The growing use of high performance composite materials has stimulated interest in the development of optimization procedures for the design of laminates. The design of composite structures against buckling presents two major challenges to the structural analyst and designer. First, the problem of laminate stacking sequence design is discrete in nature which complicates the solution process. Second, many local optima with comparable performance may be found. The present work addresses these challenges by investigating several techniques for designing stiffened composite panels. The specific focus is the minimum weight design of a compression-loaded blade-stiffened composite panel with a centrally located hole subject to stability, minimum gage and strain failure constraints. An efficient linked-plate analysis and design program PASCO is used to predict global response (buckling) of the stiffened panel. Since PASCO cannot model a hole, a finite element program, EAL, is used to model the local hole region and evaluate local strain response in the vicinity of the hole. A sequential approximate design procedure based on ply thicknesses as continuous variables is used to evaluate the relative efficiencies of softskin (designs· with no 0° plies) and stiff-skin designs (designs with 0° plies). The soft-skin design concept, which also has better damage tolerance, is found to be better for stiffened panels from weight and strength considerations. Addressing the discreteness of the problem with the continuous design procedure was found to be cumbersome leading to solutions that were not necessarily optimum. In order to address the limitations of the continuous optimization procedure, two integer programming procedures were investigated. A sequential linear integer programming procedure proved t o be less effective than a genetic algorithm (GA). The GA based discrete design approach provided results which were found to be about 5% lighter than results obtained previously with continuous optimization followed by rounding up of the ply thicknesses. Furthermore, many designs with similar performance were easily obtained, giving a choice of designs for the analyst. The integer programming formulations also permitted easy implementation of additional constraints such as ply contiguity (integer type constraints) that are difficult to enforce in continuous optimization based design procedures. Tests on optimal baseline designs were carried out in parallel with the analytical study to investigate the buckling and failure characteristics of stiffened quasi-static compression loaded panels with holes and to assess the validity of analytical models used for the design of such panels. Results from quasi-static tests indicate that the optimized designs without holes were susceptible to be imperfection sensitive. This is to be expected as the optimization process led to the coincidence of an overall and a local skin buckling modes. Quasi-static tests thus emphasized the need for the optimization process to include additional constraints on the separation of consecutive buckling modes in order to alleviate the tendency of the optimizer to produce designs which may be imperfection sensitive. / Ph. D.

Hamilton's principle and a third-order shear-deformation theory are used to derive a set of five coupled partial-differential equations governing the nonlinear response of composite plates. The reduction of these equations by using classical plate theory is discussed and the corresponding partial-differential equations governing both rectangular and circular plates are derived. Generalized Levy-type solutions are obtained for the problem of linear free vibrations and linear stability of shear-deformable cross-ply laminated plates. The governing equations are transformed into a set of first-order linear ordinary-differential equations with constant coefficients. The general solution of these equations is obtained by using the state-space concept. Then, the application of the boundary conditions yields equations for the natural frequencies and critical loads. However, a straightforward application of the state-space concept yields numerically ill-conditioned problems as the plate thickness is reduced. Various methods for overcoming this problem are discussed. An initial-value method with orthonormalization is selected. It is shown that this method not only yields results that are in excellent agreement with the results in the literature, but it also converges fast and gives all the frequencies and buckling loads regardless of the plate thickness. Further It is shown that the application of classical plate theory to thick plates yields inaccurate results. The influence of modal interactions on the response of harmonically excited plates is investigated in detail. The case of a two-to-one autoparametric resonance in shear-deformable composite laminated plates is considered. Four first-order ordinary-differential equations describing the modulation of the amplitudes and phases of the internally resonant modes are derived using the averaged Lagrangian when the higher mode is excited by a primary resonance. The fixed-point solutions are determined using a homotopy algorithm and their stability is analyzed. It is shown that besides the single-mode solution, two-mode solutions exist for a certain range of parameters. It is further shown that in the multi-mode case the lower mode, which is indirectly excited through the internal resonance may dominate the response. For a certain range of parameters, the fixed points lose stability via a Hopf bifurcation, thereby giving rise to limit cycle solutions. It is shown that these limit-cycles undergo a series of period-doubling bifurcations, culminating in chaos. Finally, the case of a combination resonance involving the first three modes of axisymmetric circular plates is studied. The method of multiple scales is used to determine a set of ordinary-differential equations governing the modulation of phases of the modes involved and that the excited mode is not necessarily the dominant one. Furthermore, it is shown that for a choice of parameters the multi-mode response loses stability through a Hopf bifurcation, resulting in periodically or chaotically modulated motions of the plate. / Ph. D.

This thesis provides a general theory of the diffraction of ultrasonic waves. The theory is then used to find the apparent attenuation which would result if certain damage states (transverse cracks and delaminations) are introduced into a graphite/epoxy laminate through which the ultrasonic wave passes. and [0, ±45, 90]s) is presented which shows changes in the apparent attenuation of, about 1 dB. These changes generally occur at loads which correspond to the range predicted for the formation of the above mentioned damage. Though no exact correlation between theoretical and experimental results is given, the predicted changes in the attenuation for several simple and common damage states are well within the range of experimental values. It is hoped that the technique described herein can be further developed and used to detect the formation and growth of damage in composite specimens in regions not readily visible by conventional techniques. / Master of Science

No description available.

The Layerwise Shell Theory is used to model discretely stiffened laminated composite cylindrical shells for stress, vibration, pre-buckling and post-buckling analysis. The layerwise theory reduces a three-dimensional problem to a two-dimensional problem by expanding the three-dimensional displacement field as a function of a surface-wise two-dimensional displacement field and a one-dimensional interpolation through the shell thickness. Any required degree of accuracy can be obtained by an appropriate, independent selection of the one-dimensional interpolation functions through the thickness and the two-dimensional interpolation of the variables on the surface. Using a layerwise format, discrete axial and circumferential stiffeners are modeled as two-dimensional beam elements. Similar displacement fields are prescribed for both the stiffener and shell elements. The contribution of the stiffeners to the membrane stretching, bending and twisting stiffnesses of the laminated shell is accounted for by forcing compatibility of strains and equilibrium of forces between the stiffeners and the shell skin. The layerwise theory is also used to model initial imperfections of the unstressed configuration. A finite element scheme of the layerwise model is developed and applied here to investigate the effect of imperfections on the response of laminated cylindrical shells. Using a finite element model of the layerwise theory for shells and shell stiffener elements, the accuracy and reliability of the elements is investigated through a wide variety of examples. The examples include laminated stiffened and unstiffened plates and shells and stand-alone beams under different types of external destabilizing loads. Finally, the study identifies the particular types of problems where the layerwise elements possess a clear advantage and superiority over the conventional equivalent single-layer models. / Ph. D.

The effect of laminate thickness on the fracture behavior of laminated graphite/epoxy (T300/5208) composites has been studied. The predominantly experimental research program included the study of the [0/±45/90]_ns and [0/90]_ns laminates with thicknesses of 8, 32, 64, 96 and 120 plies and the [0/±45]_ns laminate with thicknesses of 6, 30, 60, 90 and 120 plies. The research concentrated on the measurement of fracture toughness utilizing the center-cracked tension, compact tension and three point bend specimen configurations. Fracture toughness was computed using the stress intensity factor results of a finite element stress analysis of each specimen geometry which treated the composite as homogeneous but anisotropic. The development of subcritical damage at the crack tip was studied nondestructively using enhanced x-ray radiography and destructively using the laminate deply technique. The test results showed fracture toughness to be a function of laminate thickness. The fracture toughness of the [0/±45/90]_ns and [0/90]_ns laminates decreased with increasing thickness and asymptotically approached lower bound values of 30 ksi√in (1043 MP a√mm) and 25 ksi√in (869 √mm) respectively. The fracture toughness of the [0/±45/90]_ns laminate was independent of crack length at 8 and 120 plies. The fracture of the thin and thick [0/±45/90]_ns laminates were self-similar, macroscopically. However, the [0/90]_2s laminate (8 plies) exhibited fracture toughness values that increased sharply as a function of increasing crack size. This was attributed to large axial splits which formed perpendicular to the crack tip in the 0° plies and extended in the direction of applied load. The fracture toughness of the [0/90]_ns laminate was independent of crack length at 90 plies. The axial splits in the 0° plies of the thicker specimens were confined to the surface and the final fracture was self-similar. For both the [0/±45/90]_ns and [0/90]_ns laminates, the center-cracked tension, three-point bend and compact tension specimens gave comparable results. In contrast to the other two laminates, the fracture toughness of the [0/±45]_ns laminate increased sharply with increasing thickness but reached an upper plateau value of 40 ksi√in (1390 MP a√mm) at 30 plies. Fracture toughness was independent of crack size at 6 and 90 plies. The 6 ply specimens failed by an apparent uncoupling mechanism where the two interior -45° plies delaminated from the adjacent +45° plies and failed by matrix splitting parallel to the fibers. The surface 0° plies failed by broken fibers along a +45° line in association with matrix splitting parallel to the fibers in the +45° plies. The thick [0/±45]_ns laminates exhibited a surface boundary layer in which 45° fiber breaks and splits were evident along with delaminations. However, the interior of the specimens failed in a self-similar manner with fibers in the 0° plies breaking along a line collinear with the starter notch. The compact tension and three-point bend specimens defined a constant fracture toughness at about 15% below the plateau exhibited by the center-cracked tension specimens. The general toughness parameter model, a strain criterion developed by C. C. Poe, Jr. of NASA Langley, was the only candidate thin laminate failure criterion that was successful in using thin laminate parameters to predict the fracture of thick laminates. The "universal” general toughness parameter value of 1.5 √mm quite closely predicted the fracture of the thick laminates. / Ph. D.

Two straight and one curved Southern Pine glued-laminated beams are subjected to bending, bending and compression, and biaxial bending. The beams are tested at service loads and only one beam is loaded to failure. The analysis is performed by using the finite element program ABAQUS. The 3-D beam finite element model used is formulated on engineering theory and includes shear deformations. The engineering elastic constants needed to specify the constitutive matrix of the beam element are obtained experimentally. Strain measurements in wood with small bonded strain gages are not accurate. A simple clip-type transducer is fabricated and used to measure the strains in the test glulam beams. The distribution of normal stresses is investigated for symmetrically applied concentrated loads. Experimental and analytical values agree very well. / M.S.

The strength reduction of a graphite-epoxy laminate due to dropping plies is investigated experimentally and analytically. Laminates were tested under uniaxial tension and compression. All the laminates were flat on one side with the plies dropped from the middle of a [( ± 45/0/90)_s (N_d) ( ± 45/0/90)_s]_T laminate, where N_d denotes the number of dropped-plies and their orientations. A total of 54 specimens were tested consisting of eight dropped-ply configurations, or values of N_d. This geometry creates an eccentric load path which causes local bending moments in the region of the ply drop-off. The strength of a laminate with dropped-plies is less than the strength of its thin section, and the compression specimens exhibited a lower strength than a tension specimen of the same configuration and width. For the laminates in this study, the reduction in strength is directly related to the axial stiffness change between the thick and thin sections of the laminate. The three-dimensional state of stress in the laminate was evaluated by the finite element method. The magnitude of the interlaminar stresses at the ply drop-off for N_d = [0₄]_T are greater than for N_d = [90₄]_T . The initial failure event for N_d = [0₄]_T was a delamination between the dropped plies and upper sublaminate at the drop-off. The tensile interlaminar failure criterion predicts this as the critical location in the finite element model as well. However, the tensile interlaminar criterion underestimates the failure initiation load. The cause for this may be due to the inaccuracies in the modeling of the ply drop-off geometry in the finite element analysis. The magnitude of the stresses at the ply drop-off are sensitive to changes in the finite element mesh geometry. The N_d = [90₄]_T laminates were stronger than the N_d = [0₄]_T laminates and the N_d = [90₄]_T laminates failed in the thin section away from the drop-off. / M.S.

Three dimensional contact problems of square orthotropic laminates indented by a rigid spherical indenter are solved. Simplified problems of indentations of beam and isotropic square plate are studied first to develop an efficient numerical technique and to gather the knowledge of the shape of the contact area in order to solve for the three dimensional orthotropic cases. The approach combines an exact solution method in conjunction with a simple discretization numerical scheme. Numerical sensitivity due to the ill-posed nature of the problem was experienced but was cured by enhancing the numerical approach with a least square spirit. Well agreement is obtained by comparing the results of these simplified studies with available published solutions. For isotropic plate, contact area is found to be either a circle or a hypotrochoid of four lobes featured with a shorter length of contact along the through-the- corner directions of the plate. Hertz's theory fails earlier than assuming the contact area to be a circle. In-plane dependence of the contact stress is presented to illustrate the difference of contact behavior between a square plate and a circular plate. Load-indentation relation reveals indenting a square plate is harder than indenting a circular plate of a diameter equal to the side length of the square plate. Solutions of multi-layered orthotropic cases are achieved by employing a modified analytical approach with the same numerical method. Three different configurations of plate are implemented for the orthotropic case, namely, a single layered magnesium (Mg) plate, which is slightly orthotropic, and a single and double layered plates of graphite-epoxy (G-E), which are highly orthotropic. Results for the (Mg) plate agrees with the previous isotropic case. Concept of modifying the previous hypotrochoids is introduced to seek for the contact stresses for comparatively large indentation conditions. Single-layered (G-E) plate was implemented for small indentations. The result supports the validity of Hertz's theory for small indentation and shows a relatively longer contact length in the direction of less stiffness. Two layered (G-E) plate illustrates similar distributions for the contact stresses along both of the in-plane directions with a smaller range of validity of Hertzian type behavior than the previous cases. The boundary effect prevails at the initial stage of indentation but is overcome by the effect of material orthotropy as the indentation proceeds. Thus, the contact area for small indentation appears to be the same kind of hypotrochoids as located in the isotropic case but changes to be the other type of hypotrochoids as the indentation advances. / Ph. D.

Free-edge effects in composite laminates were studied experimentally. Strains were determined and compared on a ply-by-ply basis for the curved edges of a hole in thick composite panels and along the straight free-edge of the panels. The experimental technique of moire interferometry was extended to take measurements of in-plane deformations on singly-curved surfaces. A replication scheme was developed to produce high-frequency diffraction gratings on singly-curved surfaces. Two different techniques were developed to interrogate specimen gratings on 25.4 mm (1 in.) diameter holes. Eight thick composite laminates from three material systems were tested in uniaxial compression on a screw-driven testing machine. Interlaminar deformations were measured at the straight free-edge on four of the specimens. Strain distributions on the straight free-edge were compared with FEM results for two specimens. Good agreement was obtained for one specimen while poor agreement was obtained for the other. / Ph. D.