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Results for “Finite deformation theory”

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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Dynamic analysis of pretwisted elastically-coupled rotor blades

The accuracy of using a one-dimensional analysis to predict frequencies of elastically-coupled highly-twisted rotor blades is addressed. Degrees of freedom associated with shear deformation are statically condensed from the formulation, so the analysis uses only those degrees of freedom associated with classical beam theory. The effects of cross section deformation (warping) are considered, and are shown to become significant for some types of elastic coupling. Improved results are demonstrated for highly-coupled blade structures through account of warping in a local cross section analysis, without explicit inclusion of these effects in the beam analysis. A convergence study is also provided which investigates the potential for improving efficiency of elastically-coupled beam analysis through implementation of a p-version beam finite element.

Nixon, Mark W.↗
NASA NTRS1989

Sublaminate analysis of interlaminar fracture in composites. I - Analytical model

A simple analysis method based on a transverse shear-deformation theory and a sublaminate approach is utilized to analyze a mixed-mode edge delamination specimen. The analysis provides closed-form expressions for the interlaminar shear stresses ahead of the crack, the total strain-energy release rate, and the strain-energy release-rate components. The parameters controlling the behavior are identified. The effect of specimen stacking sequence and delamination interface on the strain energy release rate components is investigated. Results are compared with a finite-element simulation for reference. The simple nature of the method makes it suitable for preliminary design analyses which require a large number of configurations to be evaluated quickly and economically.

Armanios, Erian A.↗
DOE OSTI2021

Effect of static local distortions vs. dynamic motions on the stability and band gaps of cubic oxide and halide perovskites

Ternary ABX 3 perovskites made of corner-sharing BX 6 octahedra have long featured prominently in solid-state chemistry and condensed matter physics. Still, the joint understanding of their two main subgroups—halides and oxides—has not been fully developed. Indeed, unlike the case in simpler compounds having a single, robust repeated motif (“monomorphous”), certain cubic perovskites can manifest a non-thermal (= intrinsic) distribution of local motifs (“polymorphous networks”). Such static deformations can include positional degrees of freedom (e.g., atomic displacements and octahedral tilting) or magnetic moment degrees of freedom in paramagnets. Unlike thermal motion, such static distortions do not time-average to zero, being an expression of the intrinsic symmetry breaking preference of the chemical bonding. Here, the present study compares electronic structure features of oxide and halide perovskites starting from the static polymorphous distribution of motifs described by Density Functional Theory (DFT) minimization of the internal energy, continuing to finite temperature thermal disorder modeled via finite temperature DFT molecular dynamics. We find that (i) different oxide vs. halide ABX 3 compounds adopt different energy-lowering symmetry-breaking modes. The calculated pair distribution function (PDF) of SrTiO 3 from the first-principles agrees with recently measured PDF. (ii) In both oxides and halides, such static distortions lead to band gap blueshifts with respect to undistorted cubic Pm-3m structure. (iii) For oxide perovskites, high-temperature molecular dynamics simulations initiated from the statically distorted polymorphous structures reveal that the thermally-induced distortions can lead to a band gap redshift. (iv) In contrast, for cubic halide perovskite CsPbI 3 , both the intrinsic distortions and the thermal distortions contribute in tandem to band gap blueshift, the former, intrinsic effect being dominant. (v) In the oxide SrTiO 3 and CaTiO 3 (but not in halide) perovskites, octahedral tilting leads to the emergence of a distinct Γ–Γ direct band gap component as a secondary valley minimum to the well-known indirect R–Γ gap. Understanding such intrinsic vs. thermal effects on oxide vs. halide perovskites holds the potential for designing target electronic properties.

36 MATERIALS SCIENCE↗
NASA NTRS2005

Computing Gravitational Fields of Finite-Sized Bodies

A computer program utilizes the classical theory of gravitation, implemented by means of the finite-element method, to calculate the near gravitational fields of bodies of arbitrary size, shape, and mass distribution. The program was developed for application to a spacecraft and to floating proof masses and associated equipment carried by the spacecraft for detecting gravitational waves. The program can calculate steady or time-dependent gravitational forces, moments, and gradients thereof. Bodies external to a proof mass can be moving around the proof mass and/or deformed under thermoelastic loads. An arbitrarily shaped proof mass is represented by a collection of parallelepiped elements. The gravitational force and moment acting on each parallelepiped element of a proof mass, including those attributable to the self-gravitational field of the proof mass, are computed exactly from the closed-form equation for the gravitational potential of a parallelepiped. The gravitational field of an arbitrary distribution of mass external to a proof mass can be calculated either by summing the fields of suitably many point masses or by higher-order Gauss-Legendre integration over all elements surrounding the proof mass that are part of a finite-element mesh. This computer program is compatible with more general finite-element codes, such as NASTRAN, because it is configured to read a generic input data file, containing the detailed description of the finiteelement mesh.

Quadrelli, Marco↗
NASA NTRS2016

Applications of Displacement Transfer Functions to Deformed Shape Predictions of the G-III Swept-Wing Structure

In support of the Adaptive Compliant Trailing Edge [ACTE] project at the NASA Armstrong Flight Research Center, displacement transfer functions were applied to the swept wing of a Gulfstream G-III airplane (Gulfstream Aerospace Corporation, Savannah, Georgia) to obtain deformed shape predictions. Four strainsensing lines (two on the lower surface, two on the upper surface) were used to calculate the deformed shape of the G III wing under bending and torsion. There being an insufficient number of surface strain sensors, the existing G III wing box finite element model was used to generate simulated surface strains for input to the displacement transfer functions. The resulting predicted deflections have good correlation with the finite-element generated deflections as well as the measured deflections from the ground load calibration test. The convergence study showed that the displacement prediction error at the G III wing tip can be reduced by increasing the number of strain stations (for each strain-sensing line) down to a minimum error of l.6 percent at 17 strain stations; using more than 17 strain stations yielded no benefit because the error slightly increased to 1.9% when 32 strain stations were used.

displacement theory↗
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 NTRS1990

Postbuckling response of long thick plates loaded in compression including higher order transverse shearing effects

Buckling and postbuckling results are presented for compression-loaded simply-supported aluminum plates and composite plates with a symmetric lay-up of thin + or - 45 deg plies composed of many layers. Buckling results for aluminum plates of finite length are given for various length-to-width ratios. Asymptotes to the curves based on buckling results give N(sub xcr) for plates of infinite length. Postbuckling results for plates with transverse shearing flexibility are compared to results from classical theory for various width-to-thickness ratios. Characteristic curves indicating the average longitudinal direct stress resultant as a function of the applied displacements are calculated based on four different theories: Classical von Karman theory using the Kirchoff assumptions, first-order shear deformation theory, higher-order shear deformation theory, and 3-D flexibility theory. Present results indicate that the 3-D flexibility theory gives the lowest buckling loads. The higher-order shear deformation theory has fewer unknowns than the 3-D flexibility theory but does not take into account through-the-thickness effects. The figures presented show that small differences occur in the average longitudinal direct stress resultants from the four theories that are functions of applied end-shortening displacement.

Stein, Manuel↗
NASA NTRS1990

Postbuckling response of long thick plates loaded in compression including higher order transverse shearing effects

This paper presents buckling and postbuckling results for compression-loaded simply-supported aluminum plates and composite plates with a symmetric lay-up of thin +/-45-deg plies composed of many layers. Buckling results for aluminum plates of finite length are given for various length-to-width ratios. Asymptotes to the curves based on the buckling results give N(XCr) for plates of infinite length. Postbuckling results for plates with transverse shearing flexibility are compared to results from classical theory for various width-to-thickness ratios. Characteristic curves indicating the average longitudinal direct stress resultant as a function of the applied displacements are calculated based on four different theories: classical von Karman theory using the Kirchhoff assumptions, first-order shear deformation theory, higher-order shear deformation theory, and three-dimensional flexibility theory. Present results indicate that the three-dimensional flexibility theory gives the lowest buckling loads. The higher-order shear deformation theory has fewer unknowns than the three-dimensional flexibility theory but does not take into account through-the-thickness effects. The figures presented show that small differences occur in the average longitudinal direct stress resultants from the four theories that are functions of applied end-shortening displacement.

Stein, Manuel↗
NASA NTRS2000

Optical Performance Modeling of FUSE Telescope Mirror

We describe the Metrology Data Processor (METDAT), the Optical Surface Analysis Code (OSAC), and their application to the image evaluation of the Far Ultraviolet Spectroscopic Explorer (FUSE) mirrors. The FUSE instrument - designed and developed by the Johns Hopkins University and launched in June 1999 is an astrophysics satellite which provides high resolution spectra (lambda/Delta(lambda) = 20,000 - 25,000) in the wavelength region from 90.5 to 118.7 nm The FUSE instrument is comprised of four co-aligned, normal incidence, off-axis parabolic mirrors, four Rowland circle spectrograph channels with holographic gratings, and delay line microchannel plate detectors. The OSAC code provides a comprehensive analysis of optical system performance, including the effects of optical surface misalignments, low spatial frequency deformations described by discrete polynomial terms, mid- and high-spatial frequency deformations (surface roughness), and diffraction due to the finite size of the aperture. Both normal incidence (traditionally infrared, visible, and near ultraviolet mirror systems) and grazing incidence (x-ray mirror systems) systems can be analyzed. The code also properly accounts for reflectance losses on the mirror surfaces. Low frequency surface errors are described in OSAC by using Zernike polynomials for normal incidence mirrors and Legendre-Fourier polynomials for grazing incidence mirrors. The scatter analysis of the mirror is based on scalar scatter theory. The program accepts simple autocovariance (ACV) function models or power spectral density (PSD) models derived from mirror surface metrology data as input to the scatter calculation. The end product of the program is a user-defined pixel array containing the system Point Spread Function (PSF). The METDAT routine is used in conjunction with the OSAC program. This code reads in laboratory metrology data in a normalized format. The code then fits the data using Zernike polynomials for normal incidence systems or Legendre-Fourier polynomials for grazing incidence systems. It removes low order terms from the metrology data, calculates statistical ACV or PSD functions, and fits these data to OSAC models for the scatter analysis. In this paper we briefly describe the laboratory image testing of FUSE spare mirror performed in the near and vacuum ultraviolet at John Hopkins University and OSAC modeling of the test setup performed at NASA/GSFC. The test setup is a double-pass configuration consisting of a Hg discharge source, the FUSE off-axis parabolic mirror under test, an autocollimating flat mirror, and a tomographic imaging detector. Two additional, small fold flats are used in the optical train to accommodate the light source and the detector. The modeling is based on Zernike fitting and PSD analysis of surface metrology data measured by both the mirror vendor (Tinsley) and JHU. The results of our models agree well with the laboratory imaging data, thus validating our theoretical model. Finally, we predict the imaging performance of FUSE mirrors in their flight configuration at far-ultraviolet wavelengths.

Saha, Timo T.↗
NASA NTRS1986

Application of multiple objective optimization techniques to finite element model tuning

This report examines tuning a finite element model using vector optimization techniques. Structural models using finite element theory often need to be adjusted so they can accurately simulate the real structure. The goal is to tune the model such that it will reproduce data derived from structural tests. First, the performance indices are extremized using multiple objective optimization theory, producing a set of possible solutions. Next, the solutions are rank ordered according to a decision maker's preferences to select the best answer. The tuning process was applied to a T-38 horizontal stabilizer. Numerous weighted solutions contained a best static deformation model, a best frequency model and three intermediate combinations of these two models. This automated procedure proved to be a versatile method capable of producing solutions for many types of tuning problems.

Devore, Charles R.↗
NASA NTRS1994

Equivalent plate structural modeling for wing shape optimization including transverse shear

A new technique for structural modeling of airplanes wings is presented taking transverse shear effects into account. The kinematic assumptions of first-order shear deformation plate theory in combination with numerical analysis, where simple polynomials are used to define geometry, construction, and displacement approximations, lead to analytical expressions for elements of the stiffness and mass matrices and load vector. Contributions from the cover skins, spar and rib caps, and spar and rib webs are included as well as concentrated springs and concentrated masses. Limitations of wing modeling techniques based on classical plate theory are discussed, and the improved accuracy of the new equivalent plate technique is demonstrated through comparison with finite element analysis and test results. Expressions for analytical derivatives of stiffness, mass, and load terms with respect to wing shape are given. Based on these, it is possible to obtain analytic sensitivities of displacements, stresses, and natural frequencies with respect to planform shape and depth distribution. This makes the new capability an effective structural tool for wing shape optimization.

Livne, Eli↗
NASA NTRS1994

Equivalent Plate Structural Modeling for Wing Shape Optimization Including Transverse Shear

A new technique for structural modeling of airplane wings is presented taking transverse shear effects into account. The kinematic assumptions of first-order shear deformation plate theory In combination with numerical analysis, where simple polynomials are used to define geometry, construction, and displacement approximations, lead to analytical expressions for elements of the stiffness and mass matrices and load vector. Contributions from the cover skins, spar and rib caps, and spar and rib webs are included as well as concentrated springs and concentrated masses. Limitations of wing modeling techniques based on classical plate theory are discussed, and the Improved accuracy of the new equivalent plate technique is demonstrated through comparison with finite element analysis and test results. Expressions for analytical derivatives of stiffness, mass, and load terms with respect to wing shape are given. Based on these, it is possible to obtain analytic sensitivities of displacements, stresses, and natural frequencies with respect to planform shape and depth distribution. This makes the new capability an effective structural tool for wing shape optimization.

Livne, Eli↗
NASA NTRS1998

Influence of Material Distribution on Impact Resistance of Hybrid Composites

Impact events occur in a wide variety of circumstances. A typical example is a bullet impacting a target made of composite material. These impact events produce time-varying loads on a structure that can result in damage. As a first step to understanding the damage resistance issue in composite laminates, an accurate prediction of the transient response during an impact event is necessary. The analysis of dynamic loadings on laminated composite plates has undergone considerable development recently. Rayleigh-Ritz energy method was used to determine the impact response of laminated plates. The impact response of composite plates using shear deformation plate theory was analyzed. In recent work a closed-form solution was obtained for a rectangular plate with four edges simply supported subjected to a center impact load using classical plate theory. The problem was further investigated and the analysis results compared of both classical plate theory and shear deformation theory, and found that classical plate theory predicts very accurate results for the range of small deformations considered. In this study, the influence of cross sectional material distribution on the comparative impact responses of hybrid metal laminates subjected to low and medium velocity impacts is investigated. A simple linear model to evaluate the magnitude of the impact load is proposed first, and it establishes a relation between the impact velocity and the impact force. Then a closed-form solution for impact problem is presented. The results were compared with the finite element analysis results. For an 11 layer-hybrid laminate, the impact response as a function of material distribution in cross-section is presented. With equal areal weight, the effect of the number of laminate layers on the impact resistance is also investigated. Finally, the significance of the presented results is discussed.

Abatan, Ayu↗
NASA NTRS1985

Constitutive Modeling of Superalloy Single Crystals and Directionally Solidified Materials

A unified viscoplastic constitutive relation based on crystallographic slip theory was developed for the deformation analysis of nickel base face centered cubic superalloy single crystals at elevated temperature. The single crystal theory is embedded in a self consistent method to derive a constitutive relation for a directionally solidified material comprised of a polycrystalline aggregate of columnar cylindrical grains. One of the crystallographic axes of the cylindrical crystals points in the columnar direction while the remaining crystallographic axes are oriented at random in the basal plane perpendicular to the columnar direction. These constitutive formulations are coded in FORTRAN for use in nonlinear finite element and boundary element programs.

Walker, K. P.↗
NASA NTRS1993

Recent developments in equivalent plate modeling for wing shape optimization

A new technique for structural modeling of airplane wings is presented taking transverse shear effects into account. The kinematic assumptions of first order shear deformation plate theory in combination with numerical analysis based on simple polynomials which define geometry, construction and displacement approximations lead to analytical expressions for elements of the stiffness and mass matrices and load vector. Contributions from the cover skins, spar and rib caps and spar and rib webs are included as well as concentrated springs and concentrated masses. Limitations of current equivalent plate wing modeling techniques based on classical plate theory are discussed, and the improved accuracy of the new equivalent plate technique is demonstrated through comparison to finite element analysis and test results. Analytical derivatives of stiffness, mass and load terms with respect to wing shape lead to analytic sensitivities of displacements, stresses and natural modes with respect to planform shape and depth distribution. This makes the new capability an effective structural tool for wing shape optimization.

Livne, Eli↗
NASA NTRS2024

Out of Plane Stresses Using a Beam-Based Elastic Foundation Bonded Joint Model

Efficient, semi-analytical models of bonded joints are utilized for initial joint design and sizing due to their convenience and speed. Many of these models are based on beam and plate theories, which are most applicable when in-plane stresses/strains dominate. While this can be a sensible assumption for obtaining the deformations of the joint, out of plane (transverse) stresses are often of critical importance for failure in bonded joints composed of fiber reinforced composite materials. Since through-thickness strains are neglected in these semi-analytical theories, the present study shows a method to back-calculate the out of plane stresses based on stress balance equations, which use the in-plane stresses and displacements that have already been obtained. The method was implemented within the Joint Element Designer (JED) software, and verification and validation examples have been shown. As is typical for these types of models, corner stress singularities are not captured by the JED model, but the general trends of the stress and deformation fields agreed with a higher fidelity finite element model. As such, this method for obtaining out of plane stresses, when coupled with the JED code, is very useful for the complete stress analysis of bonded composite joints.

composites↗
NASA NTRS2021

Numerical Validation of Composite Panel Impact Tests

Researchers have met the challenge of modeling impact events involving composite targets for a variety of applications in a variety of ways. In this paper, the theory and implementation details of an orthotropic visco-elastic-visco-plastic material model with strain rate dependence are discussed. The model is driven by experimental data from quasi-static as well as high strain rate tests, and the data is used in defining the deformation, damage and failure sub-models. Validation data is generated by shooting a hollow 50 g Al-2024 projectile at different velocities against a flat panel target made of unidirectional composite material in a 16-ply [(0/90/45/-45)_(2)]_(S) layup. Explicit dynamic finite element analyses of four high speed tests involving one contained (projectile rebounded) and three uncontained (projectile penetrated) impact tests show that the developed material model and modeling techniques yield reasonable and acceptable predictions.

Orthotropic Composite↗
DOE OSTI2024

Chiral limit of 2d QCD revisited with lightcone conformal truncation

We study the chiral limit of 2d QCD with a single quark flavor at finite Nc using LCT. By modifying the LCT basis according to the quark mass in a manner motivated by ’t Hooft’s analysis, we are able to restore convergence for quark masses much smaller than the QCD strong coupling scale. For such small quark masses, the IR of the theory is expected to be well described by the Sine-Gordon model. We verify that LCT numerics are able to capture in detail the spectrum and correlation functions of the Sine-Gordon model. This opens up the possibility for studying deformations of various integrable CFTs using LCT by considering the chiral limit of QCD like theories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗