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NASA NTRS1993

A sublaminate analysis method for predicting disbond and delamination loads in composite structures

A method is proposed for assessing the forces that can delaminate composite laminates and bonded structures. The approach employs a higher-order plate theory to represent portions of the laminate. The ply properties are integrated through the thickness in a manner that is consistent with the displacement assumptions in the plate theory, thus providing for accurate representation of the stacking sequence effects. In addition to stress analysis, the method also provides the strain energy release rate for the growth of existing delaminations. The analysis has been incorporated into a computer code, TTSS (through thickness stretching and shear). Application examples, including a double cantilever beam and a curved laminate, are examined.

Flanagan, G.↗

NASA NTRS1996

Vibration Characteristics of Partially Covered Double-Sandwich Cantilever Beam

The differential equations of motion together with the boundary conditions for a partially covered, double-sandwich cantilever beam are derived. Bending and extension, rotational and longitudinal inertia of damping layers, and shear deformation and rotational and longitudinal inertia of the constraining layers and the primary beam are included in the equations. The theory is applicable for long as well as short, soft, or stiff damping layer, double-sandwich beams. Also, the effects of different parameters on the system loss factor and resonance frequency are discussed. Differences are found to exist with the previous beam model (called the Euler beam model) when the damping layers are stiff, when the thickness of the damping layer is large compared to the primary-beam thickness, and in the case of higher modes of vibration.

Chen, Qinghua↗

NASA NTRS1988

Optical modeling of a space relay experiment

The optical modeling of laser beam propagation between two points on the earth's surface is discussed with reference to a space relay experiment using relay mirrors on one or more satellites. A two-dimensional laser beam propagation code is applied, and several novel modules are developed to realistically model the environment of the experiment. These are the Kolmogorov atmosphere, a deformable mirror, a segmented aperture, and wind shear. The model allows the calculation of the beam-Strehl ratio and efficiency of the energy transfer for an arbitrary input beam distribution.

Scholl, Marija S.↗

NASA NTRS1994

Method and apparatus for removing unwanted reflections from an interferometer

A device for eliminating unwanted reflections from refractive optical elements in an optical system is provided. The device operates to prevent desired multiple fringe patterns from being obscured by reflections from refractive elements positioned in proximity to a focal plane of the system. The problem occurs when an optical beam is projected into, and reflected back out of, the optical system. Surfaces of the refractive elements reflect portions of the beam which interfere with portions of the beam which are transmitted through the refractive elements. Interference between the reflected and transmitted portions of the beam produce multiple fringe sets which tend to obscure desired interference fringes. With the refractive optical element in close proximity to the focal plane of the system, the undesired reflected light reflects at an angle 180 degrees opposite from the desired transmitted beam. The device exploits the 180-degree offset, or rotational shear, of the undesired reflected light by providing an optical stop for blocking one-half of the cross-section of the test beam. By blocking one-half of the test beam, the undesired offset beam is blocked, while the returning transmitted beam passes into the optical system unaffected. An image is thereby produced from only the desired transmitted beam. In one configuration, the blocking device includes a semicircular aperture which is caused to rotate about the axis of the test beam. By rotating, all portions of the test beam are cyclically projected into the optical system to thereby produce a complete test image. The rotating optical stop is preferably caused to rotate rapidly to eliminate flicker in the resulting image.

Steimle, Lawrence J.↗

NASA NTRS1989

Mixed finite element models for free vibrations of thin-walled 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.

Noor, Ahmed K.↗

NASA NTRS1989

Mixed finite element models for free vibrations of thin-walled beams

Noor, Ahmed K.↗

NASA NTRS2002

Three-Dimensional Postbuckling Analysis of Curved Beams

Presented here is a method of solving highly flexible curved beam undergoing huge static or quasi-static deformations. A geometrically exact beam theory based on the use of Jaumann stresses and strains and exact coordinate transformation is presented in terms of 17 first-order ordinary differential equations, and a multiple shooting method is used to solve the corresponding nonlinear two-point boundary value problems. The geometrically exact beam theory accounts far large rotations, large displacements, initial curvatures, extensionality, and transverse shear strains. Four examples are used to demonstrate this method, including a rotating clamped-free beam under the influence of gravity and centrifugal forces, an L-frame subjected to an in-plane tip load, a circular arch subjected to a concentrated load, and a clamped-hinged helical spring subjected to an axial displacement. Results show that the combination of the multiple shooting method and the geometrically exact beam theory works very well. Moreover, the obtained numerically exact solutions can be used to verify the accuracy of nonlinear finite element codes for nonlinear analysis of complex structures.

Pai, P. Frank↗

NASA NTRS1993

Design of multiple-ply laminated composite tapered beams

A study of a special case of symmetric laminated composite cantilever beams is presented. The approach models beams that are tapered both in depth and width and investigates the effect of the ply layup angle and the ply taper on bending and interlaminar shearing stresses. For the determination of stresses and deflections, the beam stiffness matrices are expressed as linear functions of the beam length. Using classical lamination theory (CLT) the stiffness matrices are determined and assembled at strategic locations along the length of the beam. They are then inverted and necessary stiffness parameters are obtained numerically and extracted for determination of design information at each location chosen. Several ply layup configurations are investigated, and design considerations are presented based on the findings. Finally, recommendations for the design of these beams are presented, and a means for anticipating the location of highest stresses is offered.

Rodriguez, P.↗

NASA NTRS1987

Nonlinear beam kinematics by decomposition of the rotation tensor

A simple matrix expression is obtained for the strain components of a beam in which the displacements and rotations are large. The only restrictions are on the magnitudes of the strain and of the local rotation, a newly-identified kinematical quantity. The local rotation is defined as the change of orientation of material elements relative to the change of orientation of the beam reference triad. The vectors and tensors in the theory are resolved along orthogonal triads of base vectors centered along the undeformed and deformed beam reference axes, so Cartesian tensor notation is used. Although a curvilinear coordinate system is natural to the beam problem, the complications usually associated with its use are circumvented. Local rotations appear explicitly in the resulting strain expressions, facilitating the treatment of beams with both open and closed cross sections in applications of the theory. The theory is used to obtain the kinematical relations for coupled bending, torsion, extension, shear deformation, and warping of an initially curved and twisted beam.

Danielson, D. A.↗

NASA NTRS1987

Nonlinear Beam Kinematics by Decomposition of the Rotation Tensor

A simple matrix expression is obtained for the strain components of a beam in which the displacements and rotations are large. The only restrictions are on the magnitudes of the strain and of the local rotation, a newly-identified kinematical quantity. The local rotation is defined as the change of orientation of material elements relative to the change of orientation of the beam reference triad. The vectors and tensors in the theory are resolved along orthogonal triads of base vectors centered along the undeformed and deformed beam reference axes, so Cartesian tensor notation is used. Although a curvilinear coordinate system is natural to the beam problem, the complications usually associated with its use are circumvented. Local rotations appear explicitly in the resulting strain expressions, facilitating the treatment of beams with both open and closed cross sections in applications of the theory. The theory is used to obtain the kinematical relations for coupled bending, torsion extension, shear deformation, and warping of an initially curved and twisted beam.

Danielson, D. A.↗

NASA NTRS1940

Investigations on the Incompletely Developed Plane Diagonal-Tension Field

This report presents the results of an investigation on the incompletely developed diagonal-tension field. Actual diagonal-tension beams work in an intermediate stage between pure shear and pure diagonal tension; the theory developed by wagner for diagonal tension is not directly applicable. The first part of the paper reviews the most essential items of the theory of pure diagonal tension as well as previous attempts to formulate a theory of incomplete diagonal tension. The second part of the paper describes strain measurement made by the N. A. C. A. to obtain the necessary coefficients for the proposed theory. The third part of the paper discusses the stress analysis of diagonal-tension beams by means of the proposed theory.

Kuhn, Paul↗

DOE OSTI2024

Non-Rare Earth Magnesium Bumper Beams

Magna will team with the Pacific Northwest National Laboratory (PNNL) to develop Shear Assisted Processing and Extrusion (ShAPE™) of rectangular and multi-zoned extrusion profiles using non-RE Mg. It is envisioned that the ShAPE™ process, developed during this project for non-circular profiles, will serve as the foundation for fabrication of full-scale bumper beams of the future where near net-shapes are extruded directly from castings in a single step, without the need for costly rare earth additives. In this project, the ShAPE™ process will be developed for a rectangular profile measuring 1” x 2” with a 0.06” wall thickness. Successful extrusion of rectangular cross sections is a critical step along the path toward profiles with multiple zones. With the process established for a rectangular profile, the project will then make advancements toward multi-zoned cross sections. A magnesium alloy bumper beam offers a 35% weight savings compared to aluminum alloys and 60% compared to high strength steels. The bumper beam was chosen as the first component to target because the geometry can have a fairly simple 0.6-0.12 inch wall/web thickness, generally compatible with PNNL’s knowledge base and equipment capability surrounding ShAPE™. The bumper component offers commercial value by providing mass reduction in the front of the vehicle along with ride and handling benefit. PNNL has demonstrated the ability to ShAPE™ process non-RE Mg tubing with high strength, ductility and energy absorption. It has been shown that ShAPE™ extruded ZK60 and Mg2Si tubing with 0.30 inch diameter and 0.03 inch wall thickness have similar energy absorption to AA6061-T6. This is due to significant grain refinement, breakdown and dispersion of second phases, and the ability to eliminate anisotropy in compressive/tensile strength by aligning texture 45 degrees to the extrusion axis. Scalability of the ShAPE™ process has been demonstrated in ZK60 by fabricating 2.0 inch diameter tubing with 0.06 and 0.12 inch wall thicknesses having concentricity as tight as 1.3%. These tubes exhibit an ultimate tensile strength of 260-300 MPa and room temperature ductility of >20% parallel, perpendicular and 45 degrees to the extrusion axis. Aluminum bumpers represent approximately 54% of the NA light vehicle market. If the research effort is successful, providing a 30% mass reduction at equal cost relative to aluminum bumpers, it is anticipated that 25% market penetration would be realized over the next 5 year and 50% market share by 2030. 100% of the aluminum automotive bumpers are sourced from the tier network, providing resourcing opportunity based on equal performance, reduced mass and cost equivalent lower than aluminum bumpers. Due to the relatively low vehicle content, magnesium components are currently shredded and 100% recycled with aluminum content in the US, presenting a positive life cycle impact.

42 ENGINEERING↗

NASA NTRS1990

Analytical and experimental study of the vibration of bonded beams with a lap joint

A theoretical model to study the flexural vibration of a bonded lap joint system is described in this paper. First, equations of motion at the joint region are derived using a differential element approach. The transverse displacements of the upper and lower beam are considered to be different. The adhesive is assumed to be linearly viscoelastic and the widely used Kelvin-Voight model is used to represent the viscoelastic behavior of the adhesive. The shear force at the interface between the adhesive and the beam is obtained from the simple bending motion equations of the two beams. The resulting equations of motion are combined with the equations of transverse vibration of the beams in the unjointed regions. These are later solved as a boundary value problem to obtain the eigenvalues and eigenvectors of the system. The model can be used to predict the natural frequencies, modal damping ratios, and mode shapes of the system for free vibration. Good agreement between numerical and experimental results was obtained for a system of graphite epoxy beams lap-jointed by an epoxy adhesive.

Rao, M. D.↗

NASA NTRS1992

Shear failure and impact resistance in graphite fiber laminates

The multispan beam (MSB) test was evaluated as a predictor of damage resistance and damage tolerance in quasi-isotropic graphite laminates. Materials studied were five commercial prepreg system using high-strain and intermediate-modulus carbon fibers, as well as an amorphous thermoplastic system. Failure loads and displacements in the MSB tests showed little rate dependence. Values of compressive strength after a standard low-velocity impact correlated fairly well with the MSB results.

Srinivasan, Krishna↗

NASA NTRS1988

Power flow in a beam using a 5-accelerometer probe

A method to determine structure-borne power flow is examined which uses central finite differences to approximate the field variables required to calculate the shear and bending components of flexural vibration. An experimental study using a beam driven by a shaker was performed with the aim of comparing estimates using this proposed five-accelerometer method and the conventional two-accelerometer, free-field method. The advantages and disadvantages of the new method are pointed out.

Downing, J. Micah↗

NASA NTRS2008

Simplified Shear Solution for Determination of the Shear Stress Distribution in a Composite Panel from the Applied Shear Resultant

The simplified shear solution method is presented for approximating the through-thickness shear stress distribution within a composite laminate or panel based on laminated beam theory. The method does not consider the solution of a particular boundary value problem; rather it requires only knowledge of the global shear loading, geometry, and material properties of the laminate or panel. It is thus analogous to lamination theory in that ply level stresses can be efficiently determined from global load resultants (as determined, for instance, by finite element analysis) at a given location in a structure and used to evaluate the margin of safety on a ply by ply basis. The simplified shear solution stress distribution is zero at free surfaces, continuous at ply boundaries, and integrates to the applied shear load. Comparisons to existing theories are made for a variety of laminates, and design examples are provided illustrating the use of the method for determining through-thickness shear stress margins in several types of composite panels and in the context of a finite element structural analysis.

Bednarcyk, Brett A.↗

NASA NTRS1981

Dual-beam skin friction interferometer

A portable dual-laser beam interferometer is described that nonintrusively measures skin friction by monitoring the thickness change of an oil film at two locations while said oil film is subjected to shear stress. An interferometer flat is utilized to develop the two beams. Light detectors sense the beam reflections from the oil film and the surface thereunder. The signals from the detectors are recorded so that the number of interference fringes produced over a given time span may be counted.

Monson, D. J.↗

DOE OSTI2023

Generation and characterization of magnetized electron beam from a DC high voltage photogun for electron beam cooling application

One of the most challenging requirements for the proposed Electron-Ion Collider is the strong cooling of the proton beam, which is key to achieving the collider’s desired luminosity of order 10 33 -10 34 cm -2 s -1 . Magnetized bunched-beam electron cooling could be a means to achieve the required high luminosity, where strong cooling is accomplished inside a cooling solenoid where the ions co-propagate with an electron beam generated from a source immersed in a magnetic field. To increase the cooling efficiency, a bunched electron beam with high bunch charge and high repetition rate is required. This work describes the production and characterization of magnetized electron beam using a compact 300 kV DC high voltage photogun and bi-alkali antimonide photocathode. Beam magnetization was studied using a diagnostic beamline that includes viewer screens for measuring the shearing angle of the electron beamlet passing through a narrow upstream slit. Simulations and corresponding measurements of beam magnetization are presented as a function of laser spot size and magnetic field strength. Correlated beam emittance with magnetic field (0–0.15 T) at the photocathode was measured for various laser spot sizes. Measurements of photocathode lifetime were carried out at different magnetized electron beam currents up to 28 mA, and bunch charge up to 0.7 nC (not simultaneously).

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗