Laminated composite plates have become an important and proven structural material in aerospace and ocean vehicles. However, because of the inherent orthotropy of laminated composite materials the analysis of these structures is complex and usually cannot be adequately performed using classical methods. In this dissertation the formulation of the fully coupled fluid-structure interaction of a laminated composite plate and its surrounding fluid medium is presented. The solution technique involves the finite element method for modeling the structural response and the boundary element method for modeling the acoustic field. The model incorporates the Mindlin plate theory which includes five degrees of freedom. An improved integration technique is demonstrated which significantly reduces the approximation error. Storage requirements are reduced by grouping complex numbers. Finally the fully coupled fluid-structure interaction involving laminated composite plates is modeled using the combined FEM-BEM approach demonstrating the usefulness and the significance of the method. / Ph. D.

A micromechanics-based model for progressive failure analysis of laminated composite shell structures has been developed and implemented. The model couples a finite element model for nonlinear analysis of laminated shells with a micro mechanics elasticity solution for predicting failure and effective composite properties. The nonlinear laminate theory and finite element model are based on a third-order expansion of displacements through the thickness of the shell, thus allowing for both transverse normal and shearing deformations. The initiation and evolution of damage in the shell is modeled at the constituent (i.e., fiber, matrix, interphase) level using an elasticity solution for quasi-three-dimensional hygro-thermo-mechanical loading of continuous fiberreinforced composites. The model is used to predict failure in laminated composite structures and to study the effects of constituent properties (stiffness and strength) on structural behavior. / Ph. D.

A finite element model based on the quasi-three dimensional displacement field of Pipes and Pagano [1] with nonlinear strain-displacement relations is developed to study the free edge problem of composite laminates. Numerical results are presented to show the difference between the results of the nonlinear and the linear analyses. It is observed that the stresses obtained in the nonlinear analysis differ from the stresses obtained in the linear analysis by 10% in most of the cases, and in some cases they differ as much as 40%. / Master of Science

Vlasov’s one-dimensional structural theory for thin-walled open section bars was originally developed and used for metallic elements. The theory was recently extended to laminated bars fabricated from advanced composite materials. The purpose of this research is to provide a study and assessment of the extended theory. The focus is on flexural and torsional-flexural buckling of thin-walled, open section, laminated composite columns. Buckling loads are computed from the theory using a linear bifurcation analysis, and are compared to available experimental data. Also, a geometrically nonlinear beam column analysis by the finite element method is developed from the theory. Results from the nonlinear compression response analysis are compared to limited available test data. The merits of the theory and its implementation are discussed. / Master of Science / incomplete_metadata

In this study two one-dimensional finite element formulations based on higher-order displacement models have been developed. Both theories account for geometric nonlinearities, a parabolic shear strain distribution through the thickness, and satisfy the shear stress free boundary conditions at the upper and lower surfaces of the beam. The theories also account for the bend-stretch, shear-stretch, and bend-twist couplings inherent to generally laminated composite beams. Further, a coupling between the shear deformation and the twisting is introduced. The lateral strains are assumed nonzero and retained in the formulation. The first model termed SVHSDT also accounts for the continuity of the interlaminar shear stresses at the layer interfaces, while keeping the number of degrees of freedom independent of the number of layers. This theory though is restricted to the analysis of symmetrically laminated cross-ply beams. The formulation has been applied to the linear static and free vibration analysis. The second model termed RHSDT is valid for generally laminated beams. This model has been applied to the nonlinear static and transient analysis of generally laminated beams, free vibration analysis, and impact analysis. The effect of axial stresses on the nonlinear transient response has also been investigated using this theory. For generally laminated beams the lateral strains and the shear-twist coupling were found to have a significant effect on the vibrations frequencies. Also, as expected, initial stresses, boundary conditions and the lamination scheme were found to have a significant effect on the nonlinear responses. / Master of Science

Presented is a model for predicting SMA-induced deformations in an unsymmetric cross ply laminate. A previously developed theory is used to predict the room-temperature shape of the cross-ply laminate by minimizing its total potential energy. Then, using the principle of virtual work, equations relating the shape of the laminate to a force applied on supports fastened to the laminate are derived. Induced strains and displacements are predicted as a function of the applied force. Experiments where the force is generated by known weights are conducted. Good correlations are established between the experimental results and the predictions. The developed theory is able to predict with good accuracy the shape, strains and, displacements of an unsymmetric cross-ply laminate to the force applied on the laminate. This theory is then used to develop a model relating the laminate response to forces produced by a SMA actuator, the actuator being a SMA wire. To describe the mechanics of the SMA actuator, constitutive equations derived by other researchers are used. These constitutive equations relate the temperature of the wire to forces generated in it. Experiments where a SMA wire is used as an actuator are conducted. These experiments consist of resistively heating a SMA wire attached to supports fastened to the laminate. During these experiments, laminate deformations are measured as a function of the applied voltage. Comparisons with the temperature-based constitutive model predictions are not made since the relation between the applied voltage and the SMA temperature is very difficult to establish. However, the experiments show that a SMA used in conjunction with cross-ply unsymmetric laminates can induce very large changes in the laminate shapes. Thus, the concept of using a SMA actuator to control the shape of cross-ply unsymmetric laminates is validated. / Master of Science

The objective of this study was to determine the effect of nonlinear material behavior on the response and failure of unnotched and notched angle-ply laminates under uniaxial compressive loading. The endochronic theory was chosen as the constitutive theory to model the AS4/3502 graphite-epoxy material system. Three-dimensional finite element analysis incorporating the endochronic theory was used to determine the stresses and strains in the laminates. An incremental/iterative initial strain algorithm was used in the finite element program. To increase computational efficiency, a 180° rotational symmetry relationship was utilized and the finite element program was vectorized to run on a super computer. Laminate response was compared to experiment revealing excellent agreement for both the unnotched and notched angle-ply laminates. Predicted stresses in the region of the hole were examined and are presented, comparing linear elastic analysis to the inelastic endochronic theory analysis. A failure analysis of the unnotched and notched laminates was performed using the quadratic tensor polynomial. Predicted fracture loads compared well with experiment for the unnotched laminates, but were very conservative in comparison with experiments for the notched laminates. / Master of Science

A Global-Local finite element approach was used to investigate the interlaminar stresses in laminated composite plates with a central circular hole. Detailed solutions were sought for the interlaminar normal stress distributions close to the free straight edge of the plate as well as around the edge of the hole. The Global model was analyzed as a two-dimensional problem. The displacements obtained a distance away from the regions of interest in the two-dimensional model were used as imposed boundary conditions to the three-dimensional models of the edges. The results obtained were found to be accurate, thus demonstrating the validity and strength of the Global-Local technique. The results further concluded that for symmetric cross-ply laminated plates with large central circular holes, the interlaminar normal stresses at the free edges are affected to a small degree by the size of the hole. The CSM Testbed and ANISAP were the two finite element analysis programs used throughout this investigation. The CSM Testbed element library was augmented with 16, 20, 24 and 32 node displacement formulation based elements which were implemented as Experimental elements. / Master of Science

The probabilistic stability of a laminated composite plate is investigated. Three different models are considered in this study, namely, the classical laminated plate theory, a first-order shear deformation theory, and a higher-order shear deformation theory. The probabilistic characteristics, such as the probability density and cumulative distribution functions for the resistance to buckling of the plate are obtained by employing the first-order second-moment method of reliability analysis. Uncertainties associated with material mechanical properties and fiber orientations of individual layers are modeled as statistically independent random variables. Numerical results are presented for rectangular simply-supported laminates, showing the effects of thickness ratio, stacking sequence, and number of layers on the probabilistic stability of the plates. / Master of Science

Composite materials are increasingly finding use in structures, such as aircraft components, and thus, an accurate method of predicting response is required. Even laminated structures that are considered thin can be significantly affected by transverse shear effects, and as a result, transverse shear should not be neglected. The free vibration response of generally-laminated, thick, skew, trapezoidal plates is investigated as there appears to be a lack of information in this area. In the method developed, Chebychev polynomials are used as displacement functions in the Rayleigh-Ritz method. Various edge supports are considered, and appropriate linear and rotational springs are introduced to approximately satisfy the essential boundary conditions associated with simply-supported and clamped edges. First-order shear theory is used to account for transverse shear effects, and rotary inertia is also included.in the model. Convergence of the solution resulting from changes in spring values and number of terms in the series is investigated. The accuracy of the method is demonstrated by comparing the present method to available results for plates of various quadrilateral shape, material systems, and boundary conditions. Thick laminated plates of both symmetric and unsymmetric construction and of various planforms and boundary conditions are then presented. Cantilever, thick, skew, and trapezoidal plates are then extensively studied, and variations in natural frequencies due to geometric parameter changes, such as taper ratio, sweep angle, and value of the parameter q, are discussed. The parameter, q, is a root length multiplier which determines the length of the quarter-chord line, thus representing a measure of the span. Mode shapes for a number of plates of various planform and support conditions are included. / Master of Science