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At least 199 records · Page 11

Exact vacuum solution to conformal Weyl gravity and galactic rotation curves

The complete, exact exterior solution for a static, spherically symmetric source in locally conformal invariant Weyl gravity is presented. The solution includes the familiar exterior Schwarzschild solution as a special case and contains an extra gravitational potential term which grows linearly with distance. The obtained solution provides a potential explanation for observed galactic rotation curves without the need for dark matter. The solution also has some interesting implications for cosmology.

Mannheim, Philip D.↗

A complete analytical solution for the inverse instantaneous kinematics of a spherical-revolute-spherical (7R) redundant manipulator

Using a method based upon resolving joint velocities using reciprocal screw quantities, compact analytical expressions are generated for the inverse solution of the joint rates of a seven revolute (spherical-revolute-spherical) manipulator. The method uses a sequential decomposition of screw coordinates to identify reciprocal screw quantities used in the resolution of a particular joint rate solution, and also to identify a Jacobian null-space basis used for the direct solution of optimal joint rates. The results of the screw decomposition are used to study special configurations of the manipulator, generating expressions for the inverse velocity solution for all non-singular configurations of the manipulator, and identifying singular configurations and their characteristics. Two functions are therefore served: a new general method for the solution of the inverse velocity problem is presented; and complete analytical expressions are derived for the resolution of the joint rates of a seven degree of freedom manipulator useful for telerobotic and industrial robotic application.

Podhorodeski, R. P.↗

The steady state solutions of radiatively driven stellar winds for a non-Sobolev, pure absorption model

The steady state solution topology for absorption line-driven flows is investigated for the condition that the Sobolev approximation is not used to compute the line force. The solution topology near the sonic point is of the nodal type with two positive slope solutions. The shallower of these slopes applies to reasonable lower boundary conditions and realistic ion thermal speed v(th) and to the Sobolev limit of zero of the usual Castor, Abbott, and Klein model. At finite v(th), this solution consists of a family of very similar solutions converging on the sonic point. It is concluded that a non-Sobolev, absorption line-driven flow with a realistic values of v(th) has no uniquely defined steady state. To the extent that a pure absorption model of the outflow of stellar winds is applicable, radiatively driven winds should be intrinsically variable.

Poe, C. H.↗

The convergence rate of approximate solutions for nonlinear scalar conservation laws

The convergence rate is discussed of approximate solutions for the nonlinear scalar conservation law. The linear convergence theory is extended into a weak regime. The extension is based on the usual two ingredients of stability and consistency. On the one hand, the counterexamples show that one must strengthen the linearized L(sup 2)-stability requirement. It is assumed that the approximate solutions are Lip(sup +)-stable in the sense that they satisfy a one-sided Lipschitz condition, in agreement with Oleinik's E-condition for the entropy solution. On the other hand, the lack of smoothness requires to weaken the consistency requirement, which is measured in the Lip'-(semi)norm. It is proved for Lip(sup +)-stable approximate solutions, that their Lip'convergence rate to the entropy solution is of the same order as their Lip'-consistency. The Lip'-convergence rate is then converted into stronger L(sup p) convergence rate estimates.

Nessyahu, Haim↗

Solution techniques for the vorticity-streamfunction formulation of two-dimensional unsteady incompressible flows

A review of the solution techniques of Tezduyar et al. (1988 and 1989) for the vorticity-streamfunction formulation of two-dimensional incompressible flows is presented. While both the viscous and inviscid cases are considered, the derivation of the proper finite-element formulations for multiply connected domains is emphasized. In all formulations associated with the vorticity transport equation, the streamline upwind/Petrov-Galerkin method is used. The adaptive implicit-explicit and grouped element-by-element solution strategies are employed to maximize the computational efficiency. The solutions obtained in all test cases compare well with solutions from previously published investigations. The convergence and benchmark studies performed in this paper show that the solution techniques presented are accurate, reliable, and efficient.

Tezduyar, T. E.↗

Development of a solution adaptive unstructured scheme for quasi-3D inviscid flows through advanced turbomachinery cascades

The objective of the present research is to develop a general solution adaptive scheme for the accurate prediction of inviscid quasi-three-dimensional flow in advanced compressor and turbine designs. The adaptive solution scheme combines an explicit finite-volume time-marching scheme for unstructured triangular meshes and an advancing front triangular mesh scheme with a remeshing procedure for adapting the mesh as the solution evolves. The unstructured flow solver has been tested on a series of two-dimensional airfoil configurations including a three-element analytic test case presented here. Mesh adapted quasi-three-dimensional Euler solutions are presented for three spanwise stations of the NASA rotor 67 transonic fan. Computed solutions are compared with available experimental data.

Usab, William J., Jr.↗

Grid generation and flow solution method for Euler equations on unstructured grids

A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme, which uses Delaunay triangulation, generates the field points for the mesh based on cell aspect ratios and allows clustering of grid points near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss-Seidel procedure that is completely vectorizable. Also, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for an NACA 0012 airfoil as well as a two element configuration. Flow solution results are shown for a two dimensional flow over the NACA 0012 airfoil and for a two element configuration in which the solution was obtained through an adaptation procedure and compared with an exact solution. Preliminary three dimensional results also are shown in which the subsonic flow over a business jet is computed.

Anderson, W. Kyle↗

Interactive solution-adaptive grid generation

TURBO-AD is an interactive solution-adaptive grid generation program under development. The program combines an interactive algebraic grid generation technique and a solution-adaptive grid generation technique into a single interactive solution-adaptive grid generation package. The control point form uses a sparse collection of control points to algebraically generate a field grid. This technique provides local grid control capability and is well suited to interactive work due to its speed and efficiency. A mapping from the physical domain to a parametric domain was used to improve difficulties that had been encountered near outwardly concave boundaries in the control point technique. Therefore, all grid modifications are performed on a unit square in the parametric domain, and the new adapted grid in the parametric domain is then mapped back to the physical domain. The grid adaptation is achieved by first adapting the control points to a numerical solution in the parametric domain using control sources obtained from flow properties. Then a new modified grid is generated from the adapted control net. This solution-adaptive grid generation process is efficient because the number of control points is much less than the number of grid points and the generation of a new grid from the adapted control net is an efficient algebraic process. TURBO-AD provides the user with both local and global grid controls.

Choo, Yung K.↗

An approximate solution for interlaminar stresses in laminated composites: Applied mechanics program

An approximate solution for interlaminar stresses in finite width, laminated composites subjected to uniform extensional, and bending loads is presented. The solution is based upon the principle of minimum complementary energy and an assumed, statically admissible stress state, derived by considering local material mismatch effects and global equilibrium requirements. The stresses in each layer are approximated by polynomial functions of the thickness coordinate, multiplied by combinations of exponential functions of the in-plane coordinate, expressed in terms of fourteen unknown decay parameters. Imposing the stationary condition of the laminate complementary energy with respect to the unknown variables yields a system of fourteen non-linear algebraic equations for the parameters. Newton's method is implemented to solve this system. Once the parameters are known, the stresses can be easily determined at any point in the laminate. Results are presented for through-thickness and interlaminar stress distributions for angle-ply, cross-ply (symmetric and unsymmetric laminates), and quasi-isotropic laminates subjected to uniform extension and bending. It is shown that the solution compares well with existing finite element solutions and represents an improved approximate solution for interlaminar stresses, primarily at interfaces where global equilibrium is satisfied by the in-plane stresses, but large local mismatch in properties requires the presence of interlaminar stresses.

Rose, Cheryl A.↗

A numerical method for solving systems of linear ordinary differential equations with rapidly oscillating solutions

The present numerical method for accurate and efficient solution of systems of linear equations proceeds by numerically developing a set of basis solutions characterized by slowly varying dependent variables. The solutions thus obtained are shown to have a computational overhead largely independent of the small size of the scale length which characterizes the solutions; in many cases, the technique obviates series solutions near singular points, and its known sources of error can be easily controlled without a substantial increase in computational time.

Bernstein, Ira B.↗

A coupled solution method for predicting the thermostructural response of decomposing, expanding polymeric composites

A new solution method has recently been developed to analyze the thermal and structural response of polymeric composites during chemical decomposition (Sullivan and Salamon, 1992a). This method couples the equations of energy, mass transport and momentum and solves these equations simultaneously at each time step. In this paper, the couples solution method is applied to analyze the response of a glass phenolic composite during its chemical decomposition. The numerical solution to this particular problem was originally performed by Henderson, et al. (1985) and the actual response was measured by Henderson and Hagen (1985) and Ramamurthy (1988). In addition to further verification of the coupled solution method, the present solution offers additional insight into certain physical events which occur during chemical decomposition.

Sullivan, Roy M.↗

The problem of exact interior solutions for rotating rigid bodies in general relativity

The (3 + 1) dyadic formalism for timelike congruences is applied to derive interior solutions for stationary, axisymmetric, rigidly rotating bodies. In this approach the mathematics is formulated in terms of three-space-covariant, first-order, vector-dyadic, differential equations for a and Omega, the acceleration and angular velocity three-vectors of the rigid body; for T, the stress dyadic of the matter; and for A and B, the 'electric' and 'magnetic' Weyl curvature dyadics which describe the gravitational field. It is shown how an appropriate ansatz for the forms of these dyadics can be used to discover exact rotating interior solutions such as the perfect fluid solution first published in 1968. By incorporating anisotropic stresses, a generalization is found of that previous solution and, in addition, a very simple new solution that can only exist in toroidal configurations.

Wahlquist, H. D.↗

Space marching calculations about hypersonic configurations using a solution-adaptive mesh algorithm

A solution-adaptive marching algorithm is developed and applied to a three-dimensional parabolized Navier-Stokes equation solver. The resulting algorithm obtains accurate solutions by using a spatial-marching/adaptive grid procedure. The adaptation step redistributes grid points line by line in both crossflow directions, with grid point motion controlled by forces analogous to tensional and torsional spring forces with the tensional force proportional to the error measure or weighting functions. The solution-adaptive marching procedure is applied to the hypersonic flow about two generic aircraft configurations. The first of these is an all-body-type geometry with elliptical cross sections and is studied at angles of attack of 0.5, and 15 deg. The second geometry is a generic blended-wing-body design. Results are presented that demonstrate the improvements in flowfield resolution obtainable with the solution-adaptive marching procedure over conventional fixed grid techniques. Computed pitot pressure profiles obtained using the solution-adaptive algorithm show improved agreement with experimental data compared to predictions obtained using a fixed grid.

Harvey, Albert D.↗

The exact solution of shear-lag problems in flat panels and box beams assumed rigid in the transverse direction

A mathematical procedure is herein developed for obtaining exact solutions of shear-lag problems in flat panels and box beams: the method is based on the assumption that the amount of stretching of the sheets in the direction perpendicular to the direction of essential normal stresses is negligible. Explicit solutions, including the treatment of cut-outs, are given for several cases and numerical results are presented in graphic and tabular form. The general theory is presented in a from which further solutions can be readily obtained. The extension of the theory to cover certain cases of non-uniform cross section is indicated. Although the solutions are obtained in terms of infinite series, the present developments differ from those previously given in that, in practical cases, the series usually converge so rapidly that sufficient accuracy is afforded by a small number of terms. Comparisons are made in several cases between the present results and the corresponding solutions obtained by approximate procedures devised by Reissner and by Kuhn and Chiarito.

STRESSED SKIN-PLATES, FLAT↗

On the flow of a compressible fluid by the hodograph method II : fundamental set of particular flow solutions of the Chaplygin differential equation

The differential equation of Chaplygin's jet problem is utilized to give a systematic development of particular solutions of the hodograph flow equations, which extends the treatment of Chaplygin into the supersonic range and completes the set of particular solutions. The particular solutions serve to place on a reasonable basis the use of velocity correction formulas for the comparison of incompressible and compressible flows. It is shown that the geometric-mean type of velocity correction formula introduced in part I has significance as an over-all type of approximation in the subsonic range. A brief review of general conditions limiting the potential flow of an adiabatic compressible fluid is given and application is made to the particular solutions, yielding conditions for the existence of singular loci in the supersonic range. The combining of particular solutions in accordance with prescribed boundary flow conditions is not treated in the present paper.

Garrick, I E↗

Comparison of level-1 and level-2 buckling and postbuckling solutions

The accuracy of the solutions obtained with the Level-1 computational modules of DISDECO (Delft Interactive Shell Design Code) are investigated by comparing them with solutions obtained with ANILISA, a Level-2 computational module. Whereas the Level-1 solutions are based on the use of trigonometric functions to represent the out-of-plane displacement W and involve Galerkin type approximations to reduce the governing partial differential equations to simple algebraic expressions, the Level-2 solutions employ a truncated Fourier expansion in the circumferential direction and solve the resulting ordinary differential equations forming a nonlinear eigenvalue problem by a Stodola like technique. This involves the numerical integration of the set of ordinary differential equations, which in turn makes it possible to satisfy the specified boundary conditions exactly. It is shown that in many applications the Level-1 predictions concerning the critical buckling load of the perfect structure and its imperfection sensitivity are quite accurate and reliable. For those cases where this is not true, it is shown how the pre and postprocessing facilities of DISDECO can be used efficiently to arrive at a reliable prediction. This involves always the use of the Level-2 computational module ANILISA with its rigorous prebuckling solution and its feature which makes it possible to satisfy the specified boundary conditions exactly.

Arbocz, J.↗

The origin of spurious solutions in computational electromagnetics

The origin of spurious solutions in computational electromagnetics, which violate the divergence equations, is deeply rooted in a misconception about the first-order Maxwell's equations and in an incorrect derivation and use of the curl-curl equations. The divergence equations must be always included in the first-order Maxwell's equations to maintain the ellipticity of the system in the space domain and to guarantee the uniqueness of the solution and/or the accuracy of the numerical solutions. The div-curl method and the least-squares method provide rigorous derivation of the equivalent second-order Maxwell's equations and their boundary conditions. The node-based least-squares finite element method (LSFEM) is recommended for solving the first-order full Maxwell equations directly. Examples of the numerical solutions by LSFEM for time-harmonic problems are given to demonstrate that the LSFEM is free of spurious solutions.

Jiang, Bo-Nan↗

Application of the space-time conservation element and solution element method to two-dimensional advection-diffusion problems

The existing 2-D alpha-mu scheme and alpha-epsilon scheme based on the method of space-time conservation element and solution element, which were constructed for solving the linear 2-D unsteady advection-diffusion equation and unsteady advection equation, respectively, are tested. Also, the alpha-epsilon scheme is modified to become the V-E scheme for solving the nonlinear 2-D inviscid Burgers equation. Numerical solutions of six test problems are presented in comparison with their exact solutions or numerical solutions obtained by traditional finite-difference or finite-element methods. It is demonstrated that the 2-D alpha-mu, alpha-epsilon, and nu-epsilon schemes can be used to obtain numerical results which are more accurate than those based on some of the traditional methods but without using any artificial tuning in the computation. Similar to the previous 1-D test problems, the high accuracy and simplicity features of the space-time conservation element and solution element method have been revealed again in the present 2-D test results.

Wang, Xiao-Yen↗