Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “singular equations”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Translational control of a graphically simulated robot arm by kinematic rate equations that overcome elbow joint singularity

An operator commands a robot hand to move in a certain direction relative to its own axis system by specifying a velocity in that direction. This velocity command is then resolved into individual joint rotational velocities in the robot arm to effect the motion. However, the usual resolved-rate equations become singular when the robot arm is straightened. To overcome this elbow joint singularity, equations were developed which allow continued translational control of the robot hand even though the robot arm is (or is nearly) fully extended. A feature of the equations near full arm extension is that an operator simply extends and retracts the robot arm to reverse the direction of the elbow bend (difficult maneuver for the usual resolved-rate equations). Results show successful movement of a graphically simulated robot arm.

Barker, L. K.↗
NASA NTRS1988

Weak solutions of the three-dimensional vorticity equation with vortex singularities

The extension of the concept of vortex singularities, developed by Saffman and Meiron (1986) for the case of two-dimensional point vortices in an incompressible vortical flow, to the three-dimensional case of vortex sticks (vortons) is investigated analytically. The derivation of the governing equations is explained, and it is demonstrated that the formulation obtained conserves total vorticity and is a weak solution of the vorticity equation, making it an appropriate means for representing three-dimensional vortical flows with limited numbers of vortex singularities.

Winckelmans, G.↗
NASA NTRS1972

A layered composite with a broken laminate

The problem of a laminate composite in the presence of a crack located normal to the bond lines is considered. Stress analysis of the limiting case when the crack extends to the bond lines is carried out. An integral transform technique is used to formulate the problem in terms of a singular integral equation. The power of stress singularity around the crack tip terminating at the interface is obtained using the above technique. The singular integral equation is solved numerically and the effect of material properties on the stress intensity factor is calculated.

Gupta, G. D.↗
NASA NTRS1992

Singularities of the Euler equation and hydrodynamic stability

Equations governing the motion of a specific class of singularities of the Euler equation in the extended complex spatial domain are derived. Under some assumptions, it is shown how this motion is dictated by the smooth part of the complex velocity at a singular point in the unphysical domain. These results are used to relate the motion of complex singularities to the stability of steady solutions of the Euler equation. A sufficient condition for instability is conjectured. Several examples are presented to demonstrate the efficacy of this sufficient condition which include the class of elliptical flows and the Kelvin-Stuart Cat's Eye.

Tanveer, S.↗
NASA NTRS1993

Singularities of the Euler equation and hydrodynamic stability

Equations governing the motion of a specific class of singularities of the Euler equation in the extended complex spatial domain are derived. Under some assumptions, it is shown how this motion is dictated by the smooth part of the complex velocity at a singular point in the unphysical domain. These results are used to relate the motion of complex singularities to the stability of steady solutions of the Euler equation. A sufficient condition for instability is conjectured. Several examples are presented to demonstrate the efficacy of this sufficient condition which include the class of elliptical flows and the Kelvin-Stuart Cat's Eye.

Tanveer, S.↗
NASA NTRS1986

On the solution of integral equations with a generalized cauchy kernal

A certain class of singular integral equations that may arise from the mixed boundary value problems in nonhonogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral equations adopted, the density function is a potential or a displacement and consequently the kernal has strong singularities of the form (t-x)(-2), x(n-2) (t+x)(n), (n is = or 2, 0 x, t b). The complex function theory is used to determine the fundamental function of the problem for the general case and a simple numerical technique is described to solve the integral equation. Two examples from the theory of elasticity are then considered to show the application of the technique.

Kaya, A. C.↗
NASA NTRS1973

The problem of a finite strip compressed between two rough rigid stamps

A finite strip compressed between two rough rigid stamps is considered. The elastostatic problem is formulated in terms of a singular integral equation from which the proper stress singularities at the corners are determined. The singular integral equation is solved numerically to determine the stresses along the fixed ends of the strip. The effect of material properties and strip geometry on the stress intensity factor is presented graphically.

Gupta, G. D.↗
NASA NTRS1975

The problem of a finite strip compressed between two rough rigid stamps

A finite strip compressed between two rough rigid stamps is considered. The elastostatic problem is formulated in terms of a singular integral equation from which the proper stress singularities at the corners are determined. The singular integral equation is solved numerically to determine the stresses along the fixed ends of the strip. The effect of material properties and strip geometry on the stress-intensity factor is presented graphically.

Gupta, G. D.↗
NASA NTRS1972

An integral equation approach to the strip problem

A semi-infinite strip held rigidly on its short end is considered. Loads in the strip at infinity (far away from the fixed end) are prescribed. Integral transform technique is used to provide an exact formulation of the problem in terms of a singular integral equation. Stress singularity at the strip corner is obtained from the singular integral equation which is then solved numerically. Stresses along the rigid end are determined and the effect of the material properties on the stress intensity factor is presented. The method can also be applied to the problem of a laminate composite with a flat inclusion normal to the interfaces.

Gupta, G. D.↗
NASA NTRS1986

On the solution of integral equations with a generalized cauchy kernel

In this paper a certain class of singular integral equations that may arise from the mixed boundary value problems in nonhomogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral equations adopted, the density function is a potential or a displacement and consequently the kernel has strong singularities of the form (t-x) sup-2, x sup n-2 (t+x) sup n, (n or = 2, 0x,tb). The complex function theory is used to determine the fundamental function of the problem for the general case and a simple numerical technique is described to solve the integral equation. Two examples from the theory of elasticity are then considered to show the application of the technique.

Kaya, A. C.↗
NASA NTRS1973

A layered composite with a broken laminate.

The problem of a laminate composite in presence of a crack located normal to the bond lines is considered. Stress analysis of the limiting case when the crack extends to the bond lines is carried out. Integral transform technique is used to formulate the problem in terms of a singular integral equation from which the power of stress singularity around the crack tip terminating at the interface is obtained. The singular integral equation is solved numerically and the effect of material properties on the stress intensity factor is calculated.

Gupta, G. D.↗
NASA NTRS1989

An interpretation and solution of ill-conditioned linear equations

Data insufficiency, poorly conditioned matrices and singularities in equations occur regularly in complex optimization, correlation, and interdisciplinary model studies. This work concerns itself with two methods of obtaining certain physically realistic solutions to ill-conditioned or singular algebraic systems of linear equations arising from such studies. Two efficient computational solution procedures that generally lead to locally unique solutions are presented when there is insufficient data to completely define the model, or a least-squares error formulation of this system results in an ill-conditioned system of equations. If it is assumed that a reasonable estimate of the uncertain data is available in both cases cited above, then we shall show how to obtain realistic solutions efficiently, in spite of the insufficiency of independent data. The proposed methods of solution are more efficient than singular-value decomposition for dealing with such systems, since they do not require solutions for all the non-zero eigenvalues of the coefficient matrix.

Ojalvo, I. U.↗
NASA NTRS1973

Thermoelastic flutter models for elements of flexible satellites

Models of thermally induced flutter of the flexible elements of a satellite, such as beams, circular plates, and cylindrical shells have been obtained. These models form the necessary blocks for analyzing the motion of satellites. The heat input is considered to be caused by solar radiations. The partial differential equations for all the elements of the satellite are linear in the space dependent variables and nonlinear in the time-dependent variables. These equations are coupled through the motion of the center of mass of the satellite. Galerkin's method has been used to remove the space-dependence of these equations. In the succeeding paper, a further reduction of these equations is made into singular perturbation equations, which are amenable to solution for complex problems of extremely large number of degrees of freedom.

Huang, T. C.↗
NASA NTRS1974

An orthotropic laminate composite containing a layer with a crack

A laminate composite containing an orthotropic layer with a crack situated normal to the interfaces, and bonded to two orthotropic half-planes of dissimilar materials was considered. The solutions for two different classes of orthotropic materials are presented. In each case, the problem was first reduced to a system of dual integral equations, then to a singular integral equation which was subsequently solved numerically for the stress intensity factors at the tip of the crack. The effect of the material properties on the stress intensity factor was investigated. The generalized plane stress and the plane strain were treated simultaneously.

Arin, K.↗
NASA NTRS1977

An orthotropic laminate composite containing a layer with a crack

A laminate composite containing an orthotropic layer with a crack situated normal to the interfaces, and bonded to two orthotropic half-planes of dissimilar materials, is considered. The solutions for two different classes of orthotropic materials are presented separately. In each case, the problem is first reduced to a system of dual integral equations, then to a singular integral equation which is subsequently solved numerically for the stress intensity factors at the tip of the crack. The effect of the material properties on the stress intensity factor is investigated. Two cases, the generalized plane stress and the plane strain, are treated simultaneously.

Arin, K.↗
NASA NTRS1978

Mixed boundary-value problems in mechanics

Definitions in the case of multiple series equations and multiple integral equations are examined. In considering the solution of a given mixed boundary value problem perhaps the simplest technique is the direct application of the method of complex potentials provided the problem admits such potentials and the domain and the boundary conditions are suitable for such an application. The direct application of complex potentials is described with the aid of examples, taking into account a problem in potential theory, the case of periodic cuts, and an elasticity problem for a nonhomogeneous plane. The reduction to singular integral equations is discussed along with the numerical solution of singular integral equations of the first kind, integral equations with generalized Cauchy kernels, and singular integral equations of the second kind.

Erdogan, F.↗
NASA NTRS1973

An integral equation approach to the semi-infinite strip problem.

A semi-infinite strip held rigidly on its short end is considered. Loads in the strip at infinity (far away from the fixed end) are prescribed. The integral transform technique is used to provide an exact formulation of the problem in terms of a singular integral equation. The stress singularity at the strip corner is obtained from the singular integral equation, which is then solved numerically. Stresses along the rigid end are determined, and the effect of the material properties on the stress-intensity factor is presented. The method can also be applied to the problem of a laminate composite with a flat inclusion normal to the interfaces.

Gupta, G. D.↗