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The analytical solution presented is based on the assumption that the deformed thickness of the plate is approximately constant. The nonlinear equations governing finite axisymmetric deformations of a circular plate made of neo-Hookean material are used in the analysis. The variation of circumferential extension ratio and the variation of deformed thickness are shown in graphs.
This technical memorandum describes a method for determining the transverse deflections of a uniformly loaded, thin circular plate of constant thickness supported by single or multiple rings of equally spaced discreet points. The rotations are assumed free at each point. This could have application in the design of telescope mirror supports that must minimize structural gravitational deformations. It could also be of general use to the structural analyst.
Thick circular elastic plates stability under external forces and displacements, obtaining stability criterion from buckled state considerations
Two approaches were taken to make convenient spread sheet calculations of elastic constants from resonance data and the tables in ASTM C1259 and E1876: polynomials were fit to the tables; and an automated spread sheet interpolation routine was generated. To compare the approaches, the resonant frequencies of circular plates made of glass, hardened maraging steel, alpha silicon carbide, silicon nitride, tungsten carbide, tape cast NiO-YSZ, and zinc selenide were measured. The elastic constants, as calculated via the polynomials and linear interpolation of the tabular data in ASTM C1259 and E1876, were found comparable for engineering purposes, with the differences typically being less than 0.5 percent. Calculation of additional v values at t/R between 0 and 0.2 would allow better curve fits. This is not necessary for common engineering purposes, however, it might benefit the testing of emerging thin structures such as fuel cell electrolytes, gas conversion membranes, and coatings when Poisson s ratio is less than 0.15 and high precision is needed.
NASA Ames is conducting a program to develop improved methods for predicting suckdown and hot-gas ingestion on jet V/STOL aircraft when they are in ground effect. As part of that program a data base is being created that provides a systematic variation of parameters so that current empirical prediction procedures can be modified. The first series of tests in this program is complete. This report is one of three that presents the data obtained from tests conducted at Lockheed Aeronautical Systems - Rye Canyon Facility and the High Bay area of the 40 by 80 foot Wind Tunnel at Ames Research Center. Suckdown on two circular plates is examined.
Plastic response of circular uniform plate to axisymmetric impulse load of Gaussian distribution
The analytical solutions for the vibrational modes of a thin circular flat plate that is simply supported at three points on the circumference are presented. The mode shapes and corresponding eigenvalues are obtained. Results show that the modes can be grouped into four different types depending on the manner by which they receive the pressure at the supported points. The problem is of the mixed boundary value type in that some portion of the boundary is free while the other portion is simply supported.
A fixture is described for making normal-pressure tests of flat plates 5 inches in diameter in which particular care was taken to obtain rigid clamping at the edges. Results are given for 19 plates, ranging in thickness from 0.015 to 0.072 inch. The center deflections and the extreme-fiber stresses at low pressures were found to agree with theoretical values; the center deflections at high pressures were 4 to 12 percent greater than the theoretical values. Empirical curves are derived of the pressure for the beginning of permanent set as a function of the dimensions of the plate and the tensile properties of the material.
Hyperbolic equation for infinite elastic plate under impact loading - structural dynamics
Models of fuel bearing nuclear reactor core matrices for analysis of individual principal and circumferential stresses based on isocline isochromatic spectra of geometric configurations
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Tests were performed on two simply supported plates of aluminum alloy 2024-0, under a central concentrated load, with peak deflections up to 2.6 times the thickness. The load was provided by a small-diameter hard-steel rod. The plates had diameter-to-thickness ratios (D/h) of 20 and 41. Measurements were made of load, deflections and strains; membrane and bending strains were calculated from the test data. The test data are presented in comparison with theoretical predictions generated by the finite-element-computer code PLANS, which includes material and geometric nonlinearities. The theoretical prediction was excellent for deflections, and generally good for strains, when the central force was represented by a line load around the loading rod's contact circle.
A fixture is described for making normal-pressure tests of flat plates 5 inches in diameter in which particular care was taken to obtain rigid clamping at the edges. Results are given for 19 plates, ranging in thickness form 0.015 to 0.072 inch. The center deflections and the extreme-fiber stresses at low pressures were found to agree with theoretical values; the center deflections at high pressures were 4 to 12 percent greater than the theoretical values. Empirical curves are derived of the pressure for the beginning of the permanent set as a function of the dimensions of the plate and the tensile properties of the material.
Axisymmetrical bending of thick circular sandwich plate with layers of different elastic moduli
The problem of transient axisymmetric vibrations of thin circular elastic plates due to sonic boom excitation is investigated. The equation of motion for a solid circular plate is solved by applying the modified finite Hankel transform and the Laplace transform, and the numerical results are obtained with the help of the digital computer. From the analysis of the data, obtained for the dynamic deflections of the plates for the boom duration, it is concluded that for a normal flight the boom duration has a significant effect on the vibrations of plates as compared to the overpressure of the boom.
The vibration of an initially compressed plate having a circular geometry and orthotropy is examined in an affine space. The classical linear plate theory and Hamilton's principle are employed. The equations of motion of the plate are particularly simple in the chosen affine space, permitting a free-vibration study of the entire spectrum of composite materials with polar orthotropy. Approximate but very accurate standing-wave-type mode shapes are used in solving the essentially double eigenvalue problem to determine the effects of midplane forces on the vibration frequencies of the plate. The results indicate that the affine-space frequency increases with increasing stiffness ratio but decreases with increasing midplane compression. It is also discovered that, contrary to the trends observed for rectangular geometry and orthotropy by Oyibo (1981), Brunelle (1982), and Brunelle and Oyibo (1983), the affine-space frequency increases with increasing generalized Poisson's ratio.
Tensile tests on fiber reinforced plates with circular holes, studying fiber orientation effects