An investigation of the behavior of shear deformable plate finite elements is conducted to determine why and under what conditions these elements lock, or become overly stiff. For this purpose, a new analytical technique is developed to derive the exact form of the shear constraints which are imposed on an element when its side-tothickness ratio is large. The constraints are expressed in terms of the nodal degrees of freedom, and they are easily interpreted as being either the proper Kirchhoff constraints or spurious locking constraints. Moreover, the technique is applicable to any displacement-based shear deformable beam, plate or shell element regardless of the shear deformation theory or the order of the Gauss-Legendre integration rule which is used to numerically evaluate the stiffness coefficients. To gain a better understanding of locking phenomena, the constraints which arise under full and reduced integration are derived for various Mindlin and Reddy-type beam and plate elements. These analytical findings are then compared with numerical results of isotropic and laminated composite plates, verifying the role that shear constraints play in determining the behavior of thin shear deformable elements. The results of the present study lead to definitive conclusions regarding the origin of locking phenomena and the effect of reduced integration. / Master of Science

The stress freezing photoelastic method is a proven technique for the estimation of stress intensity factors along crack fronts in complex three dimensional problems. Comparisons between previous photoelastic and approximate analytical results have revealed discrepancies in results for the case where the crack shape is nearly quarter circular. In the present study, the frozen stress photoelastic method was applied to such geometries with varying flaw depth. Results are compared with those of other investigators. It is concluded that the flaw growth in this problem is non-self similar due to the complexity of boundary shapes. The variation of the stress intensity factor along the crack front is also studied. / Master of Science

A first-order shear deformation plate theory is used to predict free vibration frequencies in rotating laminated composite plates. The theory accounts for geometric non-linearity in the form of von Karman strains. The plate is permitted to have arbitrary orientation and offset from the axis of rotation. A finite element model is developed to obtain a solution to the problem. The model is validated by comparing the results for free vibration of non-rotating plates for various boundary conditions and material properties with the exact results based on the classical plate theory and the first-order shear deformable plate theory. Results are presented for free vibration of isotropic and laminated composite plates rotating at different angular velocities. A study has also been made on the change in the free vibration frequencies of the plate with angular velocity for different plate thicknesses and for different modulus ratios. / Master of Science

Design procedures for moment end-plate connections, which include prying action effects, have been verified for five end-plate configurations. The design procedures include the use of yield-line theory for determining the end-plate thickness and the so-called modified Kennedy method for determining bolt forces. This investigation extends these design procedures to include the four-bolt extended unstiffened moment end-plate connection. The results of four experimental tests are evaluated and compared to the predicted results obtained from yield-line theory and the modified Kennedy method. Using the finite element method, analyses to determine the stress in the beam at a cross-section near to the connection are also performed. The results from the finite element analyses are compared to experimental results. In addition, the type of construction suitable for this connection is assessed. Modifications to the analytical predictions are made based on the above comparisons. Results indicate that the flange force is distributed equally to the inner and outer end-plate. Also, prying action is included for the inner bolts at all times, and for the outer bolts when failure is controlled by the end-plates. Design recommendations and an example using the modified design procedure are presented in this thesis. / 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

An automated procedure for designing minimum-weight composite plates subject to a local damage constraint under tensile and compressive loadings has been developed. A strain based criterion was used to obtain fracture toughness of cracked plates under tension. Results of an experimental investigation of the effects of simulated through-the-thickness cracks on the buckling, postbuckling, and failure characteristics of composite flat plates are presented. A model for kinking failure of fibers at the crack tip was developed - for compression loadings. A finite element program based on linear elastic fracture mechanics for calculating stress intensity factor (SIF) was incorporated in the design cycle. A general purpose mathematical optimization algorithm was used for the weight minimization. Analytical sensitivity derivatives of the SIF, obtained by employing the adjoint variable technique, were used to enhance the computational efficiency of the procedure. Design results for both unstiffened and stiffened plates are presented. / Ph. D.

Low frequency Lamb waves in composite laminates were investigated theoretically and experimentally. To have a general solution for Lamb wave propagation in multilayered composite laminates is not practical due to a large number of boundary conditions needed to be satisfied at the interlaminar interfaces. Various approximate theories have been proposed to model low frequency Lamb wave propagation in composite laminates. In the present study, an approximate solution was derived from an elementary shear deformation plate theory and was shown to work well in the low frequency, long wavelength region. A simple method, similar in configuration to the acousto-ultrasonic technique, was used to measure Lamb wave phase velocities. Low frequency Lamb waves, usually in the range of 10 kHz to 1 MHz, were generated. Dispersion curves of the lowest symmetric Lamb mode and the lowest antisymmetric Lamb mode were obtained. The experimental data were compared with the results obtained from the approximate solution for the lowest Lamb modes in the low frequency, long wavelength region for a unidirectional laminate, a symmetric cross-ply laminate, a symmetric quasi-isotropic laminate and an aluminum plate. There is good correlation between the data and the results obtained from the approximate solution, which suggests that the lowest Lamb modes are modeled adequately by the present theory in these cases. This experimental procedure of measuring phase velocities can be used to characterize laminated composite plates with and without damage since each material and stacking sequence gives distinct lowest symmetric and antisymmetric curves. Stiffness reduction of composite laminates caused by damage can be related to the change in Lamb wave propagation speed. Damage in the form of transverse cracks in the 90° plies of a [90/90/90/0], graphite/epoxy laminate reduced the phase velocities of the Lamb modes. The lowest antisymmetric mode is sensitive to stiffness reduction in composite plates. Consequently, axial stiffness reduction in [0/45/0/45/0/45], and [0]₁₂ woven graphite/polyimide composite laminates was monitored by the lowest antisymmetric Lamb mode. / Ph. D.

The postbuckling failure of square composite plates with central holes is analyzed numerically and experimentally. The particular plates studied have stacking sequences of [± 45/0/90]₂₅, [± 45/02]₂₅, [± 45/06]₅. and [± 45]₄₅. A simple plate geometry, one with a hole diameter to plate width ratio of 0.3 , is considered. Failure load, failure mode, and failure locations are predicted numerically by using the finite-element method. The predictions are compared with experimental results. In the experiments in order to be accommodated by the test fixture it is necessary for the plates to be slightly larger than the analYSis region, extending somewhat beyond the supports. The region outside the supports is included in the numerical study. It is shown that not considering these regions can lead to erroneous numerical predictions. In numerical failure analysis the interlaminar shear stresses, as well as the inplane stresses, are taken into account. By comparing the interlaminar shear stress calculations from the finite-element method with analytical results for simple cases, a solid foundation for interlaminar shear stress calculation is established. / Ph. D.

In this study, connection classification system is developed on the basis of previous classifications. Further, flexible connections are modeled by matrix displacement method. The effect of flexible connections are studied on gable frames. Firstly, flush end-plate connections with single row of bolts at the tension flange, are classified. The classification system was developed in this study. End plate connections whose moment-rotation curves are known arc classified on the basis of moments as FR (fully restrained) and PR (partially restrained) connections. Further, the connections are also classified by entering a plot with coordinates - Ratio of Moment at the connection and plastic moment and ratio of corresponding rotation and rotation at plastic moment. Depending on the location the connection can be classified. Secondly, for connections, the rotational stiffness is determined from the moment rotation curves and used in the computer code to implement flexible connections. The effect is studied on gable frames. For the loading and frame used there is not much variation in moments at the flexible joints due to connection flexibility and hence flush end plate connections can be used in gable frames effectively / Master of Science

A simple, computationally efficient analysis approach is developed to predict the buckling of geodesically stiffened composite panels under in-plane loads. This procedure accounts for the discrete flexural contribution of each stiffener through the use of Lagrange multipliers in an energy method solution. An analysis is also implemented for the buckling of simply supported anisotropic rhombic plates. Examples are presented to verify results of the stability analyses and to demonstrate their convergence behavior. Analysis routines are coupled with a versatile numerical optimizer to create a package for the design of minimum-mass stiffened panels, subject to constraints on buckling of the panel assembly, local buckling of the stiffeners, and material strength failure. The design code is used to conduct a preliminary design study of structurally efficient stiffened aircraft wing rib panels. Design variables include thickness of the skin laminate, stiffener thickness, and stiffener height. Applied loads are uniaxial compression, pure shear, and combined compression-shear. Two different geodesically stiffened wing nib configurations with increasing numbers of stiffeners are considered. Results are presented in the form of structural efficiency curves and are compared with those for minimum-weight longitudinally stiffened panels and unstiffened flat plates. Trends in design parameters, including skin thickness and stiffener height, stiffener thickness, stiffener aspect ratio, stiffener load fraction, and stiffener mass fraction, are also examined for the geodesic panels under compression and shear. The effects of skin laminate geometry and anisotropy on the local buckling behavior of cross-stiffened geodesic panels are examined using the rhombic plate analysis. / Master of Science