The purpose of this study was to develop a simple one- dimensional finite element for the nonlinear analysis of symmetrically and unsymmetrically laminated composite beams including shear deformation. There is a need for a simple and efficient method for analyzing unsymmetrically laminated beams since no other study on this topic is currently available. The beam element has ten degrees of p freedom at each of the two nodes: the axial displacement, the transverse deflection due to bending and shear, the twisting angle, the inplane shear rotation, and their derivatives along the axial direction. The formulation, solution procedure, and the computer program have been evaluated by solving a series of examples on the static response, free vibration, buckling, and nonlinear vibrations of isotropic and laminated beams. For unsymmetrically laminated beams, the nonlinear vibrations were found to have a soft spring behavior for certain boundary conditions as opposed to a hard spring behavior observed in isotropic and symmetrically laminated beams. The inplane boundary conditions were found to have a significant effect on nonlinear responses. / Master of Science

Five angle-ply laminates ([0₄₈], [(±10)₁₂]_s, [(±20)₁₂]_s, [(±30)₁₂]_s, and [(±45)₁₂]_s with central circular holes were tested under uniaxial compressive loading. The results from these tests show that the [(±45)₁₂]_s laminate exhibited plastic deformation, with ultimate applied strains exceeding -1%. All other laminates failed in a brittle manner with ultimate strains of less than -0.5%. A three-dimensional finite element stress analysis was performed for the same laminates. A failure analysis based on the three-dimensional stress tensor polynomial predicted that failure will initiate at the intersection of the ply interface with hole edge for all laminates, and be due to a combination of the out-of-plane and in-plane shear stresses. Use of the state of stress directly on the hole edge in the prediction of laminate failure resulted in predictions of laminate ultimate strengths which were less than experimentally observed values by as much as a factor of ten. In addition, symmetry considerations for three-dimensional finite element modelling of composite laminates are discussed, and a two-dimensional finite element model based on shear-deformable plate theory is predicted. / M.S.

A numerical simulation model has been developed which describes the manufacture of composite laminates from fiber-reinforced polyimide (PMR-15) matrix prepreg materials. The simulation model is developed in two parts. The first part is the volatile formation model which simulates the production of volatiles and their transport through the composite microstructure during the imidization reaction. The volatile formation model can be used to predict the vapor pressure profile and volatile mass flux. The second part of the simulation model, the consolidation model, can be used to determine the degree of crosslinking, resin melt viscosity, temperature, and the resin pressure inside the composite during the consolidation process. Also, the model is used to predict the total resin flow, thickness change, and total process time. The simulation model was solved by a finite element analysis. Experiments were performed to obtain data for verification of the model. Composite laminates were fabricated from ICI Fiberite HMF2474/66C carbon fabric, PMR-15 prep reg and cured with different cure cycles. The results predicted by the model correlate well with experimental data for the weight loss, thickness, and fiber volume fraction changes of the composite. An optimum processing cycle for the fabrication of PMR-15 polyimide composites was developed by combining the model generated optimal imidization and consolidation cure cycles. The optimal cure cycle was used to manufacture PMR-15 composite laminates and the mechanical and physical properties of the laminates were measured. Results showed that fabrication of PMR-15 composite laminates with the optimal cure cycle results in improved mechanical properties and a significantly reduced the processing time compared with the manufacturer's suggested cure cycle. / Ph. D.

The theory is based on an assumed displacement field, in which the surface displacements are expanded in powers of the thickness coordinate up to the third order. The theory allows parabolic description of the transverse shear stresses, and therefore the shear correction factors of the usual shear deformation theory are not required in the present theory. The theory accounts for small strains but moderately large displacements (i.e., von Karman strains). Exact solutions for certain cross-ply shells and finite-element models of the theory are also developed. The finite-element model is based on independent approximations of the displacements and bending moments (i.e., mixed formulation), and therefore only C°-approximations are required. Further, the mixed variational formulations developed herein suggest that the bending moments can be interpolated using discontinuous approximations (across inter-element boundaries). The finite element is used to analyze cross-ply and angle-ply laminated shells for bending, vibration, and transient response. Numerical results are presented to show the effects of boundary conditions, lamination scheme (i.e., bending-stretching coupling and material anisotropy) shear deformation, and geometric nonlinearity on deflections and frequencies. Many of the numerical results presented here for laminated shells should serve as references for future investigations. / Ph. D.

Experimental evaluations of impact damage resistance and residual compression strengths after impact are presented for nine laminated fiber reinforced composite material systems. The experiments employ a small scale specimen for assessing the impact damage resistance and impact damage tolerance of these materials. The damage area detected by C-scan is observed to develop linearly with the impact velocity for impact velocities higher than a threshold value. Brittle material systems have lower threshold velocities and higher damage area growth rates than toughened systems. The impact damage resistance of each material system can be characterized with threshold velocity V_c and damage area growth rate C. The residual compressive Strength after impact was observed to decrease linearly with the damage area equivalent diameter. The rate of compressive strength reduction, K_d, has been observed to be independent of the material properties. The impact damage can be simulated from quasi-static indentation test in which the damage due to these two loading conditions are quite similar. The residual compressive strength can also be simulated from specimens with similar damage size resulting from quasi-static indentation load. / Ph. D.

A hierarchical, 2-D, displacement-based, global/local finite element model is developed to permit an accurate, efficient analysis of localized 3-D effects in laminated composite plates. The model is developed using hierarchical, multiple assumed displacement fields at two different levels: (1) at the element level, and (2) at the mesh level. First, by superimposing a hierarchy of assumed displacement fields within the same finite element domain, a new variable kinematic, finite element is developed. The displacement field hierarchy contains both a conventional 2-D plate expansion and a full layerwise expansion. Depending on the accuracy desired, the variable kinematic element can use various terms from the composite displacement field, thus creating a hierarchy of different elements having a wide range of kinematic complexity and representing a number of different mathematical models. Since the resulting model is hierarchic, these different element types can easily be connected together in the same computational domain to permit simultaneous multiple model analysis. Despite the obvious utility of variable kinematic finite elements, a multiple model analysis based solely on the use of these elements has a significant restriction: all subregions of the computational domain must maintain in-plane mesh compatibility along subregion boundaries. This restriction necessitates the use of 2-D transition zones. In an effort to avoid the problems associated with 2-D transition zones, hierarchical, multiple assumed displacement fields are used at the mesh level in a finite element mesh superposition scheme. In this application of the finite element mesh superposition technique. the variable kinematic elements are used to form the independent, local, overlay meshes that can be superimposed on a pre-existing mesh of conventional 2-D plate elements. Due to the hierarchical nature of the resulting composite displacement field, the overlay mesh and the original mesh need not have compatible discretization. Thus the specifications and superimposed location of the overlay mesh can be tailored to fit the needs of the analyst regardless of the global mesh topology. The resulting model is used to analyze a number of laminated composite plate problems that contain localized subregions where significant 3-D stress fields exist (e.g. free edge effects, delamination fronts, and adhesive bonds). / Ph. D.

This dissertation focuses on nonlinear modal interactions in plates. Our first investigation involved the activation of a two-to-one internal resonance in the response of a metallic cantilever plate. Although the plate was excited around the frequency of its second bending mode, its response contained a contribution from its first torsional mode. The frequency ratio between the bending and torsional modes was nearly two-to-one. Next, we investigated the energy transfer from high-frequency to low-frequency modes in a cantilever graphite-epoxy composite plate (90/30/ — 30/ — 30/30/90)_s. The plate was excited around the natural frequency of its seventh (third torsional) mode. For some excitation amplitudes and frequencies, we observed the activation of a low-frequency (first bending) mode accompanied by an amplitude and phase modulation of the seventh mode. We studied combination resonances in the responses of cantilever composite plates with the layups (90/30/ — 30/ — 30/30/90)_s and (—75/75/75/ — 75/75/ — 75)_s to harmonic base excitations. We activated the combination resonance f_e≈ ω₂ + ω₇ in the (90/30/ — 30/ — 30/30/90)_s plate, where the w; are the natural frequencies of the plate and f<sub>e<sub> is the excitation frequency. In the (—75/75/75/ — 75/75/ — 75)_s plate, we activated the external combination resonance f<sub>e<sub>≈ 1/2(ω₂+ω₅) and the combination internal resonance f_e≈1/2(ω₂+ω₁₃) ≈ ω₈. We carried out an experimental-modal analysis (EMA) of a nonclassically supported plate with and without a constrained-layer damping (CLD) patch attached on its upper left-hand side surface. The natural frequencies and mode shapes were used to ascertain the effect of the CLD patch. / Ph. D.

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Hybrid Titanium Composite Laminates (HTCL) have vast potential for future commercial aircraft development. In order for this potential to be properly utilized the HTCLs material properties must first be well understood and obtained through experimentation. Crack initiation and crack growth characteristics of HTCLs are dependent on the heat treatment of the embedded constituent titanium foil. While high strength titanium foils may delay crack initiation, there may be an adverse effect of unsuitable crack growth rates in the HTCLs. Literature has indicated that when properly designed, cracks in HTCLs can arrest due to fiber bridging mechanisms and other crack closure mechanisms. Traditional surface inspection techniques employed on facesheet laminate evaluations will not be able to properly monitor the internal crack growth and damage progression for the internal plies. The main objective of the this joint Georgia Tech/Boeing research project was to determine and compare crack initiation and crack growth characteristics of different heat-treated -Ti 15-3 titanium foil embedded in HTCLs. Georgia Tech utilized a unique capability of x-raying the internal foils of the HTCL specimen in a servo-hydraulic test frame while under load. The titanium foil in this study represented four different heat treatments that result in four increasing levels of strength and decreasing levels of elongation. Specifically, open-hole HTCL coupons were tested at four stress load levels under constant amplitude fatigue cycles to determine a-N curves for the HTCL layups evaluated. The layup evaluated was [45/0/-45/0/Ti/0/-45/0/45]. Crack growth rates were determined once the initiated crack was detected via radiographic exposure. Radiographic delamination analysis and thermoelastic stress analysis techniques were employed to determine additional damage mechanisms in the laminate. Analytical and finite element methods were utilized to determine ply stresses. Additionally, titanium foil properties were determined via dog-bone coupons for each of the four heat treatment conditions.