computer program, the results obtained by the proposed element agrees fairly well with the existing literature.

Stiffeners attached to composite panels and shells may significantly increase the overall buckling load of the resultant stiffened structure. Initially, an extensive literature review was conducted over the past ten years of published work wherein research was conducted on grid stiffened composite structures and stiffened panels, due to their applications in weight sensitive structures. Failure modes identified in the literature had been addressed and divided into a few categories including: buckling of the skin between stiffeners, stiffener crippling and overall buckling. Different methods have been used to predict those failures. These different methods can be divided into two main categories, the smeared stiffener method and the discrete stiffener method. Both of these methods were used and compared in this thesis. First, a buckling analysis was conducted for the case of a grid stiffened composite pressure vessel. Second, a buckling analysis was conducted under the compressive load on the composite stiffened panels for the case of one, two and three longitudinal stiffeners and then, using different parameters, stiffened panels under combined compressive and shear load for the case of one longitudinal centric stiffener and one longitudinal eccentric stiffener, two stiffeners and three stiffeners. / Master of Science

Ultra-lightweight thermoformed stiffened structures are emerging as a viable option for spacecraft applications due to their advantage over inflatable structures. Although pressurization may be used for deployment, constant pressure is not required to maintain stiffness. However, thermoformed stiffening features are often locally nonlinear in their behavior under loading. This thesis has three aspects: 1) to understand stiffness properties of a thermoformed stiffened ultra-lightweight panel, 2) to develop finite element models using a phased-verification approach and 3) to verify panel response to dynamic loading. This thesis demonstrates that conventional static and dynamic testing principles can be applied to test ultra-lightweight thermoformed stiffened structures. Another contribution of this thesis is by evaluating the stiffness properties of different stiffener configurations. Finally, the procedure used in this thesis could be adapted in the study of similar ultra-lightweight thermoformed stiffened spacecraft structures.

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.

An efficient beam-column approach, using an improved step-by-step numerical method, is developed in the current research for studying the ultimate strength problems of stiffened panels with two load cases: 1) under longitudinal compression, and 2) under transverse compression. Chapter 2 presents an improved step-by-step numerical integration procedure based on (Chen and Liu, 1987) to calculate the ultimate strength of a beam-column under axial compression, end moments, lateral loads, and combined loads. A special procedure for three-span beam-columns is also developed with a special attention to usability for stiffened panels. A software package, ULTBEAM, is developed as an implementation of this method. The comparison of ULTBEAM with the commercial finite element package ABAQUS shows very good agreement. The improved beam-column method is first applied for the ultimate strength analysis of stiffened panel under longitudinal compression. The fine mesh elasto-plastic finite element ultimate strength analyses are carried out with 107 three-bay stiffened panels, covering a wide range of panel length, plate thickness, and stiffener sizes and proportions. The FE results show that the three-bay simply supported model is sufficiently general to apply to any panel with three or more bays. The FE results are then used to obtain a simple formula that corrects the beam-column result and gives good agreement for panel ultimate strength for all of the 107 panels. The formula is extremely simple, involving only one parameter: the product λΠorth2. Chapter 4 compares the predictions of the new beam-column formula and the orthotropic-based methods with the FE solutions for all 107 panels. It shows that the orthotropic plate theory cannot model the "crossover" panels adequately, whereas the beam-column method can predict the ultimate strength well for all of the 107 panels, including the "crossover" panels. The beam-column method is then applied for the ultimate strength analysis of stiffened panel under transverse compression, with or without pressure. The method is based on a further extension of the nonlinear beam-column theory presented in Chapter 2, and application of it to a continuous plate strip model to calculate the ultimate strength of subpanels. This method is evaluated by comparing the results with those obtained using ABAQUS, for several typical ship panels under various pressures. / 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.