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At least 595 records · Page 33

Explicit robust schemes for implementation of a class of principal value-based constitutive models: Theoretical development

The issue of developing effective and robust schemes to implement a class of the Ogden-type hyperelastic constitutive models is addressed. To this end, explicit forms for the corresponding material tangent stiffness tensors are developed, and these are valid for the entire deformation range; i.e., with both distinct as well as repeated principal-stretch values. Throughout the analysis the various implications of the underlying property of separability of the strain-energy functions are exploited, thus leading to compact final forms of the tensor expressions. In particular, this facilitated the treatment of complex cases of uncoupled volumetric/deviatoric formulations for incompressible materials. The forms derived are also amenable for use with symbolic-manipulation packages for systematic code generation.

Saleeb, A. F.↗

Exact solution of a quantum forced time-dependent harmonic oscillator

The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator.

Yeon, Kyu Hwang↗

Analysis of delamination related fracture processes in composites

An anisotropic thin walled closed section beam theory was developed based on an asymptotical analysis of the shell energy functional. The displacement field is not assumed a priori and emerges as a result of the analysis. In addition to the classical out-of-plane torsional warping, two new contributions are identified namely, axial strain and bending warping. A comparison of the derived governing equations confirms the theory developed by Reissner and Tsai. Also, explicit closed form expressions for the beam stiffness coefficients, the stress and displacement fields are provided. The predictions of the present theory were validated by comparison with finite element simulation, other closed form analyses and test data.

Armanios, Erian A.↗

A geometrically nonlinear theory of elastic plates

A set of kinematic and intrinsic equilibrium equations is derived for plates undergoing large deflection and rotation but with small strain. The large rotation is treated by the general finite rotation of a frame in which the material points that are originally along a normal line in the undeformed plate undergo only small displacements. Exact intrinsic virtual strain-displacement relations are derived; using a reduced 2-D strain energy function from which the warping has been systematically eliminated, a set of intrinsic equilibrium equations follows. It is demonstrated that only five equilibrium equations can be derived in this way, because the component of virtual rotation about the normal is not independent. These equations include terms which cannot be obtained without the use of a finite rotation vector which contains three nonzero components. These extra terms correspond to the difference of in-plane shear stress resultants in other theories.

Hodges, Dewey H.↗

Minimizing distortion in truss structures - A Hopfield network solution

Distortions in truss structures can result from random errors in element lengths that are typical of a manufacturing process. These distortions may be minimized by an optimal selection of elements from those available for placement between the prescribed nodes - a combinatorial optimization problem requiring significant investment of computational resource for all but the smallest problems. The present paper describes a formulation in which near-optimal element assignments are obtained as minimum-energy stable states, of an analogous Hopfield neural network. This requires mapping of the optimization problem into an energy function of the appropriate Liapunov form. The computational architecture is ideally suited to a parallel processor implementation and offers significant savings in computational effort. A numerical implementation of the approach is discussed with reference to planar truss problems.

Fu, B.↗

On the development of explicit robust schemes for implementation of a class of hyperelastic models in large-strain analysis of rubbers

The issue of developing effective and robust schemes to implement a class of the Ogden-type hyperelastic constitutive models, for large-strain analysis of rubber-like materials, is addressed. To this end, explicit forms for the corresponding material tangent-stiffness tensors are developed, and these are valid for the entire deformation range; i.e., with both distinct as well as repeated principal-stretch values. Throughout the analysis the various implications of the underlying property of separability of the strain-energy functions are exploited, thus leading to compact final forms of the tensor expressions. In particular, this facilitated the treatment of the complex cases of uncoupled volumetric/deviatoric formulations for incompressible materials, which are becoming increasingly popular in recent years. The forms derived are also amenable for use with symbolic-manipulation packages for systematic code generation.

Saleeb, A. F.↗

The solution of coupled Schroedinger equations using an extrapolation method

In this paper, extrapolation to the limit in a finite-difference method is applied to solve a system of coupled Schroedinger equations. This combination results in a method that only requires knowledge of the potential energy functions for the system. This numerical procedure has several distinct advantages over the more conventional methods. Namely, initial guesses for the term values are not needed; assumptions need be made about the behavior of the wavefunctions, such as the slope or magnitude in the nonclassical region; and the algorithm is easy to implement, has a firm mathematical foundation, and provides error estimates. Moreover, the method is less sensitive to round-off error than other methods since a small number of mesh points is used and it can be implemented on small computers. A comparison of the method with another numerical method shows results agreeing within 1 part in 10 exp 4.

Goorvitch, D.↗

Optimal fixed-finite-dimensional compensator for Burgers' equation with unbounded input/output operators

The problem of using reduced order dynamic compensators to control a class of nonlinear parabolic distributed parameter systems was considered. Concentration was on a system with unbounded input and output operators governed by Burgers' equation. A linearized model was used to compute low-order-finite-dimensional control laws by minimizing certain energy functionals. Then these laws were applied to the nonlinear model. Standard approaches to this problem employ model/controller reduction techniques in conjunction with linear quadratic Gaussian (LQG) theory. The approach used is based on the finite dimensional Bernstein/Hyland optimal projection theory which yields a fixed-finite-order controller.

Burns, John A.↗

Surface disordering of Pb(110)

A molecular dynamics simulation of Pb(110), using embedded atom method energy functional and two-body potential derived for the purpose, shows that near 400 K the three surface layers begin to disorder well before the bulk (interior) layers. Transfer of atoms from the first subsurface layer to the surface layer occurs. Disordering propagates beyond the top three layers above 550 K, accompanied by formation of an adlayer and vacancies in the top three layers. Behavior of the two-dimensional layer structure factors indicates that disordering is anisotropic. Simulation results are consistent with experimental observations of surface roughening near 400 K and more extensive surface ordering above 525 K. Results are consistent with simulations for Ni and Al.

Tibbits, P.↗

Hydrodynamic instability and coalescence of binary neutron stars

We study the importance of hydrodynamic effects on the evolution of coalescing binary neutron stars. Using an approximate energy functional constructed from equilibrium solutions for polytropic binary configuration, we incorporate hydrodynamic effects into the calculation of the orbital decay driven by gravitational wave emission. In particular, we follow the transition between the quasi-static, secular decay of the orbit at large separation and the rapid dynamical evolution of confirgurations approaching contact. We show that a purely Newtonian hydrodynamic instability can significantly accelerate the coalescence at small separation. Such an instability occurs in all close binary configurations containing sufficiently incompressible stars. Calculations are performed for various neutron star masses, radii, and spins. The influence of the stiffness of the equation of state is also explored by varying the effective polytopic index. Typically, we find that the radial infall velocity just prior to contact is about 10% of the tangential orbital velocity. Once the stability limit is reached, the final evolution only takes another orbit. Post-Newtonian effects can move the stability limit to a larger binary separation, and may induce an even larger radial velocity. We also consider the possibiltiy of mass transfer form one neutron star to the other. We show that stable mass transfer is unlikely except when the mass of one of the components is very small (M is less than or approximately 0.4 solar mass) and the viscosity is high enough to maintain corotation. Otherwise, either the two stars come into contact or the dynamical instability sets in before a Roche limit can be reached.

Lai, Dong↗

Minimizing distortion in truss structures -- a Hopfield network solution

Distortions in truss structures can result from random errors in elemental lengths that are typical of a manufacturing process. These distortions may be minimized by an optimal selection of elements from those available for placement between the prescribed nodes -- a combinatorial optimization problem requiring significant investment of computational resource for all but the smallest problems. The present paper describes a formulation in which near-optimal element assignments are obtained as minimum energy, stable states, of an analogous Hopfield neural network. This requires mapping of the optimization problem into an energy function of the appropriate Lyapunov form. The computational architecture is ideally suited to a parallel processor implementation and offers significant savings in computational effort. A numerical implementation of the approach is discussed with reference to planar truss problems.

Fu, B.↗

Summary of Research/Publications

Summary of research/publications include:(1) Comment on broadening of water microwave lines by collisions with helium atoms; (2) Calculations of ion-molecule deuterium fractionation reactions involving HD; (3) Ab initio predictions on the rotational spectra of carbon-chain carbene molecules; (4) Theoretical IR spectra of ionized naphthalene; (5) Improved collisional excitation rates for interstellar water; (6) Calculations on the competition between association and reaction for C3H+ + H2; (7) Theoretical infrared spectra of some model polycyclic aromatic hydrocarbons: effect of ionization; (8) Calculations concerning interstellar isomeric abundance ratios for C3H and C3H2; (9) New calculations on the ion-molecule processes C2H2+ + H2 C2H3+ + H and C2H2+ + H2 C2H4+; (10) Anisotropic rigid rotor potential energy function for H2O-H2; (11) A correlated ab initio study of linear carbon-chain radicals CnH (n=2-7); (12) Ab initio characterization of MgCCH, MgCCH+, and MgC2 and pathways to their formation in the interstellar medium; (13) Why HOC+ is detectable in interstellar clouds: The rate of the reaction between HOC+ and H2; (14) A correlated ab initio study of the X 2A 1 and A 2E states of MgCH3; (15) On the stability of interstellar carbon clusters: The rate of the reaction between C3 and O; and (16) The rate of the reaction between CN and C2H2 at interstellar temperatures.

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STS-88 Crew Interview: Frederick "Rick" Sturckow

Frederick Sturckow discusses the seven-day mission that will be highlighted by the mating of the U.S.-built Node 1 station element to the Functional Energy Block (FGB) which will already be in orbit, and two spacewalks to connect power and data transmission cables between the Node and the FGB. Node 1 will be the first Space Station hardware delivered by the Space Shuttle. He also disscusses the assembly sequence. The crew will conduct a series of rendezvous maneuvers similar to those conducted on other Shuttle missions to reach the orbiting FGB. Once the two elements are docked, Ross and Newman will conduct two scheduled spacewalks to connect power and data cables between the Node, PMAs and the FGB. The day following the spacewalks, Endeavour will undock from the two components, completing the first Space Station assembly mission.

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STS-88 Post Flight Presentation

The flight crew of the STS-88 mission, Commander Robert D. Cabana, Pilot Frederick W. Sturckow, and Mission Specialists Nancy J. Currie, Jerry L. Ross, James H. Newman, and Sergei K. Krikalev, present a video mission over-view of their space flight. Images include prelaunch activities such as eating the traditional breakfast, crew suit-up, and the ride out to the launch pad. Also, included are various panoramic views of the shuttle on the pad. The crew can be seen being readied in the "white room" for their mission. After the closing of the hatch and arm retraction, launch activities are shown including countdown, engine ignition, launch, and the separation of the Solid Rocket Boosters. Once the seven-day mission begins, the astronauts comment on the mating of the U.S.-built Node 1 station element to the Functional Energy Block (FGB) which was already in orbit, and two EVAs that were planned to connect power and data transmission cables between the Node and the FGB. The crew can also be seen conducting a series of rendezvous maneuvers similar to those conducted on other Shuttle missions to reach the orbiting FGB.

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STS-88 Crew Interview: Nancy Currie

Nancy Currie discusses the seven-day mission that will be highlighted by the mating of the U.S.-built Node 1 station element to the Functional Energy Block (FGB) which will already be in orbit, and two spacewalks to connect power and data transmission cables between the Node and the FGB. Node 1 will be the first Space Station hardware delivered by the Space Shuttle. He also disscusses the assembly sequence. The crew will conduct a series of rendezvous maneuvers similar to those conducted on other Shuttle missions to reach the orbiting FGB. Once the two elements are docked, Ross and Newman will conduct two scheduled spacewalks to connect power and data cables between the Node, PMAs and the FGB. The day following the spacewalks, Endeavour will undock from the two components, completing the first Space Station assembly mission.

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STS-88 Crew Interview: Sergei Krikalev

Sergei Krikalev discusses the seven-day mission that will be highlighted by the mating of the U.S.-built Node 1 station element to the Functional Energy Block (FGB) which will already be in orbit, and two spacewalks to connect power and data transmission cables between the Node and the FGB. Node 1 will be the first Space Station hardware delivered by the Space Shuttle. He also discusses the assembly sequence. The crew will conduct a series of rendezvous maneuvers similar to those conducted on other Shuttle missions to reach the orbiting FGB. Once the two elements are docked, Ross and Newman will conduct two scheduled spacewalks to connect power and data cables between the Node, PMAs and the FGB. The day following the spacewalks, Endeavour will undock from the two components, completing the first Space Station assembly mission.

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STS-88 Crew Interview: Robert Cabana

Commander Robert D. Cabana discusses the seven-day mission that will be highlighted by the mating of the U.S.-built Node 1 station element to the Functional Energy Block (FGB) which will already be in orbit, and two spacewalks to connect power and data transmission cables between the Node and the FGB. Node 1 will be the first Space Station hardware delivered by the Space Shuttle. He also disscusses the assembly sequence. The crew will conduct a series of rendezvous maneuvers similar to those conducted on other Shuttle missions to reach the orbiting FGB. Once the two elements are docked, Ross and Newman will conduct two scheduled spacewalks to connect power and data cables between the Node, PMAs and the FGB. The day following the spacewalks, Endeavour will undock from the two components, completing the first Space Station assembly mission.

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STS-88 Crew Interview: Jim Newman

Jim Newman discusses the seven-day mission that will be highlighted by the mating of the U.S.-built Node 1 station element to the Functional Energy Block (FGB) which will already be in orbit, and two spacewalks to connect power and data transmission cables between the Node and the FGB. Node 1 will be the first Space Station hardware delivered by the Space Shuttle. He also discusses the assembly sequence. The crew will conduct a series of rendezvous maneuvers similar to those conducted on other Shuttle missions to reach the orbiting FGB. Once the two elements are docked, Ross and Newman will conduct two scheduled spacewalks to connect power and data cables between the Node, PMAs and the FGB. The day following the spacewalks, Endeavour will undock from the two components, completing the first Space Station assembly mission.

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