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Results for “Shear deformation”

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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.↗

NASA NTRS1988

Fracture analysis of local delaminations in laminated composites

A shear deformation model was developed to analyze local delaminations growing from transverse cracks in 90 degree plies located around the mid plane of symmetric laminates. The predictions of the model agree reasonably with experimental data from T300/934 graphite epoxy laminates. The predicted behavior is such that, in combination with an edge delamination model, the critical loads can be predicted accurately in the range of n from .5 to 8.

Sriram, P.↗

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 formulation for frictionless contact problems

Simple mixed finite element models and a computational precedure are presented for the solution of frictionless contact problems. The analytical formulation is based on a form of Reissner's large rotation theory of the structure with the effects of transverse shear deformation included. The contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the internal forces (stress resultants), the generalized displacements, and the Lagrange multipliers associated with the contact conditions. The element characteristic array are obtained by using a modified form of the two-field Hellinger-Reissner mixed variational principle. The internal forces and the Lagrange multipliers are allowed to be discontinuous at interelement boundaries. The Newton-Raphson iterative scheme is used for the solution of the nonlinear algebraic equations, and the determination of the contact area and the contact pressures.

Noor, Ahmed K.↗

NASA NTRS1989

Dynamic analysis of the Space Station truss structure based on a continuum representation

A mathematical model is developed for the real-time simulation of a Space Station. First, a continuum equivalent representation of the Space Station truss structure is presented which accounts for extensional, transverse, and shear deformations and coupling between them. The procedure achieves a significant reduction in the degrees of freedom of the system. Dynamic equations are then formulated for the continuum equivalent of the Space Station truss structure based on the matrix version of Kane's dynamical equations. Finally, constraint equations are derived for the dynamic analysis of flexible bodies with closed loop configuration.

Thomas, Segun↗

NASA NTRS1989

Fracture analysis of local delaminations in laminated composites

Armanios, E. A.↗

NASA NTRS1989

Smooth indentation of orthotropic beams

An approximate Green's function for surface displacements in an orthotropic beam is derived as the superposition of the half-plane solution for displacements and the beam theory deflections. The Green's function is used to formulate the integral equation for the problem of smooth contact between a rigid-cylinder and a simply supported orthotropic beam. The integral equation is solved using a least-squares approximation procedure. The contact stress distribution is presented for three materials with different degrees of orthotropy. Numerical results are given for contact force-contact length and contact force-indentation relations. The effects of curvature of the deflected beam, shear deformation and length-to-thickness ratio of the beam on the contact behavior are discussed.

Sankar, B. V.↗

NASA NTRS1989

Mixed finite element formulation for frictionless contact problems

Simple mixed finite element models and a computational procedure are presented for the solution of frictionless contact problems. The analytical formulation is based on a form of Reissner's large-rotation theory of the structure with the effect of transverse shear deformation included. The contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the internal forces (or stress resultants), the generalized displacements, and the Lagrange multipliers associated with the contact conditions. Numerical examples of axisymmetric deformations of a hemispherical shell and planar deformations of a circular ring are presented. Both structures are pressed against a rigid plate. Detailed information about the response of the structures is presented. The numerical studies demonstrate the high accuracy of the mixed models and the effectiveness of the computational procedure based on combining the geometrically nonlinear terms and the contact conditions in one iteration loop.

Noor, Ahmed K.↗

NASA NTRS1989

Surface dynamics of observed maritime fronts

The importance of various dynamical processes in the surface fronts over the ocean is investigated using the unique data set supplied by the Seasat-A satellite scatterometer, in conjunction with a planetary boundary layer model. The governing equations are presented, and a similarity model that includes the effects of shear and the effects of shear and deformation on an Ekman solution is derived. It is shown that surface friction is important in frontal processes through its role in determining the dissipation and the ageostrophic terms in the vorticity and divergence equations; the former normally acts to weaken a front while the latter acts to strengthen it. The magnitude and importance of these terms vary considerably at different stages and with stratification, thermal advection, and the deformation and shear forcing.

Levy, Gad↗

NASA NTRS1989

Remarks on a dynamical higher-order theory of laminated plates and its application in random vibration response

This paper presents an analysis of the equations governing the dynamics of shear-deformable composite plates, without recourse to a variational procedure. It is noted that the operator associated with the governing equations is nonsymmetric; using a first-order perturbation technique, it is shown to be positive-definite. In addition, using the biorthogonality condition, the dynamic response of the plate is formulated.

Cederbaum, G.↗

NASA NTRS1990

Interlaminar shear stress effects on the postbuckling response of graphite-epoxy panels

The influence of shear flexibility on overall postbuckling response was assessed, and transverse shear stress distributions in relation to panel failure were examined. Nonlinear postbuckling results are obtained for finite element models based on classical laminated plate theory and first-order shear deformation theory. Good correlation between test and analysis is obtained. The results presented analytically substantiate the experimentally observed failure mode.

Engelstad, S. P.↗

NASA NTRS1989

Explicit modeling of composite plates and beams in the dynamics of multibody systems

The state of the art dynamic response analysis of flexible multibody systems is currently restricted to elastic bodies with homogeneous materials. The requirements for high speed operation has made it necessary to use lightweight multi layered composite bodies in robotic systems and space structure applications. Dynamic modeling and analysis of such systems are particularly important since the effects of body flexibility to the performance are likely to be more pronounced. The eight-noded isoperimetric quadrilateral element with independent rotational and displacement degrees of freedom is extended to laminated composite elements. The element includes an arbitrary number of bonded layers, each of which may have a different thickness. The transverse shear deformation which is a predominant factor in the analysis of laminated composite structures is taken into account in developing the stiffness and mass matrices. The corresponding 3-D mode shapes are then incorporated to the multibody system dynamical equations. Floating body reference frames allow the selection of different boundary conditions, and the dynamical equations contain all the nonlinear interactions between the rigid and elastic motion. Example simulations are presented to illustrate the methods proposed.

Amirouche, F. M. L.↗

NASA NTRS1989

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

Noor, Ahmed K.↗

NASA NTRS1990

Stationary and nonstationary random vibrations of laminated composite plates via a higher order theory

Higher order shear deformation theory is utilized to study he weakly stationary and nonstationary random vibrations of cross-ply laminated plates. Normal mode method, in conjunction with the biorthogonality condition, for the nonsymmetric differential equations is applied. Detailed derivation is given for the governing equations, biorthogonality condition, the generalized mass and the generalized forces. Results are listed for a plate which is simply supported at all the edges, and subjected to a point load which is either timewise stationary or nonstationary random process.

Elishakoff, Isaac↗

NASA NTRS1990

Interlaminar shear stress effects on the postbuckling response of graphite-epoxy panels

The objectives of the study are to assess the influence of shear flexibility on overall postbuckling response, and to examine transverse shear stress distributions in relation to panel failure. Nonlinear postbuckling results are obtained for finite element models based on classical laminated plate theory and first-order shear deformation theory. Good correlation between test and analysis is obtained. The results presented in this paper analytically substantiate the experimentally observed failure mode.

Engelstad, S. P.↗

NASA NTRS1989

Frictionless contact of aircraft tires

A computational procedure for the solution of frictionless contact problems of spacecraft tires was developed using a two-dimensional laminated anisotropic shell theory incorporating the effects of variations in material and geometric parameters, transverse shear deformation, and geometric nonlinearities to model the nose-gear tire of a space shuttle. Numerical results are presented for the case when the nose-gear tire is subjected to inflation pressure and pressed against a rigid pavement. The results are compared with experimental results obtained at NASA Langley, demonstrating a high accuracy of the model and the effectiveness of the computational procedure.

Kim, Kyun O.↗