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NASA NTRS1984

Natural vibrations of laminated anisotropic plates

This paper contains a description of the three-dimensional elasticity equations and the associated finite element model for natural vibrations of laminated rectangular plates. The numerical results for natural frequencies are compared with those obtained by a shear deformable plate theory. A number of cross-ply and angle-ply rectangular plates are analyzed for natural frequencies. For relatively thick plates, the plate element predicts frequencies higher than those predicted by the 3-D element.

Reddy, J. N.↗

NASA NTRS1984

Augmented weak forms and element-by-element preconditioners: Efficient iterative strategies for structural finite elements. A preliminary study

A weak formulation in structural analysis that provides well conditioned matrices suitable for iterative solutions is presented. A mixed formulation ensures the proper representation of the problem and the constitutive relations are added in a penalized form. The problem is solved by a double conjugate gradient algorithm combined with an element by element approximate factorization procedure. The double conjugate gradient strategy resembles Uzawa's variable-length type algorithms the main difference is the presence of quadratic terms in the mixed variables. In the case of shear deformable beams these terms ensure that the proper finite thickness solution is obtained.

Muller, A.↗

NASA NTRS1984

Nonlinear dynamic analysis of sandwich panels

Two analytical techniques applicable to large deflection dynamic response calculations for pressure loaded composite sandwich panels are demonstrated. One technique utilizes finite element modeling with a single equivalent layer representing the face sheets and core. The other technique utilizes the modal analysis computer code DEPROP which was recently modified to include transverse shear deformation in a core layer. The example problem consists of a simply supported rectangular sandwich panel. Included are comparisons of linear and nonlinear static response calculations, in addition to dynamic response calculations.

Lush, A. M.↗

NASA NTRS1984

Geometrically nonlinear analysis of laminated elastic structures

Laminated composite plates and shells that can be used to model automobile bodies, aircraft wings and fuselages, and pressure vessels among many other were analyzed. The finite element method, a numerical technique for engineering analysis of structures, is used to model the geometry and approximate the solution. Various alternative formulations for analyzing laminated plates and shells are developed and their finite element models are tested for accuracy and economy in computation. These include the shear deformation laminate theory and degenerated 3-D elasticity theory for laminates.

Reddy, J. N.↗

NASA NTRS1984

Mechanical-contact-induced transformation from the amorphous to the partially crystalline state in metallic glass

Friction and wear tests were conducted with 3.2- and 6.4-millimeter-diameter aluminum oxide spheres sliding, in reciprocating motion, on a Fe67Co18B14Si1 metallic foil. Crystallites with a size range of 10 to 150 nanometers were produced on the wear surface of the amorphous alloy. A strong interaction between transition metals and metalloids such as silicon and boron results in strong segregation during repeated sliding, provides preferential transition metal-metalloid clustering in the amorphous alloy, and subsequently produces the diffused honeycomb structure formed by dark grey bands and primary crystals, that is, alpha-Fe in the matrix. Large plastic flow occurs on an amorphous alloy surface with sliding and the flow film of the alloy transfers to the aluminum oxide pin surface. Multiple slip bands due to shear deformation are observed on the side of the wear track. Two distinct types of wear debris were observed as a result of sliding: an alloy wear debris, and/or powdery-whiskery oxide debris.

Miyoshi, K.↗

NASA NTRS1986

Delamination growth in composite materials

The Double Cantilever Beam (DCB) and the End Notched Flexure (ENF) specimens are employed to characterize MODE I and MODE II interlaminar fracture resistance of graphite/epoxy (CYCOM 982) and graphite/PEEK (APC2) composites. Sizing of test specimen geometries to achieve crack growth in the linear elastic regime is presented. Data reduction schemes based upon beam theory are derived for the ENF specimen and include the effects of shear deformation and friction between crack surfaces on compliance, C, and strain energy release rate, G sub II. Finite element (FE) analyses of the ENF geometry including the contact problem with friction are presented to assess the accuracy of beam theory expressions for C and G sub II. Virtual crack closure techniques verify that the ENF specimen is a pure Mode II test. Beam theory expressions are shown to be conservative by 20 to 40 percent for typical unidirectional test specimen geometries. A FE parametric study investigating the influence of delamination length and depth, span, thickness and material properties on G sub II is presented. Mode I and II interlaminar fracture test results are presented. Important experimental parameters are isolated, such as precracking techniques, rate effects, and nonlinear load-deflection response. It is found that subcritical crack growth and inelastic materials behavior, responsible for the observed nonlinearities, are highly rate-dependent phenomena with high rates generally leading to linear elastic response.

Gillespie, J. W., Jr.↗

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.↗

NASA NTRS1984

Mechanical-contact-induced transformation from the amorphous to the partially crystalline state in metallic glass

Miyoshi, K.↗

NASA NTRS1986

A compressive failure model for anisotropic plates with a cutout under compressive and shear loads

The paper introduces a failure model for laminated composite plates with a cutout under combined compressive and shear loads. The model is based on kinking failure of the load-carrying fibers around a cutout, and includes the effect of local shearing and compressive stresses. Comparison of predictions of the model with available experimental results for quasi-isotropic and orthotropic plates with a circular hole indicated a good agreement. Predictions for orthotropic plates under combined loading are compared with the predictions of a point-stress model. The present model indicates significant reductions in axial load-carrying capacity due to shearing loads for plates with principal axis of orthotropy oriented along the axial load direction. A gain in strength is achieved by rotating the axis of orthotropy to counteract the shearing stress, or by eliminating the compressive-shear deformation coupling.

Gurdal, Z.↗

NASA NTRS1987

Plates and shells containing a surface crack under general loading conditions

Various through and part-through crack problems in plates and shells are considered. The line-spring model of Rice and Levy is generalized to the skew-symmetric case to solve surface crack problems involving mixed-mode, coplanar crack growth. Compliance functions are introduced which are valid for crack depth to thickness ratios at least up to .95. This includes expressions for tension and bending as well as expressions for in-plane shear, out-of-plane shear, and twisting. Transverse shear deformation is taken into account in the plate and shell theories and this effect is shown to be important in comparing stress intensity factors obtained from the plate theory with three-dimensional solutions. Stress intensity factors for cylinders obtained by the line-spring model also compare well with three-dimensional solution. By using the line-spring approach, stress intensity factors can be obtained for the through crack and for part-through crack of any crack front shape, without recalculation integrals that take up the bulk of the computer time. Therefore, parameter studies involving crack length, crack depth, shell type, and shell curvature are made in some detail. The results will be useful in brittle fracture and in fatigue crack propagation studies. All problems considered are of the mixed boundary value type and are reducted to strongly singular integral equations which make use of the finite-part integrals of Hadamard. The equations are solved numerically in a manner that is very efficient.

Joseph, Paul F.↗

NASA NTRS1986

Triangular element for analysis of a stretched plate weakened by a part-through hole

A C0-type triangular element formulation in orthogonal curvilinear coordinates has been developed, based on assumptions of transverse inextensibility and layerwise constant shear angle, for analysis of a stretched homogeneous plate weakened by a part-through hole. The element stiffness matrix and consistent load vector have been derived using an assumed-quadratic-displacement (in the curvilinear coordinate plane) potential-energy approach. Numerical results obtained using the straight-sided triangular element version indicate the presence of transverse shear deformation in a stretched homogeneous plate weakened by a symmetrically located concentric hole.

Chaudhuri, R. A.↗

NASA NTRS1986

On the analysis and design of the end notched flexure (ENF) specimen for Mode II testing

The end notched flexure (ENF) specimen is examined as a candidate for measuring interlaminar fracture toughness in skew symmetric loading. A simple design study for sizing the ENF specimen to minimize geometric nonlinear response and to avoid nonlinear material behavior or flexural failure is presented. Results indicate that interlaminar shear effects may be significant for tough resin systems requiring large thickness-to-length geometries. The influences of interlaminar shear deformation and friction between the crack surfaces on the strain energy release rate are examined.

Carlsson, L. A.↗

NASA NTRS1987

Dynamic response of a viscoelastic Timoshenko beam

The analysis presented in this study deals with the vibratory response of viscoelastic Timoshenko (1955) beams under the assumption of small material loss tangents. The appropriate method of analysis employed here may be applied to more complex structures. This study compares the damping ratios obtained from the Timoshenko and Euler-Bernoulli theories for a given viscoelastic material system. From this study the effect of shear deformation and rotary inertia on damping ratios can be identified.

Kalyanasundaram, S.↗

NASA NTRS1988

Optimum design of geodesically stiffened composite plates

With the goal of tailorability in mind, the in-plane stiffness characteristics of a particular grid stiffened plate configuration under axial and shear loads have been studied. The contribution of the skin to the stiffener network and the resultant skin/rib interaction is analyzed. For the given plate geometry and loads, it is shown that an optimum configuration does exist. To achieve optimally designed practical plate configurations, buckling constraints need to be included in the design. Due to the complex geometry and loading of the plates, a simplified local buckling analysis of isolated stiffeners and triangular skin elements between the stiffeners is considered. Development of a stiffener buckling analysis represent stiffeners as shear deformable plate elements is presented.

Guerdal, Zafer↗

NASA NTRS1988

Local crippling of thin-walled graphite-epoxy stiffeners

Results from an experimental and analytical study of the local buckling, postbuckling, and crippling (failure) behavior of channel, zee, and I- and J-section stiffeners made of AS4/3502 graphite-epoxy unidirectional tape are presented. Thirty-six specimens were tested in axial compression. Experimental results indicate the existence of a number of damage initiation modes, all of which involve either delamination in some part of the specimen or local material strength failure in a corner of the specimen. The flange width-to-thickness ratio is found to influence the mode of damage initiation. The inner corner radius strongly affects the crippling stress for the I- and J-section specimens, but was not found to have a significant effect on the crippling stress of channels and zees. Geometrically nonlinear analyses of five specimens were performed with the STAGS general purpose computer code. Correlation between analytical and experimental results is excellent through buckling, but agreement degrades in postbuckling. The discrepancies in postbuckling are attributed to neglect of transverse shearing deformations in the analysis and development of damage in the specimens. Hashin's compressive fiber mode failure criterion correlates reasonably well with the first major damage event in a first ply failure analysis.

Bonanni, David L.↗

NASA NTRS1987

Powder processing of nickel and other aluminides by hot consolidation

Alloys based on FeAl, NiAl, and Ni3Al have been processed by extrusion of powders over a range of compositions, powder characteristics, and extrusion parameters. It is found that extrusion leads to dynamic recrystallization and that the grain size of the extrusions depends on the powder size, extrusion temperature, and extrusion ratio. Prior particle boundary oxides play an important role in controlling the grain size and uniformity by acting as obstacles to grain growth. Hot isostatic pressing and vacuum hot pressing can be used for powder densification, but prior particle oxides are not effectively broken up due to insufficient shearing deformation.

Vedula, K.↗

NASA NTRS1988

Stress and vibraton analyses of anisotropic shells of revolution

An efficient computational strategy is presented for reducing the cost of the stress and free vibration analyses of laminated anisotropic shells of revolution. The analytical formulation is based on a form of the Sanders-Budiansky shell theory including the effects of both the transverse shear deformation and the laminated anisotropic material response. The fundamental unknowns consist of the eight strain components, the eight stress resultants and the five generalized displacements of the shell. Each of the shell variables is expressed in terms of trigonometric functions (Fourier series) in the circumferential co-ordinate, and a three-field mixed finite element model is used for the discretization in the meridional direction. The shell response associated with a range of Fourier harmonics is approximated by a linear combination of a few global approximation vectors, which are generated at a particular value of the Fourier harmonic, within that range. The full equations of the finite element model are solved for only a single Fourier harmonic, and the response corresponding to the other Fourier harmonics is generated using a reduced system of equations with considerably fewer degrees of freedom.

Noor, Ahmed K.↗

NASA NTRS1988

A mixed-mode bending apparatus for delamination testing

A mixed-mode delamination test procedure was developed combining double cantilever beam mode I loading and end notch flexure mode II loading on a split unidirectional laminate. By loading the specimen with a lever, a single applied load simultaneously produces mode I and II bending loads on the specimen. This mixed mode bending (MMB) test was analyzed using both finite element procedures and beam theory to calculate the mode I and II components of strain energy release rate, G sub I and G sub II, respectively. The analyses showed that a wide range of G sub I/G sub II ratios could be produced by varying the applied load position on the loading lever. As the delamination extended, the G sub I/G sub II ratios varied by less than 5 percent. The simple beam theory equations were modified to account for the elastic interaction between the two arms of the specimen and to account for shear deformations. The resulting equations agreed closely with the finite element results and provide a basis for selection of G sub I/G sub II test ratios and a basis for computing the mode I and II components of measured delamination toughness. The MMB specimen analysis and test procedures were demonstrated using unidirectional laminates.

Crews, John H., Jr.↗