In this thesis, we study the static and free vibration response of symmetric and antisymmetric cross-ply laminated plates using different plate theories. Governing equations for two displacement-based third-order equivalent-single-layer theories have been developed. The first one is called the General Third-Order Theory (GTOT), and the second one is called the General Third-Order Theory of Reddy (GTTR). The displacement field of the second theory can be obtained from the first by imposing the condition of zero shear stresses at the bounding planes of the plate. The governing equations, analytical solutions, and finite element model of GTTR have been obtained in terms of tracers. Proceeding in this manner, the governing equations, analytical solutions, and finite element models of some lower-order plate theories fall out by just assigning appropriate values to the tracers (typically 1 or 0). While analytical and finite element solutions have been obtained for GTTR and its derivative cases, only finite element solutions have been obtained for GTOT. The analytical solutions are of two types. The Navier-type solution is for rectangular plates simply supported on all four edges. In the Levy-type solution, two sides of the plate have to be simply-supported, while the remaining two sides can have any combination of free, clamped, or simply-supported boundary conditions. The results obtained from the different theories have been compared with exact solutions from existing literature . The response characteristics of the plates, like deflections, stresses, and frequencies, as well as the parameters affecting them have been studied. Some of the parameters investigated are span-to-thickness ratios, boundary conditions, loadings, and lamination schemes. The performance of the different theories in predicting plate responses have been evaluated. / Master of Science

Laminated composite structures have started to play a very significant role in today's aircraft industry. The application of composite materials has now gone beyond the borders of aircraft design and has entered into such fields as automotive, athletics and recreational equipment, etc. The light weight and high specific strength of composite material helps design vehicles with higher fuel efficiency and longevity. In order to understand the influence of design parameters related to the use of composite materials in these applications, a proper study of the laminated composite structures requires a complete failure analysis, which includes both initiation and propagation of damage. In this work a progressive failure methodology is developed and implemented in the commercial Finite Element software package, Abaqus. Out of the numerous failure criteria available in the literature to study damage initiation and propagation in unidirectional fiber reinforced composites, Puck and Schurmann's failure criteria have been chosen due to their ability to predict results close to those observed experimentally. Key features of the Puck and Schurmann's failure criteria for three-dimensional deformations of unidirectional fiber reinforced composites have been summarized. Failure modes in the matrix and the fiber are considered separately. The failure criteria are simplified for plane stress deformations. Whereas the failure plane can be analytically identified for plane stress deformations, a numerical search algorithm is needed for three-dimensional problems. Subsequent to the initiation of matrix failure, elastic moduli are degraded and values of these degradation parameters and fracture plane angles are found by using a Continuum Damage Mechanics (CDM) approach. It is found that the assumption that the material response remains transversely isotropic even after the matrix failure has initiated requires the degradation of the transverse Poisson's ratio. The Puck and Schurmann's failure criteria and the material degradation process have been implemented as a User Defined Field (USDFLD) subroutine in Abaqus. The implementation has been verified by analytically computing results for simple loadings and comparing them with predictions from using the USDFLD in Abaqus. Subsequently, both two- and three-dimensional problems of more realistic geometries and loadings have been analyzed and computed results compared with either experimental findings or results available in the literature. Major contributions of the work include identifying the degradation parameter for the transverse Poisson's ratio in terms of the matrix degradation parameter for the matrix failure in compression, development of the USDFLD based on Puck and Schurmann's failure criteria, implementing the USDFLD in the commercial finite element software, Abaqus, and verifying that results computing using the USDFLD for various laminates and loadings agree with those from either the analytical solution of the problem or those available in the literature. / Ph. D.

The objective of this study was to investigate the bending strength and failure characteristics of AS4/3501-6 and AS4/1806 graphite/epoxy angles sections as a function of processing induced defects and porosity. The angle sections were removed from 30-inch long angles fabricated at Lockheed Georgia Company with two quasi-isotropic stacking sequences, (± 45/90₂/ ∓ 45/0₂), and (± 45/90₂ ∓ 45/0₂)₃. Various degrees of porosity were introduced into the angles using four processing techniques: a standard lay-up, a solvent wipe during lay-up, moisture introduction between plies during lay-up, and a low pressure cure cycle. Two 2.5-inch wide angle sections, each with a 1.5-inch short leg and a 3.0-inch long leg, were bonded together along their long leg to form a T-shaped specimen. Bending of the T-specimen was introduced by pressing up on the underside of the flanges while holding the base of the specimen fixed. The experimental results have shown a significant effect of the processing induced defects on the failure load and bending stiffness for AS4/3501-6 specimens, but not for AS4/1806 specimens. An anisotropic analysis of the angle curved section was performed using Lekhnitskii's stress function approach. Stress and strain fields were studied and two failure criteria (Dual maximum stress and Tsai-Wu) were investigated in order to predict T-specimen failure load and failure mode. Reasonable correlation between prediction and experiments was found for the AS4/3501-6 (± 45/90₂/ ∓ 45/0₂)₃ T-specimens, but both failure criteria were found to be too conservative in predicting failure for the AS4/3501-6 (± 45/O₂/ ∓ 45/90₂)₃, T-specimens. The predicted failure modes were in good agreement with the experimental observations for both Iaminates. / Master of Science

"lnterlayering" - the incorporation of low-modulus film adhesive between the plies of composite Iaminates - has proved to be a successful technique for reducing debilitating out-of-pIane stresses. This work seeks to determine the effect interlayering has on a composite Iaminate's in-plane performance. Two Iaminate systems, an unnotched, 16-ply, quasi-isotropic, AS4/C985 and a centernotched, 32-ply, quasi-isotropic, AS4/C1808, were furnished in an interlayered and baseline (non-interlayered) configuration. The interlayers, 0.0005 in. each in thickness, appeared between each ply in every Iaminate tested. Both configurations of these two material systems were subjected to a regimen of in-plane loading tests. These tests included monotonic tension and compression, fully-reversed (R=-1), tension-compression fatigue cycling, and long-term tensile loading. A new test method, called the Incremental Strain Test (IST), was developed in an attempt to isolate and distinguish the long-term, tensile response of the interlayered and baseline Iaminates. This technique and its utility are described herein. The interlayered Iaminates exhibited superior performance during monotonic and IST loading. Distinctly higher ultimate loads and strains were achieved by the interlayered laminates. The notched fatigue performance of the interlayered Iaminates was sub-standard in comparison to the baseline results at the load level tested. The residual tensile strength of the fatigued interlayered Iaminates fell sharply at an early fraction of the laminates’ total life. The presence of the interlayers did not degrade the laminates’ IST performance. Several non-destructive techniques were used to monitor the damage mechanisms. These results, when combined with the experimental findings, helped explicate the disparity found between the interlayered and baseline Iaminate response. / Master of Science

Cross-Laminated Timber (CLT) combines layers of dimension lumber in alternating grain direction to form a mass timber panel that can be used to create entire wall, floor and roof elements. The viability of CLT as an element to resist lateral forces from racking has been of great interest (Dujic et al. 2004, Blass and Fellmoser 2004, and Moosbrugger et al. 2006). However, most research to date has been conducted on full-scale wall panels connected with proprietary fasteners according to European Test Methods. Little research has focused on non-proprietary connections, including nails, bolts and lag screws. The behavior of CLT full-scale wall panels is dependent upon the individual connection properties including the panel-panel connections between adjoining CLT panels within the wall. The purpose of this research is to evaluate the behavior of three small-scale CLT connection configurations using non-proprietary fasteners. Three different connections -LVL surface spline with lag screws, half-lap joint with lag screws, and butt joint with a steel plate fastened with nails - were tested in both monotonic and cyclic tests. In all, 30 connection tests were conducted, with 15 monotonic test and 15 cyclic tests. Connection strength, stiffness, and ductility were recorded for each connection. Experimental values were compared to National Design Specification for Wood Construction, or NDS (AWC 2012) predictions for connection strength. Nailed steel plate connections yielded much greater loads and behaved in a more ductile manner than did the lag screwed connections. The surface spline and half-lap connections often failed in a catastrophic manner usually due to splitting of the spline and fastener failure. Experimental results were generally lower than predicted by the yield models for the surface spline and steel plate connections. The half-lap connection resulted in higher experimental results than predicted. A discussion of the connection strength for materials with a non-homogeneous grain direction is also included. / Master of Science

Several damage modes, including fiber breakage, delamination, and transverse cracking, have been observed to contribute to the mechanical degradation of fiber-reinforced composite laminates. In this investigation, the effect of transverse cracking on laminate stiffness was studied. Four. glass-epoxy laminates ([0,90₃]_s, [90₃,0]_s, [0,90]_s, and [0,±45]_s) were evaluated. Two experimental test sequences were performed. In the first test sequence, longitudinal stiffness was measured at various stages of damage development. Damage development was monitored via edge replication. In the second test sequence, four laminate stiffnesses (E_xx, v_xy, G_xy, and D_yy) were measured in the undamaged and near-saturation damage states. Two analytical models were evaluated. A one dimensional shear lag model was used to predict longitudinal stiffness as a function of crack density for the [0,90₃]_s and 90₃,0]_s laminates. Correlation between theory and experiment was good. A modified laminate analysis was used to predict four laminate stiffnesses (E_xx, v_xy, G_xy, and D_yy). Except for the [0,±45]_s case, a laminate in which significant amounts of damage - s other than transverse cracking were observed, agreement between pre- · dieted and observed stiffness changes was good. / Master of Science

The objective of this study was to investigate the out-of-plane tensile strength of graphite/epoxy laminates as a function of porosity. An experimental test program was designed to apply tension to the faces of circular graphite/epoxy specimens in a direction perpendicular to the laminate mid-plane. The specimens were removed from the webs of angle sections fabricated by Lockheed Georgia Company using (AS4/1806 and AS4/3501-6 graphite/epoxy material systems with a stacking sequence of (±45/90₂/ ±45/0₂)_S or (±45/0₂/ +̅ 45/90₂)_S. The specimen porosities were the result of four distinct processing methods: a baseline hand lay-up, low pressure cure-cycle, a solvent wipe of pre-preg to remove resin, and the addition of water between pre-pregs. The experimental results have shown a significant reduction in the out-of-plane tensile strength as a function of increasing void content. The volume fraction of pores, pore geometry, size, and orientation were determined for a representative number of specimens by metallography and optical analysis methods. This data was combined with the out-of-plane tensile data and used in the theoretical model, prepared by Brown et al, to predict the out-of-plane strength as a function of porosity. The predicted strength values compared very well with the experimental data when the pores were found to be uniformly distributed throughout the laminate. / Master of Science

Dynamic instability in a laminated composite plate is studied using the finite element technique. The governing equations are derived based on the first order shear deformation theory with a linear strain-displacement relationship. The regions of instability for the resulting set of coupled Mathieu equations are obtained using a method of simultaneous diagonalization. Boundary frequencies generated using a first subdeterminant approximation to the infinite determinant are compared with those obtained by using the more accurate second subdeterminant as well as with frequencies from an analytical solution. These values are verified by checking the nature of responses near the boundaries between stability and instability. Results are presented for plates with different laminations, boundary conditions, thicknesses, number of layers, etc. Some unstable regions for a damped plate are also shown. Results from the first order plate theory are compared with those from a higher order shear deformation theory. / Master of Science

The effects of time and stress level were investigated in cross-ply laminates to gain more understanding on the damage events in composites. Analytical predictions of the effect of stress level were performed for the case of linear elastic materials. The predictions were based on energy methods and linear elastic fracture mechanics. Damage was simulated with a Monte Carlo numerical scheme. The predicted results corresponded well with experimental data in the literature. Experimental testing was performed on cross-ply laminates to gain a better understanding of the effect of time and rate on matrix cracking. The tests were performed on Kevlar/epoxy and graphite/epoxy [0/90₃]₈ laminates. The results indicate that the stress levels required for matrix cracking are a function of how fast the specimens were loaded. Also, significant time dependent damage was observed in cross-ply laminates which were subjected to sustained loads. / Master of Science

A higher-order shear deformation theory is used to analyze laminated anisotropic composite plates for deflections, stresses, natural frequencies, and buckling loads. The theory accounts for parabolic distribution of the transverse shear stresses, satisfies the stress-free boundary conditions on the top and bottom planes of the plate, and, as a result, no shear correction coefficients are required. Even though the displacements vary cubically through the thickness, the theory has the same number of dependent unknowns as that of the first-order shear deformation theory of Whitney and Pagano. Exact solutions for cross-ply and anti-symmetric angle-ply laminated plates with all edges simply-supported are presented. A finite element model is also developed to solve the partial differential equations of the theory. The finite element model is validated by comparing the finite element results with the exact solutions. When compared to the classical plate theory and the first-order shear deformation theory, the present theory, in general, predicts deflections, stresses, natural frequencies, and buckling loads closer to those predicted by the three dimensional elasticity theory. / Master of Science