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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

A posteriori estimates for shear correction factors in multilayered composite cylinders

A predictor-corrector approach is presented for calculating the composite shear correction factors and analyzing multilayered composite cylinders. In the predictor phase a two-dimensional first-order shear deformation theory is used to predict the gross response characteristics of the cylinder (vibration frequencies, average through-the-thickness displacements, rotations, and transverse shear strain energy per unit area) as well as the in-plane strains and stresses in the thickness direction. The three-dimensional equilibrium equations and constitutive relations are then used to compute the transverse stresses and strains as well as the transverse shear factors, and they are also used to correct the predicted response quantities of the cylinder. For simply supported multilayered cylinders the response quantities obtained by using the proposed approach are shown to be in close agreement with three-dimensional elasticity solutions for a wide range of lamination and geometric parameters. Also, the potential of the proposed approach for use in conjunction with large-scale finite element models of composite cylinders is outlined.

Noor, Ahmed K.↗
DOE OSTI2020

General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part II

X-ray Bragg coherent diffraction imaging (BCDI) has been demonstrated as a powerful 3D microscopy approach for the investigation of sub-micrometre-scale crystalline particles. The approach is based on the measurement of a series of coherent Bragg diffraction intensity patterns that are numerically inverted to retrieve an image of the spatial distribution of the relative phase and amplitude of the Bragg structure factor of the diffracting sample. This 3D information, which is collected through an angular rotation of the sample, is necessarily obtained in a non-orthogonal frame in Fourier space that must be eventually reconciled. To deal with this, the approach currently favored by practitioners (detailed in Part I) is to perform the entire inversion in conjugate non-orthogonal real- and Fourier-space frames, and to transform the 3D sample image into an orthogonal frame as a post-processing step for result analysis. In this article, which is a direct follow-up of Part I, two different transformation strategies are demonstrated, which enable the entire inversion procedure of the measured data set to be performed in an orthogonal frame. The new approaches described here build mathematical and numerical frameworks that apply to the cases of evenly and non-evenly sampled data along the direction of sample rotation ( i.e. the rocking curve). The value of these methods is that they rely on the experimental geometry, and they incorporate significantly more information about that geometry into the design of the phase-retrieval Fourier transformation than the strategy presented in Part I. Finally, two important outcomes are (1) that the resulting sample image is correctly interpreted in a shear-free frame and (2) physically realistic constraints of BCDI phase retrieval that are difficult to implement with current methods are easily incorporated. Computing scripts are also given to aid readers in the implementation of the proposed formalisms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part I

This two-part article series provides a generalized description of the scattering geometry of Bragg coherent diffraction imaging (BCDI) experiments, the shear distortion effects inherent in the 3D image obtained from presently used methods and strategies to mitigate this distortion. Part I starts from fundamental considerations to present the general real-space coordinate transformation required to correct this shear, in a compact operator formulation that easily lends itself to implementation with available software packages. Such a transformation, applied as a final post-processing step following phase retrieval, is crucial for arriving at an undistorted, correctly oriented and physically meaningful image of the 3D crystalline scatterer. As the relevance of BCDI grows in the field of materials characterization, the available sparse literature that addresses the geometric theory of BCDI and the subsequent analysis methods are generalized here. This geometrical aspect, specific to coherent Bragg diffraction and absent in 2D transmission CDI experiments, gains particular importance when it comes to spatially resolved characterization of 3D crystalline materials in a reliable nondestructive manner. This series of articles describes this theory, from the diffraction in Bragg geometry to the corrections needed to obtain a properly rendered digital image of the 3D scatterer. Part I of this series provides the experimental BCDI community with the general form of the 3D real-space distortions in the phase-retrieved object, along with the necessary post-retrieval correction method. Part II builds upon the geometric theory developed in Part I with the formalism to correct the shear distortions directly on an orthogonal grid within the phase-retrieval algorithm itself, allowing more physically realistic constraints to be applied. Taken together, Parts I and II provide the X-ray science community with a set of generalized BCDI shear-correction techniques crucial to the final rendering of a 3D crystalline scatterer and for the development of new BCDI methods and experiments.

36 MATERIALS SCIENCE↗
NASA NTRS1993

Flexure-torsion behavior of prismatic beams. I - Section properties via power series

The behavior of a tip-loaded cantilever beam with an arbitrary cross section is studied using Saint-Venant's semi-inverse method along with a power series solution for the out-of-plane flexure and torsion warping functions. The power series coefficients are determined by solving a set of variationally derived linear algebraic equations. For complex cross sections, the calculated coefficients represented a 'best-fit approximation' to the exact warping function. The resulting warping functions are used to determine the cross-sectional properties (torsion constant, shear correction factors, shear deformation coefficients, and shear center location). A new linear relation is developed for locating the shear center, where the twist rate is zero about the line of shear centers. Moreover, the kinematic relations for a new fully compatible one-dimensional beam theory are developed. Numerical results are presented first to verify the approach and second to provide section data on NACA four-series airfoils not currently found in the literature.

Kosmatka, J. B.↗
NASA NTRS1984

Shear-layer correction after Amiet under consideration of additional temperature gradient. Working diagrams for correction of signals

Amiet's correction scheme for sound wave transmission through shear-layers is extended to incorporate the additional effects of different temperatures in the flow-field in the surrounding medium at rest. Within a parameter-regime typical for acoustic measurements in wind tunnels amplitude- and angle-correction is calculated and plotted systematically to provide a data base for the test engineer.

Dobrzynski, W.↗
NASA NTRS1992

Flexure-torsion behavior of sheat-deformable beams with applications to aircraft wing sections

The flexure-torsion behavior of a tip-loaded cantilever beam with an arbitrary cross-section is studied using Saint-Venant's semi-inverse method along with a power series solution for the out-of-plane flexure and torsion warping functions. The power series coefficients are determined by solving a set of variationally derived linear algebraic equations. For complex cross-sections, the calculated coefficients represent a 'best-fit approximation' to the exact warping function. The resulting warping functions are used to determine the cross-section properties including: the torsion constant, shear deformation coefficients, shear correction factors, and the shear center location. A new linear relation is developed for locating the shear center using the Saint-Venant flexure and torsion solutions, where the twist rate is zero about the line of shear centers (not the centroidal axis). Numerical results are presented for a triangular cross-section and different NACA airfoils.

Kosmatka, J. B.↗
NASA NTRS1986

On a third-order shear deformation theory for laminated composite shells

A higher-order theory based on an assumed displacement field in which the surface displacements are expanded in powers of the thickness coordinate up to the third order is presented. The theory allows parabolic description of the transverse shear stresses, and therefore the shear correction factors of the usual shear deformation theory are not required in the present theory. The theory also accounts for small strains but moderately large displacements (i.e., von Karman strains). A finite-element model based on independent approximations of the displacements and bending moments (i.e., mixed formulation) is developed. The element is used to analyze cross-ply and angle-ply laminated shells for bending.

Liu, C. F.↗
NASA NTRS1987

A higher-order theory for geometrically nonlinear analysis of composite laminates

A third-order shear deformation theory of laminated composite plates and shells is developed, the Navier solutions are derived, and its finite element models are developed. The theory allows parabolic description of the transverse shear stresses, and therefore the shear correction factors of the usual shear deformation theory are not required in the present theory. The theory also accounts for the von Karman nonlinear strains. Closed-form solutions of the theory for rectangular cross-ply and angle-ply plates and cross-ply shells are developed. The finite element model is based on independent approximations of the displacements and bending moments (i.e., mixed finite element model), and therefore, only C sup o -approximation is required. The finite element model is used to analyze cross-ply and angle-ply laminated plates and shells for bending and natural vibration. Many of the numerical results presented here should serve as references for future investigations. Three major conclusions resulted from the research: First, for thick laminates, shear deformation theories predict deflections, stresses and vibration frequencies significantly different from those predicted by classical theories. Second, even for thin laminates, shear deformation effects are significant in dynamic and geometrically nonlinear analyses. Third, the present third-order theory is more accurate compared to the classical and firt-order theories in predicting static and dynamic response of laminated plates and shells made of high-modulus composite materials.

Reddy, J. N.↗
NASA NTRS1986

On mixed and displacement finite element models of a refined shear deformation theory for laminated anisotropic plates

An improved plate theory that accounts for the transverse shear deformation is presented, and mixed and displacement finite element models of the theory are developed. The theory is based on an assumed displacement field in which the inplane displacements are expanded in terms of the thickness coordinate up to the cubic term and the transverse deflection is assumed to be independent of the thickness coordinate. The governing equations of motion for the theory are derived from the Hamilton's principle. The theory eliminates the need for shear correction factors because the transverse shear stresses are represented parabolically. A mixed finite element model that uses independent approximations of the displacements and moments, and a displacement model that uses only displacements as degrees of freedom are developed. A comparison of the numerical results for bending with the exact solutions of the new theory and the three-dimensional elasticity theory shows that the present theory (and hence the finite element models) is more accurate than other plate-theories of the same order.

Reddy, J. N.↗
NASA NTRS1997

A Higher-Order Bending Theory for Laminated Composite and Sandwich Beams

A higher-order bending theory is derived for laminated composite and sandwich beams. This is accomplished by assuming a special form for the axial and transverse displacement expansions. An independent expansion is also assumed for the transverse normal stress. Appropriate shear correction factors based on energy considerations are used to adjust the shear stiffness. A set of transverse normal correction factors is introduced, leading to significant improvements in the transverse normal strain and stress for laminated composite and sandwich beams. A closed-form solution to the cylindrical elasticity solutions for a wide range of beam aspect ratios and commonly used material systems. Accurate shear stresses for a wide range of laminates, including the challenging unsymmetric composite and sandwich laminates, are obtained using an original corrected integration scheme. For application of the theory to a wider range of problems, guidelines for finite element approximations are presented.

Cook, Geoffrey M.↗
NASA NTRS1992

An evaluation of the Iosipescu specimen for composite materials shear property measurement

A detailed evaluation of the suitability of the Iosipescu specimen tested in the modified Wyoming fixture is presented. A linear finite element model of the specimen is used to assess the uniformity of the shear stress field in the vicinity of the notch, and demonstrate the effect of the nonuniform stress field upon strain gage measurements used for the determination of composite shear moduli. Based upon test results from graphite-epoxy laminates, the proximity of the load introduction point to the test section and the material orthotropy greatly influence the individual gage readings, however, shear modulus determination is not significantly affected by the lack of pure shear. Correction factors are needed to allow for the nonuniformity of the strain field and the use of the average shear stress in the shear modulus evaluation. The correction factors are determined for the region occupied by the strain gage rosette. A comparison of the strain gage readings from one surface of a specimen with corresponding data from moire interferometry on the opposite face documented an extreme sensitivity of some fiber orientations to eccentric loading which induced twisting and spurious shear stress-strain curves. The discovery of specimen twisting explains the apparently inconsistent shear property data found in the literature. Recommendations for improving the reliability and accuracy of the shear modulus values are made, and the implications for shear strength measurement discussed.

Morton, J.↗
NASA NTRS1989

Stress and free vibration analyses of multilayered composite plates

This paper presents a two-phase computational procedure for the accurate prediction of vibration frequencies, stresses, and deformations in simply supported bidirectional multilayered composite plates. The range of applicability of this procedure in terms of the plate's parameters is determined, and the potential of the proposed procedure for use in conjunction with large-scale finite element modeling of composite structures is discussed. It is shown that the use of the shear correction factors calculated by this procedure extends the range of the validity of the first-order shear deformation theory, used in the first phase of the procedure, to fairly thick multilayered plates with the h/L1 ratio of the order of 0.3.

Noor, Ahmed K.↗
NASA NTRS1986

A refined shear deformation theory for the analysis of laminated plates

A refined, third-order plate theory that accounts for the transverse shear strains is presented, the Navier solutions are derived for certain simply supported cross-ply and antisymmetric angle-ply laminates, and finite-element models are developed for general laminates. The new theory does not require the shear correction factors of the first-order theory (i.e., the Reissner-Mindlin plate theory) because the transverse shear stresses are represented parabolically in the present theory. A mixed finite-element model that uses independent approximations of the generalized displacements and generalized moments, and a displacement model that uses only the generalized displacements as degrees of freedom are developed. The displacement model requires C sup 1-continuity of the transverse deflection across the inter-element boundaries, whereas the mixed model requires a C sup 0-element. Also, the mixed model does not require continuous approximations (between elements) of the bending moments. Numerical results are presented to show the accuracy of the present theory in predicting the transverse stresses. Numerical results are also presented for the nonlinear bending of plates, and the results compare well with the experimental results available in the literature.

Reddy, J. N.↗
NASA NTRS1972

Vibration and damping of laminated, composite-material plates including thickness-shear effects

An analytical investigation of sinusoidally forced vibration of laminated, anisotropic plates including bending-stretching coupling, thickness-shear flexibility, all three types of inertia effects, and material damping is presented. In the analysis the effects of thickness-shear deformation are considered by the use of a shear correction factor K, analogous to that used by Mindlin for homogeneous plates. Two entirely different approaches for calculating the thickness-shear factor for a laminate are presented. Numerical examples indicate that the value of K depends on the layer properties and the stacking sequence of the laminate.

Bert, C. W.↗
NASA NTRS2009

Refined Zigzag Theory for Laminated Composite and Sandwich Plates

A refined zigzag theory is presented for laminated-composite and sandwich plates that includes the kinematics of first-order shear deformation theory as its baseline. The theory is variationally consistent and is derived from the virtual work principle. Novel piecewise-linear zigzag functions that provide a more realistic representation of the deformation states of transverse-shear-flexible plates than other similar theories are used. The formulation does not enforce full continuity of the transverse shear stresses across the plate s thickness, yet is robust. Transverse-shear correction factors are not required to yield accurate results. The theory is devoid of the shortcomings inherent in the previous zigzag theories including shear-force inconsistency and difficulties in simulating clamped boundary conditions, which have greatly limited the accuracy of these theories. This new theory requires only C(sup 0)-continuous kinematic approximations and is perfectly suited for developing computationally efficient finite elements. The theory should be useful for obtaining relatively efficient, accurate estimates of structural response needed to design high-performance load-bearing aerospace structures.

Tessler, Alexander↗
NASA NTRS1979

Turbulent shear stresses in compressible boundary layers

Hot-wire anemometer measurements of turbulent shear stresses in a Mach 3 compressible boundary layer were performed in order to investigate the effects of heat transfer on turbulence. Measurements were obtained by an x-probe in a flat plate, zero pressure gradient, two dimensional boundary layer in a wind tunnel with wall to freestream temperature ratios of 0.94 and 0.71. The measured shear stress distributions are found to be in good agreement with previous results, supporting the contention that the shear stress distribution is essentially independent of Mach number and heat transfer for Mach numbers from incompressible to hypersonic and wall to freestream temperature ratios of 0.4 to 1.0. It is also found that corrections for frequency response limitations of the electronic equipment are necessary to determine the correct shear stress distribution, particularly at the walls.

Laderman, A. J.↗
NASA NTRS1984

On dynamics of laminated anisotropic plates using a refined mixed plate element

An analysis of the free vibration and transient response of laminates using a mixed shear flexible element is presented. The element is based on a refined theory that accounts for a parabolic distribution of the transverse shear stresses through each lamina and requires no shear correction coefficients. The mixed formulation of the theory treats the five displacement functions and six stress resultants independently so that they are nodal degrees of freedom in the finite element model. Sample problems using the element are analyzed and the results of free vibration and transient response are presented. Compared to the existing shear deformation plate theory the present refined theory gives more accurate results for frequencies, displacements and stresses.

Putcha, N. S.↗