Buckling stresses of simply supported rectangular flat plates in shear
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An analysis to obtain the buckling loads of a rectangular orthotropic plate with a centrally located cutout is described. Cutout shapes can be elliptical, circular, rectangular, or square. The boundary conditions considered in the analysis are simply supported unloaded edges and either clamped or simply supported loaded edges. The plate is loaded in uniaxial compression by either uniform edge displacement or uniform edge stress. A computer program that implements this analysis is described, and the program use is demonstrated by sample problems.
Method of initial parameters used in differential equations for bending and internal stress forces occurring in rectangular orthotropic plates lying on elastic foundation
The concept of stiffness tailoring for improved shear buckling resistance of rectangular composite plates is investigated analytically. The tailoring involves only the redistribution of the given material with given orientations to create beneficial stiffening patterns across the planform of the plate. The resulting local nonuniformities in thickness and membrane and bending stiffness combine to change the buckling response of the plate. The weight and average membrane shear stiffness are essentially unaffected by the tailoring. Practical limitations on the degree to which the tailoring may be carried out are shown to govern most designs. Improvements in the shear buckling load on the order of 50 percent are shown possible with monolithic tailoring. Tailored sandwich concepts, in which a light-weight core material is added to keep both plate surfaces flat, can produce improvements well over 100 percent in specific buckling loads compared with uniform composite plates.
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Equilibrium stability of orthotropic rectangular plates
An approximate analysis for predicting buckling of rectangular orthotropic composite plates with centrally located cutouts is presented. In this analysis, prebuckling and buckling problems are converted from a two-dimensional to a one-dimensional system of linear differential equations with variable coefficients. The conversion is accomplished by expressing the displacements as series with each element containing a trigonometric function of one coordinate and a coefficient that is an arbitrary function of the other coordinate. Ordinary differential equations are then obtained from a variational principle. Analytical results obtained from the approximate analysis are compared with finite element analyses for isotropic plates and for specially orthotropic plates with central circular cutouts of various sizes. Experimental results for the specially orthotropic plates are also presented. In nearly all cases, the approximate analysis predicts the buckling mode shapes correctly and predicts the buckling loads to within a few percent of the finite element and experimental results.
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In the aircraft industry, full scale and large component testing is a very necessary, time consuming, and expensive process. It is essential to find ways by which this process can be minimized without loss of reliability. One possible alternative is the use of scaled down models in testing and use of the model test results in order to predict the behavior of the larger system, referred to herein as prototype. This viewgraph presentation provides justifications and motivation for the research study, and it describes the necessary conditions (similarity conditions) for two structural systems to be structurally similar with similar behavioral response. Similarity conditions provide the relationship between a scaled down model and its prototype. Thus, scaled down models can be used to predict the behavior of the prototype by extrapolating their experimental data. Since satisfying all similarity conditions simultaneously is in most cases impractical, distorted models with partial similarity can be employed. Establishment of similarity conditions, based on the direct use of the governing equations, is discussed and their use in the design of models is presented. Examples include the use of models for the analysis of cylindrical bending of orthotropic laminated beam plates, of buckling of symmetric laminated rectangular plates subjected to uniform uniaxial compression and shear, applied individually, and of vibrational response of the same rectangular plates. Extensions and future tasks are also described.
A finite element method is presented for the large amplitude vibrations of complex structures that can be modelled with beam and rectangular plate elements subjected to harmonic excitation. Both inplane deformation and inertia are considered in the formulation. Derivation of the harmonic force and nonlinear stiffness matrices for a beam and a rectangular plate element are presented. Solution procedures and convergence characteristics of the finite element method are described. Nonlinear response to uniform and concentrated harmonic loadings and improved nonlinear free vibration results are presented for beams and rectangular plates of various boundary conditions.
Report presents the results of an investigation conducted to determine the hydrodynamic forces and moments acting on modified rectangular flat plates with aspect ratios of 1.00, 0.25, and 0.125 mounted on a single strut and operating at several depths of submersion. A simple method has been developed by modification of Falkner's vortex-lattice theory which enables the prediction of the lift characteristics in unseparated flow at large depths. This method shows good agreement with experimental data from the present tests and with aerodynamic data at all angles investigated for aspect ratios of 1.00 and 0.25 and at angles up to 16 degrees for aspect ratio 0.125. Above 16 degrees for aspect ratio 0.125, the predicted lift proved too high.
Radar cross section (RCS) prediction of several rectangular plate geometries is discussed using high-frequency techniques such as the Uniform Theory of Diffraction (UTD) for perfectly conducting and impedance wedges and the Method of Equivalent Currents (MEC). Previous reports have presented detailed solutions to the principal-plane scattering by a perfectly conducting and a coated rectangular plate and nonprincipal-plane scattering by a perfectly conducting plate. These solutions are briefly reviewed and a modified model is presented for the coated plate. Theoretical and experimental data are presented for the perfectly conducting geometries. Agreement between theory and experiment is very good near and at normal incidence. In regions near and at grazing incidence, the disagreement between the data vary according to diffraction distances and angles involved. It is these areas of disagreement which are of extreme interest as an explanation for the disagreement will yield invaluable insight into scattering mechanisms which are not yet identified as major contributors near and at grazing incidence. Areas of disagreement between theory and experiment are identified and examined in an attempt to better understand and predict near-grazing incidence, grazing incidence, and nonprincipal-plane diffractions.
Buckling resistance is often a controlling criterion in the design of structures composed of plate elements. Design concepts that lead to increased buckling loads (or strains) of these plate elements can directly lower the structural cost and/or weight by a number of means. This study quantifies the improvements that can be achieved in compression buckling loads of rectangular composite plates by using a simple stiffness-tailoring concept. The approach is to position the unidirectional lamina through the thickness and over the planform of the plate so that the buckling load is increased with no loss in in-plane stiffness or increase in weight. Finite element analyses have been used to determine the effects of tailoring on the buckling loads of plates with various boundary conditions, aspect ratios, thicknesses, and membrane stiffnesses. Increases in buckling loads (or strains) of 200 percent or more compared to the uniform plate-buckling loads are shown possible with this tailoring concept.
The results of experiments and theoretical analysis of the nonlinear, transient response of thin, rectangular, elastic, simply supported plates are presented. In the experiments, a plane wave tube with a special pulse generator at one end and a thin glass plate mounted at the other end was used to subject the glass plate to pressure pulses of different magnitudes. Whole-field measurements of the response of the plate were obtained by the reflected moire grid technique. The largest ratio of center deflection to thickness of the plate during the experiments was 5.6. The theoretical response of the glass plate to the pressure pulses was computed by solving the von Karman equations governing large deflections in elastic plates by two methods - (1) the finite-difference method, and (2) Galerkin's method. Good agreement was found between theoretically predicted and experimentally measured response.
Buckling resistance is often a controlling criterion in the design of structural elements. Design concepts that lead to increased buckling loads (or strains) can directly lower the structural cost and/or weight by a number of means. This study quantifies the improvements that can be achieved in compression buckling loads of rectangular composite plates by using a simple stiffness tailoring concept. The approach is to position the unidirectional lamina through the thickness and over the planform of the plate so that the buckling load is increased with no loss in in-plane stiffness or increase in weight. Finite element analyses have been used to determine the effects of tailoring on the buckling load of plates with various boundary conditions, aspect ratios, thicknesses, and membrane stiffnesses. Increases in buckling loads (or strains) of nearly 200 percent over the uniform plate buckling loads are shown possible with this tailoring concept.
The principal-plane scattering from perfectly conducting and coated strips and rectangular plates is examined. Previous reports have detailed Geometrical Theory of Diffraction/Uniform Theory of Diffraction (GTD/UTD) solutions for these geometries. The GTD/UTD solution for the perfectly conducting plate yields monostatic radar cross section (RCS) results that are nearly identical to measurements and results obtained using the Moment Method (MM) and the Extended Physical Theory of Diffraction (EPTD). This was demonstrated in previous reports. The previous analysis is extended to bistatic cases. GTD/UTD results for the principal-plane scattering from a perfectly conducting, infinite strip are compared to MM and EPTD data. A comprehensive overview of the advantages and disadvantages of the GTD/UTD and of the EPTD and a detailed analysis of the results from both methods are provided. Several previous reports also presented preliminary discussions and results for a GTD/UTD model of the RCS of a coated, rectangular plate. Several approximations for accounting for the finite coating thickness, plane-wave incidence, and far-field observation were discussed. Here, these approximations are replaced by a revised wedge diffraction coefficient that implicitly accounts for a coating on a perfect conductor, plane-wave incidence, and far-field observation. This coefficient is computationally more efficient than the previous diffraction coefficient because the number of Maliuzhinets functions that must be calculated using numerical integration is reduced by a factor of 2. The derivation and the revised coefficient are presented in detail for the hard polarization case. Computations and experimental data are also included. The soft polarization case is currently under investigation.
A general forced-vibration analysis is presented for laminated anisotropic rectangular plates including material damping. The theory used is the laminated version of the Mindlin plate theory and includes thickness-shear flexibility and rotatory and coupling inertia. A solution is obtained by the Rayleigh-Ritz method, extended to include the energy dissipated and the work done by the excitation. The analysis is applied to prediction of the resonant frequencies and associated nodal patterns and damping ratios of the first five modes for a series of rectangular plates with free edges. The plates considered consist of unidirectional boron-fiber/epoxy composite material with respective fiber orientations of 0, 10, 30, 45, 60, and 90 deg.
This paper contains a description of the three-dimensional elasticity equations and the associated finite element model for natural vibrations of laminated rectangular plates. The numerical results for natural frequencies are compared with those obtained by a shear deformable plate theory. A number of cross-ply and angle-ply rectangular plates are analyzed for natural frequencies. For relatively thick plates, the plate element predicts frequencies higher than those predicted by the 3-D element.