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The formulation of the problem of finite elastic-viscoplastic deformation of thin beams is described. The finite element analysis of a representative problem is presented and various solution methods are surveyed.
Thin-walled rectangular section composite beams are built out of graphite-epoxy prepreg tape using an autoclave molding technique. Cantilevered beams are tested under static loads using a specially-built apparatus and bending slope and elastic twist at a station are measured using a laser system. Measured bending slope and bending-induced twist distributions are correlated with predicted results obtained using a simple beam analysis as well as a refined finite element analysis. Natural vibration characteristics at different rotational speeds are determined experimentally by testing beams in a specially built 10 ft diameter vacuum chamber. The rotor is excited by piezo-electric crystals and response is determined from strain gages mounted on the surface. For composite beams with bending-twisting couplings (symmetric layup), effects of section warping and transverse shear on structural response are found to be substantial. These results were substantiated by the analyses.
The vibrational behavior of cantilevered aircraft wings modeled as thin-walled beams and incorporating piezoelectric effects is studied. Based on the converse piezoelectric effect, the system of piezoelectric actuators conveniently located on the wing yield the control of its associated vertical and lateral bending eigenfrequencies. The possibility revealed by this study enabling one to increase adaptively the eigenfrequencies of thin-walled cantilevered beams could play a significant role in the control of the dynamic response and flutter of wing and rotor blade structures.
Simple, mixed finite element models are developed for the free vibration analysis of curved thin-walled beams with arbitrary open cross section. The analytical formulation is based on a Vlasov's type thin-walled beam theory with the effects of flexural-torsional coupling, transverse shear deformation and rotary inertia included. The fundamental unknowns consist of seven internal forces and seven generalized displacements of the beam. The element characteristic arrays are obtained by using a perturbed Lagrangian-mixed variational principle. Only C(sup o) continuity is required for the generalized displacements. The internal forces and the Lagrange multiplier are allowed to be discontinuous at interelement boundaries. Numerical results are presented to demonstrate the high accuracy and effectiveness of the elements developed. The standard of comparison is taken to be the solutions obtained by using 2-D plate/shell models for the beams.
Simple, mixed finite element models are developed for the free vibration analysis of curved thin-walled beams with arbitrary open cross section. The analytical formulation is based on a Vlasov's type thin-walled beam theory with the effects of flexural-torsional coupling, transverse shear deformation and rotary inertia included. The fundamental unknowns consist of seven internal forces and seven generalized displacements of the beam. The element characteristic arrays are obtained by using a perturbed Lagrangian-mixed variational principle. Only C(sup o) continuity is required for the generalized displacements. The internal forces and the Lagrange multiplier are allowed to be discontinuous at interelement boundaries. Numerical results are presented to demonstrate the high accuracy and effectiveness of the elements developed. The standard of comparison is taken to be the solutions obtained by using 2-D plate/shell models for the beams.
A two-step hybrid analytical technique is presented for the nonlinear vibration analysis of thin-walled beams. The first step involves the generation of various-order perturbation functions using the Linstedt-Poincare perturbation technique. The second step consists of using the perturbation functions as coordinate (or approximation) functions and then computing both the amplitudes of these functions and the nonlinear frequency of vibration via a direct variational procedure. The analytical formulation is based on a form of the geometrically nonlinear beam theory with the effects of in-plane inertia, rotatory inertia, and transverse shear deformation included. The effectiveness of the proposed technique is demonstrated by means of a numerical example of thin-walled beam with a doubly symmetric I-section. The solutions obtained using a single-spatial mode were compared with those obtained using multiple-spatial modes. The standard of comparison was taken to be the frequencies obtained by the direct integration/fast Fourier transform (FFT) technique. The nonlinear frequencies obtained by the hybrid technique were shown to converge to the corresponding ones obtained by the direct integration/fast Fourier transform (FFT) technique well beyond the range of applicability of the perturbation technique. The frequencies and total strain energy of the beam were overestimated by using a single-spatial mode.
This report presents an explanation of the fundamental principles and a summary of the essential formulas for the design of diagonal-tension field beams, i.e. beams with very thin webs, as developed by Professor Wagner of Germany.
The tendency toward economy of material and lightness of structure has long since led to the increased application of beams having large ratios of moment of area W to cross-sectional area F. This paper tries to provide an answer to how thin the beams can be.
This report analyzes the action of a cantilever T beam with a tension flange so thin it can only carry tensile stresses.
A composite element is presented which includes the effects of warping and offset shear centers. It is shown to be mathematically consistent with thin walled open beam theory and can be incorporated into any structural analysis program by use of NASTRAN'S standard elements. A numerical example analyzing the vibration of a channel beam is presented, and, by using the composite element, the numerical results agreed well with theoretical data.
The Department of Astronautics at the United States Air Force Academy is currently planning to fly an experiment in a NASA Get-Away-Special (GAS) canister. The experiment was named the flex beam experiment. The primary technical objective of the flex beam experiment is to measure the damping of a thin beam in the vacuum and zero G environment of space. By measuring the damping in space, it is hoped to determine the amount of damping the beam normally experiences due to the gravitational forces present on Earth. This will allow validation of models which predict the dynamics of thin beams in the space environment. The experiment will also allow the Academy to develop and improve its ability to perform experiments within the confines of a NASA GAS canister. Several experiments, of limited technical difficulty, were flown by the Academy. More complex experiments are currently planned and it is hoped to learn techniques with each space shuttle flight.
Thin sections (500 to 1000 angstroms thick) of individual micrometeorites (5 to 15 micrometers) have been prepared with an ultramicrotome equipped with a diamond knife. Electron microscope examination of these sections has revealed the internal structures of chondritic micrometeorites, and a subset of highly porous, fragile particles has been identified. Delicate meteoritic materials such as these are characteristic of debris from cometary meteors.
A refined elastic analysis of bonded joints which accounts for transverse shear deformation and transverse normal stress was developed to obtain the stresses and displacements in the adherends and in the bond. The displacements were expanded in terms of polynomials in the thicknesswise coordinate; the coefficients of these polynomials were functions of the axial coordinate. The stress distribution was obtained in terms of these coefficients by using strain-displacement and stress-strain relations. The governing differential equations were obtained by integrating the equations of equilibrium, and were solved. The boundary conditions (interface or support) were satisfied to complete the analysis. Single-lap, flush, and double-lap joints were analyzed, along with the effects of adhesive properties, plate thicknesses, material properties, and plate taper on maximum peel and shear stresses in the bond. The results obtained by using the thin-beam analysis available in the literature were compared with the results obtained by using the refined analysis. In general, thin-beam analysis yielded reasonably accurate results, but in certain cases the errors were high. Numerical investigations showed that the maximum peel and shear stresses in the bond can be reduced by (1) using a combination of flexible and stiff bonds, (2) using stiffer lap plates, and (3) tapering the plates.
Multilayer beam splitter system yielding nearly equal broadband infrared reflectance and transmittance in the 5 to 50 micron spectral region has been developed which will significantly reduce size and cost of light path compensating devices in infrared spectral instruments.
Polymer films about 150 A thick, deposited on glass substrates by electron bombardment of tetramethyltetraphenyltrisiloxane, were studied, after being sandwiched between evaporated aluminum electrodes, the top one semitransparent. The capacitance, conductance, and photoconductance of the sandwiches were measured at room temperature as a function of the electron bombarding current which formed the polymer. The polymer thickness was obtained independently from Christy's (1960) empirical formula for the rate of formation. The obtained results indicate that, with increasing bombarding current, the polymer undergoes an increase in both crosslinking bonds and dangling bonds. Exposure to air drastically reduces the density of dangling bonds, but does not affect the crosslinking.
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