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All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

Higher order accurate difference solutions of fluid mechanics problems by a compact differencing technique

A general fourth order differencing scheme is developed and applied to three viscous test problems to verify the accuracy and applicability of the technique. The procedure is atypical since only three nodes are necessary to obtain the desired fourth order accuracy. This is accomplished by a differencing technique which considers the function and all necessary derivatives as unknowns. The relations for these derivatives yield simple tridiagonal equations which can be easily solved. Comparisons of the fourth order results with those computed using second order methods are presented for the test problems and clearly indicate that the accuracy achieved by these fourth order computations is always significantly better than current second order procedures.

Hirsh, R. S.↗
NASA NTRS1999

Kinetics of template-directed pyrophosphate-linked dideoxyguanylate synthesis as a function of 2-MeImpdG and poly(C) concentration: insights into the mechanism

Aqueous solutions of deoxyguanosine 5'-monophosphate 2-methylimidazolide, 2-MeImpdG, yield primarily deoxyguanosine 5'-monophosphate, 5'dGMP, and pyrophosphate-linked dideoxyguanylate, dG5'ppdG, abbreviated G2p (see Chart 1). The initial rate of G2p formation, d[G2p]/dt in M h-1, determined at 23 degrees C, pH 7.8, 1.0 M NaCl and 0.2 M Mg2+ by timed high-performance liquid chromatography (HPLC) analysis, exhibits a second-order dependence on 2-MeImpdG concentration, [G]o, indicating a bimolecular mechanism of dimerization in the range 0.02 M < or = [G]o < or = 0.09 M. In the presence of polycytidylate, poly(C), G2p synthesis is accelerated and oligodeoxyguanylate products are formed by incorporation of 2-MeImpdG molecules. The kinetics of G2p formation as a function of both monomer and polymer concentration, expressed in C equivalents, were also determined under the above conditions and exhibited a complex behavior. Specifically, at a constant [poly(C)], values of d[G2p]/dt typically increased with [G]o with a parabolic upward curvature. At a constant [G]o, values of d[G2p]/dt increase with [poly(C)], but level off at the higher poly(C) concentrations. As [G]o increases this saturation occurs at a higher poly(C) concentration, a result opposite to expectation for a simple complexation of two reacting monomers with the catalyst prior to reaction. Nevertheless, these results are shown to be quantitatively consistent with a template-directed (TD) mechanism of dimerization where poly(C) acts as the template to bind 2-MeImpdG in a cooperative manner and lead, for the first time, to the formulation of principles that govern template-directed chemistry. Analysis of the kinetic data via a proposed TD cooperative model provides association constants for the affinity between polymer and monomer and the intrinsic reactivity of 2-MeImpdG toward pyrophosphate synthesis. To the best of our knowledge, poly(C)/2-MeImpdG is the first system that could serve as a textbook example of a TD reaction under conditions such that the template is fully saturated by monomers and under conditions that it is not.

NASA Discipline Exobiology↗
NASA NTRS2004

Integrated Force Method Solution to Indeterminate Structural Mechanics Problems

Strength of materials problems have been classified into determinate and indeterminate problems. Determinate analysis primarily based on the equilibrium concept is well understood. Solutions of indeterminate problems required additional compatibility conditions, and its comprehension was not exclusive. A solution to indeterminate problem is generated by manipulating the equilibrium concept, either by rewriting in the displacement variables or through the cutting and closing gap technique of the redundant force method. Compatibility improvisation has made analysis cumbersome. The authors have researched and understood the compatibility theory. Solutions can be generated with equal emphasis on the equilibrium and compatibility concepts. This technique is called the Integrated Force Method (IFM). Forces are the primary unknowns of IFM. Displacements are back-calculated from forces. IFM equations are manipulated to obtain the Dual Integrated Force Method (IFMD). Displacement is the primary variable of IFMD and force is back-calculated. The subject is introduced through response variables: force, deformation, displacement; and underlying concepts: equilibrium equation, force deformation relation, deformation displacement relation, and compatibility condition. Mechanical load, temperature variation, and support settling are equally emphasized. The basic theory is discussed. A set of examples illustrate the new concepts. IFM and IFMD based finite element methods are introduced for simple problems.

Patnaik, Surya N.↗
NASA NTRS1991

Closed-form solutions for linear regulator design of mechanical systems including optimal weighting matrix selection

Vibration in modern structural and mechanical systems can be reduced in amplitude by increasing stiffness, redistributing stiffness and mass, and/or adding damping if design techniques are available to do so. Linear Quadratic Regulator (LQR) theory in modern multivariable control design, attacks the general dissipative elastic system design problem in a global formulation. The optimal design, however, allows electronic connections and phase relations which are not physically practical or possible in passive structural-mechanical devices. The restriction of LQR solutions (to the Algebraic Riccati Equation) to design spaces which can be implemented as passive structural members and/or dampers is addressed. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical system. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist.

Hanks, Brantley R.↗
NASA NTRS1981

A study of crystal growth by solution technique

The mechanism of crystal growth by solution technique was studied. A low temperature solution crystal growth setup was developed. Crystals of triglycine sulfate (TGS) were grown using this arrangement. Some additional tasks were performed toward fabrication of experiments for future space flight.

Lal, R. B.↗
NASA NTRS1992

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.↗
NASA NTRS1990

Dynamic analysis of space-related linear and non-linear structures

In order to be cost effective, space structures must be extremely light weight, and subsequently, very flexible structures. The power system for Space Station Freedom is such a structure. Each array consists of a deployable truss mast and a split blanket of photovoltaic solar collectors. The solar arrays are deployed in orbit, and the blanket is stretched into position as the mast is extended. Geometric stiffness due to the preload make this an interesting non-linear problem. The space station will be subjected to various dynamic loads, during shuttle docking, solar tracking, attitude adjustment, etc. Accurate prediction of the natural frequencies and mode shapes of the space station components, including the solar arrays, is critical for determining the structural adequacy of the components, and for designing a dynamic controls system. The process used in developing and verifying the finite element dynamic model of the photo-voltaic arrays is documented. Various problems were identified, such as grounding effects due to geometric stiffness, large displacement effects, and pseudo-stiffness (grounding) due to lack of required rigid body modes. Analysis techniques, such as development of rigorous solutions using continuum mechanics, finite element solution sequence altering, equivalent systems using a curvature basis, Craig-Bampton superelement approach, and modal ordering schemes were utilized. The grounding problems associated with the geometric stiffness are emphasized.

Bosela, Paul A.↗
NASA NTRS1990

Dynamic analysis of space-related linear and non-linear structures

In order to be cost effective, space structures must be extremely light weight, and subsequently, very flexible structures. The power system for Space Station Freedom is such a structure. Each array consists of a deployable truss mast and a split blanket of photo-voltaic solar collectors. The solar arrays are deployed in orbit, and the blanket is stretched into position as the mast is extended. Geometric stiffness due to the preload make this an interesting non-linear problem. The space station will be subjected to various dynamic loads, during shuttle docking, solar tracking, attitude adjustment, etc. Accurate prediction of the natural frequencies and mode shapes of the space station components, including the solar arrays, is critical for determining the structural adequacy of the components, and for designing a dynamic control system. The process used in developing and verifying the finite element dynamic model of the photo-voltaic arrays is documented. Various problems were identified, such as grounding effects due to geometric stiffness, large displacement effects, and pseudo-stiffness (grounding) due to lack of required rigid body modes. Analysis techniques, such as development of rigorous solutions using continuum mechanics, finite element solution sequence altering, equivalent systems using a curvature basis, Craig-Bampton superelement approach, and modal ordering schemes were utilized. The grounding problems associated with the geometric stiffness are emphasized.

Bosela, Paul A.↗
NASA NTRS1990

The method of lines in analyzing solids containing cracks

A semi-numerical method is reviewed for solving a set of coupled partial differential equations subject to mixed and possibly coupled boundary conditions. The line method of analysis is applied to the Navier-Cauchy equations of elastic and elastoplastic equilibrium to calculate the displacement distributions in various, simple geometry bodies containing cracks. The application of this method to the appropriate field equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. When decoupling of the equations and their boundary conditions is not possible, the use of a successive approximation procedure permits the analytical solution of the resulting ordinary differential equations. The use of this method is illustrated by reviewing and presenting selected solutions of mixed boundary value problems in three dimensional fracture mechanics. These solutions are of great importance in fracture toughness testing, where accurate stress and displacement distributions are required for the calculation of certain fracture parameters. Computations obtained for typical flawed specimens include that for elastic as well as elastoplastic response. Problems in both Cartesian and cylindrical coordinate systems are included. Results are summarized for a finite geometry rectangular bar with a central through-the-thickness or rectangular surface crack under remote uniaxial tension. In addition, stress and displacement distributions are reviewed for finite circular bars with embedded penny-shaped cracks, and rods with external annular or ring cracks under opening mode tension. The results obtained show that the method of lines presents a systematic approach to the solution of some three-dimensional mechanics problems with arbitrary boundary conditions. The advantage of this method over other numerical solutions is that good results are obtained even from the use of a relatively coarse grid.

Gyekenyesi, John P.↗
NASA NTRS1992

Complex generalized minimal residual algorithm for iterative solution of quantum-mechanical reactive scattering equations

Complex dense matrices corresponding to the D + H2 and O + HD reactions were solved using a complex generalized minimal residual (GMRes) algorithm described by Saad and Schultz (1986) and Saad (1990). To provide a test case with a different structure, the H + H2 system was also considered. It is shown that the computational effort for solutions with the GMRes algorithm depends on the dimension of the linear system, the total energy of the scattering problem, and the accuracy criterion. In several cases with dimensions in the range 1110-5632, the GMRes algorithm outperformed the LAPACK direct solver, with speedups for the linear equation solution as large as a factor of 23.

Chatfield, David C.↗
DOE OSTI2024

Research Progress and Perspectives on Pre‐Sodiation Strategies for Sodium‐Ion Batteries

Sodium‐ion batteries (SIBs) with abundant elements have garnered significant attention from researches as a promise compensation to lithium‐ion batteries (LIBs). However, the large‐scale commercial application of SIBs is partially hindered by the limited initial coulombic efficiency (ICE) due to the irreversible formation of solid electrolyte interphase (SEI) and intercalation into the defects in the anode. Similar to pre‐lithiation techniques, pre‐sodiation approaches are considered to be one of the most direct and effective way to compensate for the loss of active sodium at the anode side of SIBs during the initial cycle. In this context, additional sodium ions are pre‐injected to the cathode/anode material by chemical/electrochemical methods, aiming to improve battery span life and energy density. Here, this review delves into the necessity and impact of pre‐sodiation techniques, compiling the latest research progress, for instance, self‐sacrificing cathode additives, over‐sodiated cathode materials, direct contact and solution chemical pre‐sodiation. Notably, the research mechanisms underlying solution chemical pre‐sodiation are highlighted. This comprehensive overview aims to foster a deeper understanding of the pre‐sodiation techniques and expects to provide guidance for realizing the commercial application of high energy density sodium‐ion batteries.

25 ENERGY STORAGE↗
NASA NTRS1983

Proposed solution methodology for the dynamically coupled nonlinear geared rotor mechanics equations

The equations which describe the three-dimensional motion of an unbalanced rigid disk in a shaft system are nonlinear and contain dynamic-coupling terms. Traditionally, investigators have used an order analysis to justify ignoring the nonlinear terms in the equations of motion, producing a set of linear equations. This paper will show that, when gears are included in such a rotor system, the nonlinear dynamic-coupling terms are potentially as large as the linear terms. Because of this, one must attempt to solve the nonlinear rotor mechanics equations. A solution methodology is investigated to obtain approximate steady-state solutions to these equations. As an example of the use of the technique, a simpler set of equations is solved and the results compared to numerical simulations. These equations represent the forced, steady-state response of a spring-supported pendulum. These equations were chosen because they contain the type of nonlinear terms found in the dynamically-coupled nonlinear rotor equations. The numerical simulations indicate this method is reasonably accurate even when the nonlinearities are large.

Mitchell, L. D.↗