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The finite element method is used to investigate stress/strain in silicon ribbon. Failure considerations such as residual stress, buckling material non-linearity and creep are discussed. Temperature profiles are presented.
Solar radiative transfer through a coupled system of atmosphere and plant canopy is modeled as a multiple-scattering problem through a layered medium of random scatterers. The radiative transfer equation is solved by the discrete-ordinates finite-element method. Analytic expressions are derived that allow the calculation of scattering and absorption cross sections for any plant canopy layer form measurable biophysical parameters such as the leaf area index, leaf angle distribution, and individual leaf reflectance and transmittance data. An expression for a canopy scattering phase function is also given. Computational results are in good agreement with spectral reflectance measurements directly above a soybean canopy, and the concept of greenness- and brightness-transforms of Landsat MSS data is reconfirmed with the computed results. A sensitivity analysis with the coupled atmosphere/canopy model quantifies how satellite-sensed spectral radiances are affected by increased atmospheric aerosols, by varying leaf area index, by anisotropic leaf scattering, and by non-Lambertian soil boundary conditions. Possible extensions to a 2-D model are also discussed.
This paper deals with the nonlinear quasi-fracture behavior of polymers. Using the finite element method, the quasi-fracture model composed of an isolated craze opening with a nonlinear boundary envelope forces represented by oriented fibril domains is analyzed in simply-stressed rectangular plate. The stress distribution, the displacement profile, as well as the yield or plastic or flow zone adjacent to the craze tips are obtained. It is found that the variation of the stress distribution near the craze tip is not as sharp as that for an elastic crack. The initial load required for yielding or flowing is greater for the quasifracture as compared with that for a classical fracture. Under the same load the yield or flow zone is somewhat smaller as compared with that obtained on the basis of linear elastic-plastic fracture mechanics theory.
This paper discusses the modelling by mechanical subelements, the general plasticity, the viscoplasticity, and the creep behavior of solids under multiaxial loading conditions. The formulation of a time-independent elastic-plastic analysis is based on the viscoplasticity theory and the assumed stress finite element method. An example of an in-plane stress problem is included.
This work presents the results of an analytical study and an experimental investigation of the three-dimensional flow in a turbine scroll. The finite element method is used in the iterative numerical solution of the locally linearized governing equations for the three-dimensional velocity potential field. The results of the numerical computations are compared with the experimental measurements in the scroll cross sections, which were obtained using laser Doppler velocimetry and hot wire techniques. The results of the computations show a variation in the flow conditions around the rotor periphery which was found to depend on the scroll geometry.
The nonlinear transient response of initially stressed composite plates is investigated using the finite element method. A nine-node isoparametric quadrilateral element is developed to model laminated plates under initial deformation and initial stress according to the Mindlin plate theory and von Karman large deflection assumptions. In the time integration, the Newmark constant acceleration method in conjunction with an efficient and accurate iteration scheme is used. Numerical results for deflections and bending moments for isotropic and laminated plates are obtained.
Papers are presented on such topics as the use of semi-Lagrangian advective schemes in meteorological modeling; computation with high-resolution upwind schemes for hyperbolic equations; dynamics of flame propagation in a turbulent field; a modified finite element method for solving the incompressible Navier-Stokes equations; computational fusion magnetohydrodynamics; and a nonoscillatory shock capturing scheme using flux-limited dissipation. Consideration is also given to the use of spectral techniques in numerical weather prediction; numerical methods for the incorporation of mountains in atmospheric models; techniques for the numerical simulation of large-scale eddies in geophysical fluid dynamics; high-resolution TVD schemes using flux limiters; upwind-difference methods for aerodynamic problems governed by the Euler equations; and an MHD model of the earth's magnetosphere.
The energy-stability of thermocapillary convection in models of the float-zone, crystal-growing process was studied. Stability limits, as functions of pertinent parameters, that will identify conditions which will not allow the existence of an undesirable oscillatory flow instability were determined. Such instabilities may occur in the space processing of semiconductor materials. The determination of the stability limits will involve two sets of numerical computations: (1) solution of the nonlinear governing equations together with the appropriate boundary conditions to determine the basic state (in general, velocity, pressure and temperature fields and the displacement of free surfaces and interfaces); and (2) solution of a nonlinear Euler-Lagrange systems for the energy-stability limit. Both computations, while difficult, should be within the scope of available computer capability and available concepts in numerical analysis. Finite-element methods are attractive candidates for the numerical work.
The purpose of this study was to improve the understanding of the transport phenomena which occurs in the directional solidification of alloy semiconductors. In particular, emphasis was placed on the strong role of convection in the melt. Analytical solutions were not deemed possible for such an involved problem. Accordingly, a numerical model of the process was developed which simulated the transport. This translates into solving the partial differential equations of energy, mass, species, and momentum transfer subject to various boundary and initial conditions. A finite element method with simple elements was initially chosen. This simulation tool will enable the crystal grower to systematically identify and modify the important design factors within her control to produce better crystals.
The overall goal of this project is to establish a modeling capability that allows a quantitative determination of atmospheric effects on remote sensing including the effects of surface heterogeneities. This includes an improved understanding of aerosol and haze effects in connection with structural, angular, and spatial surface heterogeneities. One important objective of the research is the possible identification of intrinsic surface or canopy characteristics that might be invariant to atmospheric perturbations so that they could be used for scene identification. Conversely, an equally important objective is to find a correction algorithm for atmospheric effects in satellite-sensed surface reflectances. The technical approach is centered around a systematic model and code development effort based on existing, highly advanced computer codes that were originally developed for nuclear radiation shielding applications. Computational techniques for the numerical solution of the radiative transfer equation are adapted on the basis of the discrete-ordinates finite-element method which proved highly successful for one and two-dimensional radiative transfer problems with fully resolved angular representation of the radiation field.
In low cycle fatigue, cracks are initiated and propagated under general yielding cyclic loading. For general yielding cyclic loading, Dowling and Begley have shown that fatigue crack growth rate correlates well with the measured delta J. The correlation of da/dN with delta J was also studied by a number of other investigators. However, none of thse studies have correlated da/dN with delta J calculated specifically for the test specimens. Solomon measured fatigue crack growth in specimens in general yielding cyclic loading. The crack tips fields for Solomon's specimens are calculated using the finite element method and the J values of Solomon's tests are evaluated. The measured crack growth rate in Solomon's specimens correlates very well with the calculated delta J.
Using a primitive variable formulation of the finite-element method, the differences in the surface observables, such as topography and geoid, produced by single- and double-layered thermal convection, were compared. Both constant and depth-dependent viscosities have been considered. For the same Rayleigh number, larger surface perturbations are produced by single-cell convection. For the same Nusselt number, the magnitudes of the surface observables are greater for double-layered convection. For the same surface heat-flux, surface topographies have similar magnitudes, but the relative amplitudes of geoid anomalies depend greatly on the style of viscosity stratification. This difference in the geoid between the two systems increases with greater surface heat-flow, regardless of viscosity structure.
Residual stress in a ZrO2-Y2O3 ceramic coating resulting from the plasma spraying operation is calculated. The calculations were done using the finite element method. Both thermal and mechanical analysis were performed. The resulting residual stress field was compared to the measurements obtained by Hendricks and McDonald. Reasonable agreement between the predicted and measured moment occurred. However, the resulting stress field is not in pure bending.
The ascent of a hot spherical body through a fluid with a strongly temperature-dependent viscosity has been studied using an axisymmetric finite element method. Numerical solutions range over Peclet numbers of 0.1 - 1000 from constant viscosity up to viscosity variations of 100,000. Both rigid and stress-free boundary conditions were applied at the surface of the sphere. The dependence of drag on viscosity variation was shown to have no dependence on the stress boundary condition except for a Stokes flow scaling factor. A Nusselt number parameterization based on the stress-free constant viscosity functional dependence on the Peclet number scaled by a parameter depending on the viscosity structure fits both stress-free and rigid boundary condition data above viscosity variations of 100. The temperature scale height was determined as a function of sphere radius. For the simple physical model studied in this paper pre-heating is required to reduce the ambient viscosity of the country rock to less than 10 to the 22nd sq cm/s in order for a 10 km diapir to penetrate a distance of several radii.
A methodology is described which can be used to design/analyze fiber composite structures subjected to complex hygrothermomechanical environments. This methodology includes composite mechanics and advanced structural analysis methods (finite element). Select examples are described to illustrate the application of the available methodology. The examples include: (1) composite progressive fracture; (2) composite design for high cycle fatigue combined with hot-wet conditions; and (3) general laminate design.
In this paper, all possible forms of mixed-hybrid finite element methods that are based on multi-field variational principles are examined as to the conditions for existence, stability, and uniqueness of their solutions. The reasons as to why certain 'simplified hybrid-mixed methods' in general, and the so-called 'simplified hybrid-displacement method' in particular (based on the so-called simplified variational principles), become unstable, are discussed. A comprehensive discussion of the 'discrete' BB-conditions, and the rank conditions, of the matrices arising in mixed-hybrid methods, is given. Some recent studies aimed at the assurance of such rank conditions, and the related problem of the avoidance of spurious kinematic modes, are presented.
A Taylor-Galerkin finite element method for solving large, nonlinear thermal-structural problems is presented. The algorithm is formulated for coupled transient and uncoupled quasistatic thermal-structural problems. Vectorizing strategies ensure computational efficiency. Two applications demonstrate the validity of the approach for analyzing transient and quasistatic thermal-structural problems.
The Helmholtz equation (Delta + K(2)n(2))u = f with a variable index of refraction n, and a suitable radiation condition at infinity serves as a model for a wide variety of wave propagation problems. Such problems can be solved numerically by first truncating the given unbounded domain and imposing a suitable outgoing radiation condition on an artificial boundary and then solving the resulting problem on the bounded domain by direct discretization (for example, using a finite element method). In practical applications, the mesh size h and the wave number K, are not independent but are constrained by the accuracy of the desired computation. It will be shown that the number of points per wavelength, measured by (Kh)(-1), is not sufficient to determine the accuracy of a given discretization. For example, the quantity K(3)h(2) is shown to determine the accuracy in the L(2) norm for a second-order discretization method applied to several propagation models.