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This is the first part of a study of thermal stresses and metal movement during welding. This part discusses analysis of two-dimensional thermal stresses and metal movement during bead-on-plate and butt welding. A finite-element formulation has been derived, based on the variational principle. The formulation includes temperature dependence of material properties as well as the yield criterion.
Geodetic measurements of the 1964 Niigata, Japan earthquake and of three other examples are briefly examined. They show exponentially decaying subsidence for a year after the quakes. The observations confirm the dilatancy-fluid diffusion model of earthquake precursors and clarify the extent and properties of the dilatant zone. An analysis using one-dimensional consolidation theory is included which agrees well with this interpretation.
A model to predict the distribution of water quality parameters in three dimensions was developed. The mass transport equation was solved using a non-dimensional vertical axis and an alternating-direction-implicit finite difference technique. The reaction kinetics of the constituents were incorporated into a matrix method which permits computation of the interactions of multiple constituents. Methods for the computation of dispersion coefficients and coliform bacteria decay rates were determined. Numerical investigations of dispersive and dissipative effects showed that the three-dimensional model performs as predicted by analysis of simpler cases. The model was then applied to a two dimensional vertically averaged tidal dynamics model for the Providence River. It was also extended to a steady state application by replacing the time step with an iteration sequence. This modification was verified by comparison to analytical solutions and applied to a river confluence situation.
The MACH-1 and the THERMOS codes and their use as computational tools in nuclear analysis are examined. One dimensional survey calculations were carried out for a UF fueled core surrounded by a molten blanket; two dimensional calculations were made later with r-z geometry using the EXTERMINATOR program. Results and comparisons of the calculations are given in tabular form.
A mathematical model describing ground-wind induced flow fields around surface obstructions such as buildings, bridges or other man-made structures is presented. The Navier-Stokes equations with a two-equation turbulence model are used to analyze the flow over a two-dimensional forward facing step. A study of the assumed logarithmic approach velocity profile shows that an increase of surface roughness produces a rise to higher turbulence levels in the shear layer originating from the step corner. This rise leads to higher Reynolds stress and to faster reattachment of the separated flow.
Exact inviscid flow-field codes are used together with a quasi-three-dimensional boundary-layer analysis to provide estimates of the windward surface heating and streamline patterns of the shuttle orbiter vehicle. The accuracy and limitations of the methods are established by comparison with available wind-tunnel experiments and with more exact numerical solutions for simple flows. Flight predictions are presented showing the effects of finite-rate (nonequilibrium) chemical reactions, and the effects of varying boundary-layer edge conditions due to the growth of the boundary-layer into the inviscid flow (entropy layer swallowing). Differences between flow-field predictions at wind-tunnel and nominal flight conditions are discussed.
A comparison of four computer codes for the analysis of two-dimensional single element airfoil sections is presented for three classes of section geometries. Two of the computer codes utilize vortex singularities methods to obtain the potential flow solution. The other two codes solve the full inviscid potential flow equation using finite differencing techniques, allowing results to be obtained for transonic flow about an airfoil including weak shocks. Each program incorporates boundary layer routines for computing the boundary layer displacement thickness and boundary layer effects on aerodynamic coefficients. Computational results are given for a symmetrical section represented by an NACA 0012 profile, a conventional section illustrated by an NACA 65A413 profile, and a supercritical type section for general aviation applications typified by a NASA LS(1)-0413 section. The four codes are compared and contrasted in the areas of method of approach, range of applicability, agreement among each other and with experiment, individual advantages and disadvantages, computer run times and memory requirements, and operational idiosyncrasies.
A numerical minimization scheme is used in conjunction with two-dimensional and three-dimensional inviscid transonic flow analysis codes to provide procedures for wing leading edge aerodynamic design. The procedures are demonstrated in the design of a new leading edge to improve C-141 cruise performance. For the high aspect ratio moderately swept C-141 wing, the 2-D procedure is shown to yield results which are in close agreement with those obtained using the 3-D technique. Although the 2-D approach uses much less computation time than the 3-D technique, the latter requires fewer manhours than the former. Comparisons of predicted and wind tunnel measured performance improvements are presented which verify the design procedures.
A statistical theory coupled with a finite element theory is employed for investigation of sound radiation from a two-dimensional lined duct. The analysis does not utilize duct modes, and can be applied to a non-uniform duct with variable wall liner properties. Numerical results are presented for various shapes of the incident wave. The results are in good agreement with the Wiener-Hopf calculation for cases where the latter can be made.
Multidimensional heat conduction program computes transient temperature history and steady state temperatures of complex body geometries in three dimensions. Emphasis is placed on type of problems associated with Space Shuttle thermal protection system, but program could be used in thermal analysis of most three dimensional systems.
A two dimensional, boundary collocation stress analysis was used to analyze various round compact specimens. The influence of the round external boundary and of pin-loaded holes on stress intensity factors and crack opening displacements was determined as a function of crack-length-to-specimen-width ratios. A wide-range equation for the stress intensity factors was developed. Equations for crack-surface displacements and load-point displacements were also developed. In addition, stress intensity factors were calculated from compliance methods to demonstrate that load-displacement records must be made at the loading points and not along the crack line for crack-length-to-specimen-width ratios less than about 0.4.
A viscous-inviscid interaction algorithm is developed for prediction of two-dimensional mean and fluctuating velocity distributions in the wake immediately downstream of an airfoil trailing edge. A composite pressure field is defined, and a Poisson equation solved for transverse pressure variations. A parabolized form of the time-averaged steady Navier-Stokes equations are solved in conjunction with a viscous-augmented two-dimensional inviscid potential flow analysis. A tensor constitutive equation is employed to predict Reynolds stress distributions from solutions of a turbulence kinetic energy two equation closure model. Numerical predictions compared favorably with detailed experimental data for mean and fluctuating velocities, and Reynolds shear stress distributions, in the trailing edge region of a NACA 63-012 airfoil.
An analysis of three-dimensional energetic particle distributions for 14 consecutive ISEE satellite orbits during magnetopause crossings and close approaches is presented. The data were collected from the Nov. 10 through Dec. 11, 1977, time period and cover local times of 0840 to 1040 hours. It was found that the magnetopause in this period defined by energetic particles can be represented as sharp particles and a well defined boundary for magnetospherically trapped particles for a wide range of magnetospheric activity and magnetosheath field conditions. The magnetopause position, orientation, and velocity were determined for all identified magnetopause crossings and close approaches using the technique of Williams (1979); it was found that the magnetopause is nearly always in motion with velocities ranging from near zero to at least plus or minus 25 km/s. Correlations with published plasma, magnetic field, and plasma wave magnetopause identifications show the energetic particle results to be accurate and an important factor in determining magnetopause characteristics and behavior.
Future sensor systems will utilize massively parallel computing systems for rapid analysis of two-dimensional data. The Goddard Space Flight Center has an ongoing program to develop these systems. A single-instruction multiple data computer known as the Massively Parallel Processor (MPP) is being fabricated for NASA by the Goodyear Aerospace Corporation. This processor contains 16,384 processing elements arranged in a 128 x 128 array. The MPP will be capable of adding more than 6 billion 8-bit numbers per second. Multiplication of eight-bit numbers can occur at a rate of 2 billion per second. Delivery of the MPP to Goddard Space Flight Center is scheduled for 1983.
A quasi-three-dimensional finite-element analysis was used to analyze the edge-stress problem in four-ply, composite laminates. The seven laminates that were considered belong to the laminate family where the outer ply angle is between 0 and 90 deg. Systematic convergence studies were made to explore the existence of stress singularities near the free edge. The present analysis appears to confirm the existence of stress singularities at the intersection of the interface and the free edge. The power of the stress singularity was the same for all seven laminates considered.
This paper presents an empirical stress-intensity factor equation for a surface crack as a function of parametric angle, crack depth, crack length, plate thickness and plate width for tension and bending loads. The stress-intensity factors used to develop the equation were obtained from a previous three-dimensional, finite-element analysis of semielliptical surface cracks in finite elastic plates subjected to tension or bending loads. A wide range of configuration parameters was included in the equation. The ratios of crack length to plate thickness and the ratios of crack depth to crack length ranged from 0 to 1.0. The effects of plate width on stress-intensity variations along the crack front were also included. The equation was used to predict patterns of surface-crack growth under tension or bending fatigue loads. The equation was also used to correlate surface-crack fracture data for a brittle epoxy material within + or - 10 percent for a wide range of crack shapes and crack sizes.
Computational fluid dynamics are used to discuss problems inherent to transonic three-dimensional flow past supercritical swept wings. The formulation for a boundary value problem for the flow past the wing is provided, including consideration of weak shock waves and the use of parabolic coordinates. A swept wing code is developed which requires a mesh of 152 x 10 x 12 points and 200 time cycles. A formula for wave drag is calculated, based on the idea that the conservation form of the momentum equation becomes an entropy inequality measuring the drag, expressible in terms of a small-disturbance equation for a potential function in two dimensions. The entropy inequality has been incorporated in a two-dimensional code for the analysis of transonic flow over airfoils. A method of artificial viscosity is explored for optimum pressure distributions with design, and involves a free boundary problem considering speed over only a portion of the wing.
The present work extends the recently reported implicit analogue of MacCormack's earlier widely-used explicit method to external axisymmetric laminar flows with strong entropy gradients. The details of the 'numerics' of the implicit part are provided in a body-oriented coordinate system with a moving outer (shock) boundary during the transient part of the solutions. The limiting values of the Courant number are obtained when the shock boundary is treated explicitly. The solution algorithm outlined includes the treatment of the source term associated with the equations in weak conservation form. From the results obtained for two sample problems, it becomes clear that accuracy of predictions is, indeed, very good at higher values of the Courant number. There is a significant saving in overall computing time, depending on the Courant number used and the flow Reynolds number. These properties combined with the simplicity of programming the implicit analogue may appeal to researchers for using it in the analysis of three-dimensional flow problems.