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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.

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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1952

On a solution of the nonlinear differential equation for transonic flow past a wave-shaped wall

The Prandtl-Busemann small-perturbation method is utilized to obtain the flow of a compressible fluid past an infinitely long wave-shaped wall. When the essential assumption for transonic flow (that all Mach numbers in the region of flow are nearly unity) is introduced, the expression for the velocity potential takes the form of a power series in the transonic similarity parameter. On the basis of this form of the solution, an attempt is made to solve the nonlinear differential equation for transonic flow past the wavy wall. The analysis utilized exhibits clearly the difficulties inherent in nonlinear-flow problems.

Kaplan, Carl↗
NASA NTRS1978

An integral solution to a nonlinear diffusion problem

The generalized Galerkin method (or the method of integral relations) is applied to the type of problem described by quasilinear parabolic equations. As an example the problem of nonlinear transient slab diffusion with a general reservoir boundary condition is worked out. The integral relations are given for an arbitrary number of strips, and solutions using up to seven strips have been obtained in order to investigate the convergence of the method.

Hussaini, M. Y.↗
NASA NTRS2017

Order-Reduced Solution of the Nonlinear High-Fidelity Generalized Method of Cells Micromechanics Relations

The High-Fidelity Generalized Method of Cells (HFGMC) is one technique for accurately simulating nonlinear composite material behavior. The HFGMC uses a higher-order approximation for the subcell displacement field that allows for a more accurate determination of the subcell stressstrain fields at the cost of some computational efficiency. In order to reduce computational costs associated with the solution of the ensuing system of simultaneous equations, the HFGMC global system of equations for doubly-periodic repeating unit cells with nonlinear constituents was reduced in size through the use of a Petrov-Galerkin-based Proper Orthogonal Decomposition order-reduction scheme. A number of cases were presented that address the computational feasibility of using order-reduction techniques to solve solid mechanics problems involving complex microstructures.

order-reduction↗
NASA NTRS1977

A Green's function formulation for a nonlinear potential flow solution applicable to transonic flow

Routine determination of inviscid subsonic flow fields about wing-body-tail configurations employing a Green's function approach for numerical solution of the perturbation velocity potential equation is successfully extended into the high subsonic subcritical flow regime and into the shock-free supersonic flow regime. A modified Green's function formulation, valid throughout a range of Mach numbers including transonic, that takes an explicit accounting of the intrinsic nonlinearity in the parent governing partial differential equations is developed. Some considerations pertinent to flow field predictions in the transonic flow regime are discussed.

Baker, A. J.↗
NASA NTRS1991

Solution of geometrically nonlinear statics problems by the p-version of the finite element method

This project is concerned with the possibility of using computers for the simulation of structural systems with the same degree of reliability as full scale physical experiments. Reliable numerical simulation will make it possible to reduce the costs of engineering and improve the quality of engineering decisions based on computed information. An error of idealization is an error between the actual physical quantities on which engineering decisions are based (e.g., maximum principal stress, first natural frequency, etc.) and the same data corresponding to the exact solution of the mathematical model. An error of discretization is an error between the quantities of interest corresponding to the exact and approximate solutions of a mathematical model. A high degree of reliability can be achieved in numerical simulation only if both the errors of idealization and errors of discretization can be shown to be small.

Szabo, Barna A.↗
NASA NTRS1967

Generalized superposition.

Generalization of superposition principle for linear systems applied to classification of nonlinear systems and solution of nonlinear filtering problems

Oppenheim, A. V.↗
NASA NTRS1982

Construction of solutions for some nonlinear two-point boundary value problems

Constructive existence and uniqueness results for boundary value problems associated with some simple special cases of the second order equation y'' = f(x,y,y') 0 or = x or = 1, are sought. The approach considered is to convert the differential equation and boundary conditions to an integral equation via Green's functions, and then to apply fixed point and contraction map principles to a sequence of successive approximations. The approach is tested on several applied problems. Difficulties in trying to prove general theorems are discussed.

Pennline, J. A.↗
NASA NTRS1981

A family of solution algorithms for nonlinear structural analysis based on relaxation equations

A family of hierarchical algorithms for nonlinear structural equations are presented. The algorithms are based on the Davidenko-Branin type homotopy and shown to yield consistent hierarchical perturbation equations. The algorithms appear to be particularly suitable to problems involving bifurcation and limit point calculations. An important by-product of the algorithms is that it provides a systematic and economical means for computing the stepsize at each iteration stage when a Newton-like method is employed to solve the systems of equations. Some sample problems are provided to illustrate the characteristics of the algorithms.

Park, K. C.↗
NASA NTRS1984

Element-by-element Solution Procedures for Nonlinear Structural Analysis

Element-by-element approximate factorization procedures are proposed for solving the large finite element equation systems which arise in nonlinear structural mechanics. Architectural and data base advantages of the present algorithms over traditional direct elimination schemes are noted. Results of calculations suggest considerable potential for the methods described.

Hughes, T. J. R.↗
NASA NTRS1985

Bounding solutions of geometrically nonlinear viscoelastic problems

Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.

Stubstad, J. M.↗
NASA NTRS1986

Bounding solutions of geometrically nonlinear viscoelastic problems

Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.

Stubstad, J. M.↗
NASA NTRS1992

Fast neural solution of a nonlinear wave equation

A neural algorithm for rapidly simulating a certain class of nonlinear wave phenomena using analog VLSI neural hardware is presented and applied to the Korteweg-de Vries partial differential equation. The corresponding neural architecture is obtained from a pseudospectral representation of the spatial dependence, along with a leap-frog scheme for the temporal evolution. Numerical simulations demonstrated the robustness of the proposed approach.

Toomarian, Nikzad↗