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Results for “Elastic bending energy”

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NASA NTRS1974

Photomechanical vibration of thin crystals of polar semiconductors

It was found that thin crystals of polar (non-centrosymmetric) semiconductors constitute a new type of photosensitive system in which incident illumination is converted into mechanical energy: thus, illumination-induced elastic deformation (bending) was observed on thin (00.1) CdS and (111) GaAs crystals; furthermore, by employing chopped light the crystals were excited to their resonant vibration (photomechanical vibration); the dependence of the amplitude of this vibration on the energy of the incident radiation was found to be similar to the dependence of the surface photovoltage on the energy of the incident radiation (surface photovoltage spectrum). The present findings are consistent with a model based on light-induced modulation of the piezoelectric surface stresses.

Lagowski, J.↗

NASA NTRS1997

The Upper Atmosphere Research Satellite In-Flight Dynamics

Upper Atmosphere Research Satellite flight data from the first 737 days after launch (September 1991) was used to investigate spacecraft disturbances and responses. The investigation included two in-flight dynamics experiments (approximately three orbits each). Orbital and configuration influences on spacecraft dynamic response were also examined. Orbital influences were due to temperature variation from crossing the Earth's terminator and variation of the solar incident energy as the orbit precessed. During the terminator crossing, the rapid ambient temperature change caused the spacecraft's two flexible appendages to experience thermal elastic bending (thermal snap). The resulting response was dependent upon the orientation of the solar array and the solar incident energy. Orbital influences were also caused by on-board and environmental disturbances and spacecraft configuration changes resulting in dynamic responses which were repeated each orbit. Configuration influences were due to solar array rotation changing spacecraft modal properties. The investigation quantified the spacecraft dynamic response produced by the solar array and high gain antenna harmonic drive disturbances. The solar array's harmonic drive output resonated two solar array modes. Friction in the solar array gear drive provided sufficient energy dissipation which prevented the solar panels from resonating catastrophically; however, the solar array vibration amplitude was excessively large. The resulting vibration had a latitude-specific pattern.

Woodard, Stanley E.↗

NASA NTRS1976

Sensitivity of inelastic response to numerical integration of strain energy

The exact solution to the quasi-static, inelastic response of a cantilever beam of rectangular cross section subjected to a bending moment at the tip is obtained. The material of the beam is assumed to be linearly elastic-linearly strain-hardening. This solution is then compared with three different numerical solutions of the same problem obtained by minimizing the total potential energy using Gaussian quadratures of two different orders and a Newton-Cotes scheme for integrating the strain energy of deformation. Significant differences between the exact dissipative strain energy and its numerical counterpart are emphasized. The consequence of this on the nonlinear transient responses of a beam with solid cross section and that of a thin-walled beam on elastic supports under impulsive loads are examined.

Kamat, M. P.↗

NASA NTRS2018

New O+CO2 Scattering Cross Sections and Their Impact on Photochemical Atmospheric Escape of Oxygen from Mars

Dissociative recombination of O2+ and CO2+ molecular ions in the upper atmosphere of Mars is a major source of suprathermal (hot) oxygen atoms. A significant fraction of hot O atoms are sufficiently fast to overcome Mars' gravitational potential and escape to space. This mechanism is known as photochemical escape (PE) and found to be one of the major escape mechanisms presently active on Mars. The Mars Atmosphere and Volatile Evolution Mission (MAVEN) can constrain the PE rate from measurements of electron temperature and density and ion temperature and density. Escape probabilities of hot O can then be constructed from in-situ neutral densities and escaping O flux loss due to collisions with atmospheric background gases. Due to CO2 abundance in the upper atmosphere, O+CO2 scattering is the most important sink of the escaping hot O flux that strongly affects estimates of total atomic oxygen escape rate obtained from MAVEN data, as outlined above. New O+CO2 elastic and inelastic cross sections were constructed from first principles for collision energies from 0.01-5 eV. O(3P)+CO2 collisions were described using new 4D electronic potential energy surfaces (PESs) for restricted geometries. Three lowest triplet states of CO2 were considered for symmetric, bending, and asymmetric vibrational modes. The cross sections were determined from close-coupling calculations performed on individual surfaces using vibrating rotor approximations for CO2 molecule. Differential and momentum transfer cross sections, of use in energy transfer atmospheric models, were also constructed. The obtained cross sections are in excellent agreement with published results. Our new elastic cross sections are significantly smaller than assumed in earlier atmospheric escape models, resulting in larger photochemical escape rate of O from Mars, as estimated from a 1D escape model. Our results agree well with estimated hot O flux (about 9 x 10(sup 25) s(sup -1)) derived from altitude profiles of 130.4 nm O emission measured up to ~4,000 km by the Imaging Ultraviolet Spectrograph on MAVEN orbiter.

Atmospheric↗

NASA NTRS1950

Contribution to the problem of buckling of orthotropic plates, with special reference to plywood

Planar stress-strain relations and bending stress-strain relations are presented for elastic orthotropic plates and specialized to plywood. These relations are used to derive the differential equation and energy expression for the buckling of orthotropic rectangular plates whose principal stiffness directions are not parallel to the plate edges. Buckling analyses are made for the case of pure compression and pure shear of a long plate-strip.

WOODS↗

NASA NTRS1983

Effect of load introduction in compression testing of composite laminates

Compression testing of composite materials is affected by the manner in which the compressive load is introduced. Two such effects are studied in this paper: (a) the constrained edge effect, in which transverse expansion of the edges is prevented while the axial load is introduced, and (b) nonuniform gripping, as manifested by inplane bending of the test specimen. The principle of minimum complementary energy is used to develop an analytical model that quantifies these two effects upon the measured elastic properties of laminated composites. Numerical results are presented for selected high-strength graphite/epoxy composites.

Reiss, R.↗

NASA NTRS1978

Transverse shear stiffness of laminated anisotropic shells

Equations are derived for the transverse shear stiffness of laminated anisotropic shells. Without making assumptions for thickness distribution for either transverse shear stresses or strains, constitutive equations for the transverse shear deformation theory of anisotropic heterogeneous shells are found. The equations are based on Taylor series expansions about a generic point for stress resultants and couples, identically satisfying plate equilibrium equations. These equations are used to find statically correct expressions for in-surface stresses, transverse shear stresses, and the area density of transverse shear strain energy, in terms of transverse shear stress resultants and redundants. The application of Castigliano's theorem of least work minimizes shear strain energy with respect to the redundants. Examples are presented for several laminated walls. Good agreement is found between the results and those of exact three-dimensional elasticity solutions for the cylindrical bending of a plate.

Cohen, G. A.↗

NASA NTRS2005

Stress Analysis of Composite Cylindrical Shells With an Elliptical Cutout

A special-purpose, semi-analytical solution method for determining the stress and deformation fields in a thin laminated-composite cylindrical shell with an elliptical cutout is presented. The analysis includes the effects of cutout size, shape, and orientation; nonuniform wall thickness; oval-cross-section eccentricity; and loading conditions. The loading conditions include uniform tension, uniform torsion, and pure bending. The analysis approach is based on the principle of stationary potential energy and uses Lagrange multipliers to relax the kinematic admissibility requirements on the displacement representations through the use of idealized elastic edge restraints. Specifying appropriate stiffness values for the elastic extensional and rotational edge restraints (springs) allows the imposition of the kinematic boundary conditions in an indirect manner, which enables the use of a broader set of functions for representing the displacement fields. Selected results of parametric studies are presented for several geometric parameters that demonstrate that analysis approach is a powerful means for developing design criteria for laminated-composite shells.

Nemeth, M. P.↗

NASA NTRS2007

Stress Analysis of Composite Cylindrical Shells with an Elliptical Cutout

A special-purpose, semi-analytical solution method for determining the stress and deformation fields in a thin laminated-composite cylindrical shell with an elliptical cutout is presented. The analysis includes the effects of cutout size, shape, and orientation; non-uniform wall thickness; oval-cross-section eccentricity; and loading conditions. The loading conditions include uniform tension, uniform torsion, and pure bending. The analysis approach is based on the principle of stationary potential energy and uses Lagrange multipliers to relax the kinematic admissibility requirements on the displacement representations through the use of idealized elastic edge restraints. Specifying appropriate stiffness values for the elastic extensional and rotational edge restraints (springs) allows the imposition of the kinematic boundary conditions in an indirect manner, which enables the use of a broader set of functions for representing the displacement fields. Selected results of parametric studies are presented for several geometric parameters that demonstrate that analysis approach is a powerful means for developing design criteria for laminated-composite shells.

Oterkus, E.↗

NASA NTRS1954

A Nonlinear Theory of Bending and Buckling of Thin Elastic Shallow Spherical Shells

The problem of the finite displacement and buckling, of a shallow spherical dome is investigated both theoretically and experimentally. Experimental results seem to indicate that the classical criterion of buckling is applicable to very shallow spherical domes for which the theoretical calculation was made. A transition to energy criterion for higher domes is also indicated.

Kaplan, A↗

NASA NTRS1987

A simple and efficient shear-flexible plate bending element

A shear-flexible triangular element formulation, which utilizes an assumed quadratic displacement potential energy approach and is numerically integrated using Gauss quadrature, is presented. The Reissner/Mindlin hypothesis of constant cross-sectional warping is directly applied to the three-dimensional elasticity theory to obtain a moderately thick-plate theory or constant shear-angle theory (CST), wherein the middle surface is no longer considered to be the reference surface and the two rotations are replaced by the two in-plane displacements as nodal variables. The resulting finite-element possesses 18 degrees of freedom (DOF). Numerical results are obtained for two different numerical integration schemes and a wide range of meshes and span-to-thickness ratios. These, when compared with available exact, series or finite-element solutions, demonstrate accuracy and rapid convergence characteristics of the present element. This is especially true in the case of thin to very thin plates, when the present element, used in conjunction with the reduced integration scheme, outperforms its counterpart, based on discrete Kirchhoff constraint theory (DKT).

Chaudhuri, Reaz A.↗

NASA NTRS1989

Extension-torsion coupling behavior of advanced composite tilt-rotor blades

An analytic model was developed to study the extension-bend-twist coupling behavior of an advanced composite helicopter or tilt-rotor blade. The outer surface of the blade is defined by rotating an arbitrary cross section about an initial twist axis. The cross section can be nonhomogeneous and composed of generally anisotropic materials. The model is developed based upon a three dimensional elasticity approach that is recast as a coupled two-dimensional boundary value problem defined in a curvilinear coordinate system. Displacement solutions are written in terms of known functions that represent extension, bending, and twisting and unknown functions for local cross section deformations. The unknown local deformation functions are determined by applying the principle of minimum potential energy to the discretized two-dimensional cross section. This is an application of the Ritz method, where the trial function family is the displacement field associated with a finite element (8-node isoparametric quadrilaterals) representation of the section. A computer program was written where the cross section is discretized into 8-node quadrilateral subregions. Initially the program was verified using previously published results (both three-dimensional elasticity and technical beam theory) for pretwisted isotropic bars with an elliptical cross section. In addition, solid and thin-wall multi-cell NACA-0012 airfoil sections were analyzed to illustrate the pronounced effects that pretwist, initial twist axis location, and spar location has on coupled behavior. Currently, a series of advanced composite airfoils are being modeled in order to assess how the use of laminated composite materials interacts with pretwist to alter the coupling behavior of the blade. These studies will investigate the use of different ply angle orientations and the use of symmetric versus unsymmetric laminates.

Kosmatka, J. B.↗

NASA NTRS1993

A theory for the fracture of thin plates subjected to bending and twisting moments

Stress fields near the tip of a through crack in an elastic plate under bending and twisting moments are reviewed assuming both Kirchhoff and Reissner plate theories. The crack tip displacement and rotation fields based on the Reissner theory are calculated. These results are used to calculate the J-integral (energy release rate) for both Kirchhoff and Reissner plate theories. Invoking Simmonds and Duva's (1981) result that the value of the J-integral based on either theory is the same for thin plates, a universal relationship between the Kirchhoff theory stress intensity factors and the Reissner theory stress intensity factors is obtained for thin plates. Calculation of Kirchhoff theory stress intensity factors from finite elements based on energy release rate is illustrated. It is proposed that, for thin plates, fracture toughness and crack growth rates be correlated with the Kirchhoff theory stress intensity factors.

Hui, C. Y.↗

NASA NTRS1983

Impact damage resistance of flat glass/cellular glass solar mirror experimental panels

An attempt is made to characterize the hail-impact behavior of a solar concentrator structural material which consists of thin, second-surface silvered glass sheets bonded to structural support panels of cellular glass. The resulting glass/cellular glass panel can be described as a thin, brittle plate supported by an elastic foundation, with the adhesive bonding the two as a third component. The plate will bend during impact. Attention is experimentally given to how variations in the characteristics or geometry of the flat glass, adhesive and cellular glass affect hail-impact damage resistance. The critical energy needed to cause impact damage is calculated from the critical velocity of the iceball by means of the kinetic energy formula. The complexity of this structural system and the variability of the specimens render it impossible to completely develop an analytical treatment for the prediction of impact damage resistance.

Varner, J. R.↗

NASA NTRS1992

Delamination failure in a unidirectional curved composite laminate

Delamination failure in a unidirectional curved composite laminate was investigated. The curved laminate failed unstably by delaminations developing around the curved region of the laminate at different depths through the thickness until virtually all bending stiffness was lost. Delamination was assumed to initiate at the location of the highest radial stress in the curved region. A closed form curved beam elasticity solution and a 2D finite element analysis (FEA) were conducted to determine this location. The variation in the strain energy release rate, G, with delamination growth was then determined using the FEA. A strength-based failure criteria adequately predicted the interlaminar tension failure which caused initial delamination onset. Using the G analysis the delamination was predicted to extend into the arm and leg of the laminate, predominantly in mode I. As the initial delamination grew around the curved region, the maximum radial stress in the newly formed inner sublaminate increased to a level sufficient to cause a new delamination to initiate in the sublaminate with no increase in applied load. This failure progression was observed experimentally.

Martin, Roderick H.↗

NASA NTRS1962

BUCKLING AND POST-BUCKLING OF ELASTIC SHELLS

Some theoretical investigations of buckling of elastic shells are surveyed in this report. Only geometrically perfect shells are considered; initial dents and out-of-roundness are not taken into account. Several questions raised by the studies are: (a) Under what conditions is the infinitesimal theory of buckling of shells adequate? (b) How does the energy theory of buckling of shells correlate with the method based on equilibrium equations for bending moments, tensions, and shears in a buckled configuration? (c) How important are nonlinear terms in the tangential displacements u, v in the strain-displacement relations for buckling and post-buckling studies? (d) How important are the boundary conditions for u, v in affecting stability? (e) If a condition of snap-through is approached, how much external work is required to push the shell "over the hump" into the buckled configuration? (f) How reliable are mathematical approximations used previously in the infinitesimal theory of buckling of shells? Tentative and incomplete answers to some of these questions are suggested.

ELASTIC BUCKLING↗

NASA NTRS1990

Delamination failure in a unidirectional curved composite laminate

Delamination failure in a unidirectional curved composite laminate was investigated. The curved laminate failed unstably by delaminations developing around the curved region of the laminate at different depths through the thickness until virtually all bending stiffness was lost. Delamination was assumed to initiate at the location of the highest radial stress in the curved region. A closed form curved beam elasticity solution and a 2-D finite element analysis (FEA) were conducted to determine this location. The variation in the strain energy release rate, G, with delamination growth was then determined using the FEA. A strength-based failure criteria adequately predicted the interlaminar tension failure which caused initial delamination onset. Using the G analysis the delamination was predicted to extend into the arm and leg of the laminate, predominantly in mode I. As the initial delamination grew arould the curved region, the maximum radial stress in the newly formed inner sublaminate increased to a level sufficient to cause a new delamination to initiate in the sublaminate with no increase in applied load. This failure progression was observed experimentally.

Martin, Roderick H.↗

NASA NTRS1992

A three-dimensional nonlinear Timoshenko beam based on the core-congruential formulation

A three-dimensional, geometrically nonlinear two-node Timoshenkoo beam element based on the total Larangrian description is derived. The element behavior is assumed to be linear elastic, but no restrictions are placed on magnitude of finite rotations. The resulting element has twelve degrees of freedom: six translational components and six rotational-vector components. The formulation uses the Green-Lagrange strains and second Piola-Kirchhoff stresses as energy-conjugate variables and accounts for the bending-stretching and bending-torsional coupling effects without special provisions. The core-congruential formulation (CCF) is used to derived the discrete equations in a staged manner. Core equations involving the internal force vector and tangent stiffness matrix are developed at the particle level. A sequence of matrix transformations carries these equations to beam cross-sections and finally to the element nodal degrees of freedom. The choice of finite rotation measure is made in the next-to-last transformation stage, and the choice of over-the-element interpolation in the last one. The tangent stiffness matrix is found to retain symmetry if the rotational vector is chosen to measure finite rotations. An extensive set of numerical examples is presented to test and validate the present element.

Crivelli, Luis A.↗