A probabilistic finite element analysis procedure for laminated composite shells has been developed. A total Lagrangian finite element formulation, employing a degenerated 3-D laminated composite shell element with the full Green-Lagrange strains and first-order shear deformable kinematics, forms the modeling foundation. The first-order second-moment technique for probabilistic finite element analysis of random fields is employed and results are presented in the form of mean and variance of the structural response. The effects of material nonlinearity are included through the use of a rate-independent anisotropic plasticity formulation with the macroscopic point of view. Both ply-level and micromechanics-level random variables can be selected, the latter by means of the Aboudi micromechanics model. A number of sample problems are solved to verify the accuracy of the procedures developed and to quantify the variability of certain material type/structure combinations. Experimental data is compared in many cases, and the Monte Carlo simulation method is used to check the probabilistic results. In general, the procedure is quite effective in modeling the mean and variance response of the linear and nonlinear behavior of laminated composite shells. / Ph. D.

Techniques for shear property measurements for composite and isotropic materials were investigated. A new strain gage called the shear gage was conceived, designed, and tested for routine shear characterization on notched shear specimens. The shear gage integrates the shear strain in the entire test section of the losipescu and compact shear specimens. The result was consistent and accurate determination of the shear stress/strain response of materials. Prior knowledge of material properties or shear strain distributions were not required. Deficiencies in the losipescu shear test were automatically compensated when shear gages were placed on the two faces of the specimen. The shear gages were tested on composite and isotropic materials and produced higher accuracy and consistency than could be produced using current technology. Moir© interferometry was used to evaluate the ability of the shear gage to measure the average shear strains. The results from the evaluation program confirmed the attributes of the concept. / Ph. D.

A one-dimensional cylindrical cure model was developed to describe the curing process of an axisymmetric filament wound composite structure. For a specified cure cycle, the cure model can be used to calculate the temperature distribution, the degree of cure of the resin, and the resin viscosity inside the composite case. Solutions to the cylindrical cure model were obtained numerically using the finite element technique. The cylindrical cure model was verified by measuring the temperature distribution in a small 5.75 inch graphite - epoxy test bottle. The data were compared with the results calculated with the computer code for conditions employed in the tests. Good agreement was found between the data and the results of the computer code. The error between the experimental data and the results of the computer code was less than 10 %. A cure cycle optimization problem is formulated for the curing process using a calculus of variations approach. The optimum cure cycle should tailor the temperature in the composite such that a uniform temperature and degree of cure distribution is achieved in the composite while minimizing the reaction exotherms and thermal lag. Cure simulations of an one inch thick graphite - epoxy composite case predict a minimization of the reaction exotherms and the thermal lag. The the final process time needed to achieve uniform degree of cure and uniform temperature distribution in the composite is also predicted. The resultant cure cycle appears to approach the boundary temperatures specified as limits on the cure cycle temperature. / Master of Science

A two-dimensional to three-dimensional global/local finite element approach was developed, verified, and applied to a laminated composite plate of finite width and length containing a central circular hole. The resulting stress fields for axial compression loads were examined in detail for several symmetric stacking sequences and hole sizes. Verification was based on comparison of the displacements and the stress fields with those accepted trends from previous free edge investigations and a complete three-dimensional finite element solution of the plate. Hole diameters of one, three, and six inches in plates 18 inches long, 12 inches wide, and 0.1 inches thick were considered. The laminates in the compression study included symmetric cross-ply, angle-ply and quasi-isotropic stacking sequences. The entire plate was selected as the global model and analyzed with two-dimensional finite elements. Displacements along a region identified as the global/local interface were applied in a kinematically consistent fashion to independent three-dimensional local models. Local areas of interest in the plate included a portion of the straight free edge near the hole, and the immediate area around the hole. It was found that the global/local interface should not be placed inside or through any region where the stress field exhibits three-dimensional effects. Interlaminar stress results obtained from the global/local analyses compared well with previously reported trends, and some new conclusions about interlaminar stress fields in plates with different laminate orientations and hole sizes are presented for compressive loading. The effectiveness of the global/local procedure in reducing the computational effort required to solve these problems is clearly demonstrated through examination of the computer time required to formulate and solve the linear, static system of equations which result for the global and local analyses to those required for a complete three-dimensional formulation for a cross-ply laminate. The Testbed, which is under continuing development by the Computational Structural Mechanics Group, now the Computational Mechanics Branch, was used throughout this investigation. Specific processors used during the analyses are described in general terms herein. The application of this global/local technique is not limited to this software system, and was developed and described in as general a manner as possible. The methodology developed is thus applicable to other large-scale structural analysis systems. / Master of Science

The purpose of this study is to develop a simple one-dimensional model to analyze axially loaded beam-plates containing cracks which extend through the thickness of the beam-plates. Although the material analyzed is isotropic, these cracks will be referred to as delaminations. Buckling, postbuckling, and growth of delaminations in these beam-plates will be analyzed. A finite element method in which all of the terms of the stiffness matrices are obtained by exact integration is employed to determine the linear buckling load and postbuckling solution. The energy release rate is then determined using the postbuckling solution. Curves are provided to show the effect of delamination length and location on buckling loads, energy release rates, and strengths of the beam-plates. The problem of buckling and postbuckling of beams with multiple delaminations is also considered. A method of calculating the energy release rate for beams with multiple delaminations using numerical differentiation is introduced. / Master of Science

A presentation is given of an acousto-ultrasonic system for the evaluation of composite materials. First, a brief statement will be made on the acousto-ultrasonic technique and its relative worth compared to other nondestructive testing techniques as applied to composite materials. The following two chapters describe the system instrumentation and system software, respectively. Next, comments are given regarding the implementation of the system for research on graphite/epoxy laminates, with additional remarks concerning efforts to evaluate aluminum/graphite tubes with the system. This includes physical descriptions of the composite systems. Subsequently, results are presented comparing parameters and forms of presentation which can be employed to relate results. Finally, conclusions are made on the application of the acousto-ultrasonic system to nondestructive testing of composite materials, with specific results on its application to graphite/epoxy plates. More specifically, comments are made on the variation of SWF factors with azimuthal angle on the graphite/epoxy plates, the identification of specific frequency peaks, and the relationships these may have to certain modes of vibration and material properties. For example, a low frequency mode was found to vary in a manner reminiscent of E_x and to show characteristics of an extensional Lamb wave. In general, results are presented and discussed in order to show how the system can be implemented to gain physical information on composite materials, such as the property of anisotropy. / Master of Science

A comparison of rectangular finite elements based on a first order shear deformation plate theory and a refined higher order plate theory is presented. Special attention is given to the representation of transverse shear strain, the phenomenon of "shear locking", and the selection of the interpolating polynomial. Both C⁰ and C¹ continuity elements are represented; the elements range from: 3 or 5 DOF per node, and 12 - 27 DOF per element. Static and free vibration analysis of isotropic and laminated plates with thicknesses ranging from extremely thin to very thick are presented, along with a convergence study. The finite element results are compared with the exact plate theory solutions. Of the elements investigated, the modified refined higher order theory element exhibits the best overall behavior. / Master of Science

The objective of this study was to develop tests that could be used to characterize autohesive strength development in amorphous thermoplastic resins and fiber-reinforced thermoplastic prepregs. All tests were performed using polysulfone P1700 thermoplastic resin and AS4/P1700 graphite-polysulfone prepreg. Two test methods were examined to measure autohesion in neat resin samples. These included an interfacial tension test based on the ASTM tensile adhesion test (ASTM D897) and a fracture toughness test using a compact tension (CT) specimen (based on the ASTM toughness test for metals ASTM E399-83). The interfacial tensile test proved to be very difficult to perform and with an unacceptable amount of data scatter. The data obtained using the compact tension test were repeatable and could be correlated with temperature and contact time. Autohesive strength development in fiber-reinforced prepreg samples was measured using a double cantilever beam (DCB) interlaminar fracture toughness test. The fracture mechanisms were determined to be different in the healed DCB specimen than the virgin specimen due to resin flow at the crack plane during the healing tests. The CT test was found suitable for use in determining the autohesive properties and self-diffusion coefficient of neat resin. The DCB test, although not suitable for autohesive testing, indicated that repair of thermoplastic matrix composites is possible; however, the repair will not be as tough as the virgin material. / Master of Science

This study addresses the issue of adjusting the proportion of load transmitted by each hole in a multiplehole joint so that the joint capacity is a maximum. Specifically two-hole-in-series joints are examined. The results indicate that when each hole reacts 50% of the total load, the joint capacity is not a maximum. One hole generally is understressed at joint failure. The algorithm developed to determine the load proportion at each hole which results in maximum capacity is discussed. The algorithm includes two-dimensional finite-element stress analysis and a failure criteria. The algorithm is used to study the effects of joint width, hole spacing, and hole to joint-end distance on load proportioning and capacity. To study hole size effects, two hole diameters are considered. Three laminates are considered: a quasi-isotropic laminate; a cross-ply laminate; and a 45 degree angle-ply laminate. By proportioning the load, capacity can be increased generally from 5 to 10%. In some cases a greater increase is possible. / M.S.

Since advanced composite materials generally experience coincidence at lower frequencies than metals when used in aircraft fuselage sidewalls, they may allow more transmission of airborne noise thereby requiring heavier acoustical treatments. A sequential design approach of addressing first structural and then acoustical design does not take advantage of structural/acoustical coupling. A simultaneous approach is expected to help minimize the total sidewall mass. This thesis uses numerical optimization to examine structural/acoustical interactions and compare the sequential and simultaneous design approaches. Acoustical performance is defined in terms of the infinite panel transmission loss at frequencies surrounding the coincidence region (1600 Hz - 12800 Hz for the panels studied.) Impedance transfer theory is used to predict the acoustical properties of a flat unstiffened anisotropic panel treated with a fibrous acoustic blanket, airgap, and limp-mass septum. Structural analysis is based on a fatigue damage resistance criterion. Sequentially designed treated composite panels exibit transmission losses 15 dB - 45 dB higher (transmitted pressure is 6 - 180 times smaller) than a structurally equivalent, equal-mass aluminum panel. Depending on the type of acoustic excitation (specific incidence direction or diffuse source) and the acoustic frequency considered, the simultaneous approach alters the sequential minimum-mass panel in order to 1) improve low frequency performance by raising coincidence frequencies, 2) improve high frequency performance by lowering coincidence frequencies, or 3) make the coincidence region as narrow as possible. Since these structural alterations require that more mass be allotted to the panel and less to the treatment, they only occur for strong structural/acoustical interactions (i.e. near coincidence.) The simultaneous design approach can achieve a moderate improvement (TL increased up to 10 dB, transmitted pressure decreased by a factor or 3) over a sequential design for a particular acoustic performance index, although computation time is increased and acoustic performance may be sacrificed in other regions. / M.S.