SEARCH · Search NASA
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.
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.
Explore the source record for details and available documents.
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.
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.
Explore the source record for details and available documents.
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.
Explore the source record for details and available documents.
Neural algorithm for simulation of class of nonlinear wave phenomena devised. Numerically solves special one-dimensional case of Korteweg-deVries equation. Intended to be executed rapidly by neural network implemented as charge-coupled-device/charge-injection device, very-large-scale integrated-circuit analog data processor of type described in "CCD/CID Processors Would Offer Greater Precision" (NPO-18972).
An algorithm for solving a particular nonlinear independent-component-analysis (ICA) problem, that differs from prior algorithms for solving the same problem, has been devised. The problem in question of a type known in the art as a post nonlinear mixing problem is a useful approximation of the problem posed by the mixing and subsequent nonlinear distortion of sensory signals that occur in diverse scientific and engineering instrumentation systems.
The High-Fidelity Generalized Method of Cells (HFGMC) is one technique, distinct from traditional finite element approaches, for accurately simulating nonlinear composite material behavior. In this work, the HFGMC global system of equations for doubly-periodic repeating unit cells with nonlinear constituents has been reduced in size through the novel application of a Petrov-Galerkin Proper Orthogonal Decomposition order-reduction scheme in order to improve its computational efficiency. Order-reduced models of an E-glass/Nylon 12 composite led to a 4.8 to 6.3x speedup in the equation assembly/solution runtime while maintaining model accuracy. This corresponded to a 21 to 38 percent reduction in total runtime. The significant difference in assembly/solution and total runtimes was attributed to the evaluation of integration point inelastic field quantities; this step was identical between the unreduced and order-reduced models. Nonetheless, order-reduced techniques offer the potential to significantly improve the computational efficiency of multiscale calculations.
Nonlinear analysis of building structures and numerical solution of nonlinear algebraic equations and Newton's method are discussed. Other topics include: nonlinear interaction problems; solution procedures for nonlinear problems; crash dynamics and advanced nonlinear applications; material characterization, contact problems, and inelastic response; and formulation aspects and special software for nonlinear analysis.
This paper develops an algorithmic solution strategy which allows the handling of positive/indefinite stiffness characteristics associated with the pre- and post-buckling of structures subject to complex thermomechanical loading fields. The flexibility of the procedure is such that it can be applied to both finite difference and element-type simulations. Due to the generality of the algorithmic approach developed, both kinematic and thermal/mechanical type material nonlinearity including inelastic effects can be treated. This includes the possibility of handling completely general thermomechanical boundary conditions. To demonstrate the scheme, the results of several benchmark problems is presented.
Numerical solution of boundary layer differential equations
Numerical solution for variety of nonlinear degenerate elliptic boundary value problems, and convergence of associated iterative procedures
Exact solution of nonlinear relativistic equations of motion for electron in right circularly polarized wave propagating in whistler mode parallel to external magnetic field
Existence and uniqueness of periodic solution to single nonlinear differential equation of hyperbolic type
An investigation was conducted to continue the development of perturbation procedures and associated computational codes for rapidly determining approximations to nonlinear flow solutions, with the purpose of establishing a method for minimizing computational requirements associated with parametric design studies of transonic flows in turbomachines. The results reported here concern the extension of the previously developed successful method for single parameter perturbations to simultaneous multiple-parameter perturbations, and the preliminary application of the multiple-parameter procedure in combination with an optimization method to blade design/optimization problem. In order to provide as severe a test as possible of the method, attention is focused in particular on transonic flows which are highly supercritical. Flows past both isolated blades and compressor cascades, involving simultaneous changes in both flow and geometric parameters, are considered. Comparisons with the corresponding exact nonlinear solutions display remarkable accuracy and range of validity, in direct correspondence with previous results for single-parameter perturbations.
Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.