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Results for “VARIATIONAL PRINCIPLE”

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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

The prediction of pseudo-resonance positions in the Schwinger variational principle

The Schwinger Variational Principle is appled to s-wave electron-hydrogen atom scattering. It is shown computationally, that, consistent with a paper by B. Apagyi, P. Levay, and K. Ladanyi, there are pseudo-resonances at the static exchange level of approximation, but not at the static level. The T-matrix was employed, as well as, the K-matrix version of the Schwinger Principle, with a real Slater basis, and obtained the same results in both. The origin of the pseudo-resonances as resulting from singularities in the separable potential that is effectively employed in the Lippmann-Schwinger equation from which the Schwinger Variational Principle can be derived. The determination of the pseudo-resonance parameters from the separable potential is computationally inexpensive and may be used to predict the pseudo-resonance parameters for the scattering calculations so that they may be avoided.

Weatherford, Charles A.↗
NASA NTRS1991

Analysis of superconducting electromagnetic finite elements based on a magnetic vector potential variational principle

Electromagnetic finite elements are extended based on a variational principle that uses the electromagnetic four potential as primary variable. The variational principle is extended to include the ability to predict a nonlinear current distribution within a conductor. The extension of this theory is first done on a normal conductor and tested on two different problems. In both problems, the geometry remains the same, but the material properties are different. The geometry is that of a 1-D infinite wire. The first problem is merely a linear control case used to validate the new theory. The second problem is made up of linear conductors with varying conductivities. Both problems perform well and predict current densities that are accurate to within a few ten thousandths of a percent of the exact values. The fourth potential is then removed, leaving only the magnetic vector potential, and the variational principle is further extended to predict magnetic potentials, magnetic fields, the number of charge carriers, and the current densities within a superconductor. The new element produces good results for the mean magnetic field, the vector potential, and the number of superconducting charge carriers despite a relatively high system condition number. The element did not perform well in predicting the current density. Numerical problems inherent to this formulation are explored and possible remedies to produce better current predicting finite elements are presented.

Schuler, James J.↗
DOE OSTI2025

A Type II Hamiltonian Variational Principle and Adjoint Systems for Lie Groups

We present a novel Type II variational principle on the cotangent bundle of a Lie group which enforces Type II boundary conditions, i.e., fixed initial position and final momentum. In general, such Type II variational principles are only globally defined on vector spaces or locally defined on general manifolds; however, by left translation, we are able to define this variational principle globally on cotangent bundles of Lie groups. Type II boundary conditions are particularly important for adjoint sensitivity analysis, which is our motivating application. As such, we additionally discuss adjoint systems on Lie groups, their properties, and how they can be used to solve optimization problems subject to dynamics on Lie groups.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

A study of pseudoresonances in the application of the Schwinger variational principle to electron scattering from atomic hydrogen

The Schwinger variational principle is applied to s-wave electron-hydrogen atom scattering. Computationally, consistent with a recent paper by Apagyi et al. (1988), there are pseudoresonances at the static exchange level of approximation, but not at the static level. The T-matrix as well as the K-matrix version of the Schwinger principle is used with a real Slater basis, and the same results are obtained in both. The origin of the pseudoresonances from singularities in the separable potential that is effectively employed in the Lippman-Schwinger equation from which the Schwinger variational principle can be derived. The determination of the pseudoresonance parameters from the separable potential is computationally inexpensive and may be used to predict the pseudoresonance parameters for the scattering calculations so as to avoid them.

Weatherford, Charles A.↗
NASA NTRS1987

A coupled mode formulation by reciprocity and a variational principle

A coupled mode formulation for parallel dielectric waveguides is presented via two methods: a reciprocity theorem and a variational principle. In the first method, a generalized reciprocity relation for two sets of field solutions satisfying Maxwell's equations and the boundary conditions in two different media, respectively, is derived. Based on the generalized reciprocity theorem, the coupled mode equations can then be formulated. The second method using a variational principle is also presented for a general waveguide system which can be lossy. The results of the variational principle can also be shown to be identical to those from the reciprocity theorem. The exact relations governing the 'conventional' and the new coupling coefficients are derived. It is shown analytically that the present formulation satisfies the reciprocity theorem and power conservation exactly, while the conventional theory violates the power conservation and reciprocity theorem by as much as 55 percent and the Hardy-Streifer (1985, 1986) theory by 0.033 percent, for example.

Chuang, Shun-Lien↗
NASA NTRS1987

A probabilistic Hu-Washizu variational principle

A Probabilistic Hu-Washizu Variational Principle (PHWVP) for the Probabilistic Finite Element Method (PFEM) is presented. This formulation is developed for both linear and nonlinear elasticity. The PHWVP allows incorporation of the probabilistic distributions for the constitutive law, compatibility condition, equilibrium, domain and boundary conditions into the PFEM. Thus, a complete probabilistic analysis can be performed where all aspects of the problem are treated as random variables and/or fields. The Hu-Washizu variational formulation is available in many conventional finite element codes thereby enabling the straightforward inclusion of the probabilistic features into present codes.

Liu, W. K.↗
NASA NTRS1989

Treatment of coupled fluid-structure interaction problems by a mixed variational principle

A general three-field variational principle is obtained for the motion of an acoustic fluid enclosed in a rigid or flexible container by the method of canonical decomposition applied to a modified form of the wave equation in the displacement potential. The general principle is specialized to a mixed two-field principle that contains the fluid displacement potential and pressure as independent fields. Semidiscrete finite-element equations of motion based on this principle are displayed.

Felippa, Carlos A.↗
NASA NTRS2003

A Variational Principle for Reconstruction of Elastic Deformations in Shear Deformable Plates and Shells

A variational principle is formulated for the inverse problem of full-field reconstruction of three-dimensional plate/shell deformations from experimentally measured surface strains. The formulation is based upon the minimization of a least squares functional that uses the complete set of strain measures consistent with linear, first-order shear-deformation theory. The formulation, which accommodates for transverse shear deformation, is applicable for the analysis of thin and moderately thick plate and shell structures. The main benefit of the variational principle is that it is well suited for C(sup 0)-continuous displacement finite element discretizations, thus enabling the development of robust algorithms for application to complex civil and aeronautical structures. The methodology is especially aimed at the next generation of aerospace vehicles for use in real-time structural health monitoring systems.

Tessler, Alexander↗
NASA NTRS1993

A survey of parametrized variational principles and applications to computational mechanics

This survey paper describes recent developments in the area of parametrized variational principles (PVP's) and selected applications to finite-element computational mechanics. A PVP is a variational principle containing free parameters that have no effect on the Euler-Lagrange equations. The theory of single-field PVP's based on gauge functions (also known as null Lagrangians) is a subset of the inverse problem of variational calculus that has limited value. On the other hand, multifield PVP's are more interesting from theoretical and practical standpoints. Following a tutorial introduction, the paper describes the recent construction of multifield PVP's in several areas of elasticity and electromagnetics. It then discusses three applications to finite-element computational mechanics: the derivation of high-performance finite elements, the development of element-level error indicators, and the constructions of finite element templates. The paper concludes with an overview of open research areas.

Felippa, Carlos A.↗
NASA NTRS1977

Analysis of magnetic fields using variational principles and CELAS2 elements

Prospective techniques for analyzing magnetic fields using NASTRAN are reviewed. A variational principle utilizing a vector potential function is presented which has as its Euler equations, the required field equations and boundary conditions for static magnetic fields including current sources. The need for an addition to this variational principle of a constraint condition is discussed. Some results using the Lagrange multiplier method to apply the constraint and CELAS2 elements to simulate the matrices are given. Practical considerations of using large numbers of CELAS2 elements are discussed.

Frye, J. W.↗
NASA NTRS1990

Electromagnetic finite elements based on a four-potential variational principle

Electromagnetic finite elements based on a variational principle that uses the electromagnetic four-potential as primary variable are derived. This choice is used to construct elements suitable for downstream coupling with mechanical and thermal finite elements for the analysis of electromagnetic/mechanical systems that involve superconductors. The main advantages of the four-potential as a basis for finite element formulation are: (1) the number of degrees of freedom per node remains modest as the problem dimensionality increases, (2) jump discontinuities on interfaces are naturally accommodated, and (3) statics as well as dynamics may be treated without any a priori approximations. The new elements are tested on an axisymmetric problem under steady-state forcing conditions. The results are in excellent agreement with analytical solutions.

Schuler, James↗
NASA NTRS1991

Electromagnetic finite elements based on a four-potential variational principle

Electromagnetic finite elements based on a variational principle that uses the electromagnetic four-potential as a primary variable are derived. This choice is used to construct elements suitable for downstream coupling with mechanical and thermal finite elements for the analysis of electromagnetic/mechanical systems that involve superconductors. The main advantages of the four-potential as a basis for finite element formulation are that the number of degrees of freedom per node remains modest as the problem dimensionally increases, that jump discontinuities on interfaces are naturally accommodated, and that statics as well as dynamics may be treated without any a priori approximations. The new elements are tested on an axisymmetric problem under steady state forcing conditions. The results are in excellent agreement with analytical solutions.

Schuler, James J.↗
NASA NTRS1974

The discrete complementary variational principle and optimal control systems

A discrete complementary variational principle is developed and applied to linear and nonlinear discrete-time optimal control systems. Using the variational approach, a primal-dual relationship is established. This relationship provides a precise measure of system suboptimality independent of any a priori knowledge of the optimal solution.

Chan, W. L.↗