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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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Postbuckling analysis using a general purpose code

A new capability for solving postbuckling problems in shell structures is described. The matrix theory to adapt Newton's method to nonlinear finite element shell analysis is outlined first. The matrix theory is directed at writing consistent linear algebratic equations for problems where the tangent stiffness matrix is singular or nearly singular. The matrix theory suggests a change of variables as part of the usual iterative procedure in Newton's method. The change of variables is shown to be feasible for introduction into the algorithm programmed in general purpose codes for finite element analysis of structures. Numerical results from a new option that has been programmed in an existing general purpose code are presented. The analysis of shell structures for collapse and for branching at bifurcation loads is illustrated by the numerical examples.

Thurston, G. A.↗
NASA NTRS1992

Grounding of space structures

Space structures, such as the Space Station solar arrays, must be extremely light-weight, flexible structures. Accurate prediction of the natural frequencies and mode shapes is essential for determining the structural adequacy of components, and designing a controls system. The tension pre-load in the 'blanket' of photovoltaic solar collectors, and the free/free boundary conditions of a structure in space, causes serious reservations on the use of standard finite element techniques of solution. In particular, a phenomenon known as 'grounding', or false stiffening, of the stiffness matrix occurs during rigid body rotation. This paper examines the grounding phenomenon in detail. Numerous stiffness matrices developed by others are examined for rigid body rotation capability, and found lacking. A force imbalance inherent in the formulations examined is the likely cause of the grounding problem, suggesting the need for a directed force formulation.

Bosela, P. A.↗
NASA NTRS1994

Superconducting axisymmetric finite elements based on a gauged potential variational principle. Part 2: Solutions and numerical results

This paper discusses an incremental-iterative nonlinear solution technique for solving the nonlinear finite element equations of the superconducting state of a superconductor. The untreated equations are highly ill-conditioned and are impossible to solve within the typical 16-place double precision supplied by most computers. A combination of matrix scaling and mesh grading techniques is used to reduce the condition number of the tangent stiffness matrix and increase the accuracy of the current carrying boundary layer representation. Numerical results for a one-dimensional model of a time-independent superconductor treated by the Ginzburg-Landau model are presented and discussed. The computed solutions clearly display the Meissner effect of magnetic field expulsion from the central region of the superconductor. These results are compared to the physics of a low-viscosity fluid problem. From this analogy, a physical argument is advanced about the macroscopic behavior of superconductors.

Schuler, James J.↗
NASA NTRS1966

Matrix methods and automation in structural engineering

The partial differential equations of motion of shell structures subject to arbitrary loads may be extremely difficult or even impossible to solve. Since the digital computer is now an available tool for the structural engineer, current research has been directed toward methods which involve matrix formulation of large systems of algebraic equations and matrix solutions for discrete elements rather than the solution of the partial differential equations. These methods require rapid and accurate computer solutions. Recognizing the accuracy problems inherent in working with large matrices, a comprehensive survey of available computer programs was performed for large matrix inversion and for eigenvalue and eigenvector solutions under a Research Grant from the National Aeronautics and Space Administration and the techniques are developed in this paper for using these programs most efficiently for structural applications. The contents of the paper include: automation of matrix compilation, methods of very large matrix inversion and solution of simultaneous equation, and techniques for finding eigenvalues and vectors. In addition, a finite element stiffness matrix approach developed at the Denver Research Institute for both plates and shells subject to arbitrary dynamic loads is described as it was instrumented with complete automation on the digital computer.

Anita S West↗
NASA NTRS1990

Vibration transmission through rolling element bearings. I - Bearing stiffness formulation. II - System studies

How vibratory motion can be transmitted from the rotating shaft to the casing and other connecting structures in rotating mechanical equipment is addressed here by developing a new mathematical model of precision rolling element bearings. A new grating stiffness matrix is proposed in order to demonstrate a coupling between the shaft bending motion and the flexural motion of the casing plate. It is shown that the translational bearing stiffness coefficients currently used in rotor dynamic models are a small subset of the proposed matrix. The theory is validated by examples, and the proposed bearing formulation is then extended to demonstrate its superiority over existing models in vibration transmission analyses. It is shown that the model can easily be incorporated into analytical or numerical models typically used for dynamic analyses.

Lim, T. C.↗
NASA NTRS1983

Vibration control of large linear quadratic symmetric systems

Some unique properties on a class of the second order lambda matrices were found and applied to determine a damping matrix of the decoupled subsystem in such a way that the damped system would have preassigned eigenvalues without disturbing the stiffness matrix. The resulting system was realized as a time invariant velocity only feedback control system with desired poles. Another approach using optimal control theory was also applied to the decoupled system in such a way that the mode spillover problem could be eliminated. The procedures were tested successfully by numerical examples.

Jeon, G. J.↗
NASA NTRS2015

3D Progressive Damage Modeling for Laminated Composite Based on Crack Band Theory and Continuum Damage Mechanics

A simple continuum damage mechanics (CDM) based 3D progressive damage analysis (PDA) tool for laminated composites was developed and implemented as a user defined material subroutine to link with a commercially available explicit finite element code. This PDA tool uses linear lamina properties from standard tests, predicts damage initiation with an easy-to-implement Hashin-Rotem failure criteria, and in the damage evolution phase, evaluates the degradation of material properties based on the crack band theory and traction-separation cohesive laws. It follows Matzenmiller et al.'s formulation to incorporate the degrading material properties into the damaged stiffness matrix. Since nonlinear shear and matrix stress-strain relations are not implemented, correction factors are used for slowing the reduction of the damaged shear stiffness terms to reflect the effect of these nonlinearities on the laminate strength predictions. This CDM based PDA tool is implemented as a user defined material (VUMAT) to link with the Abaqus/Explicit code. Strength predictions obtained, using this VUMAT, are correlated with test data for a set of notched specimens under tension and compression loads.

Wang, John T.↗
NASA NTRS1976

Efficient reanalysis of structures by a direct modification method

A procedure for the local stiffness modifications of large structures is described. It enables structural modifications without an a priori definition of the changes in the original structure and without loss of efficiency due to multiple loading conditions. The solution procedure, implemented in NASTRAN, involved the decomposed stiffness matrix and the displacement vectors of the original structure. It solves the modified structure exactly, irrespective of the magnitude of the stiffness changes. In order to investigate the efficiency of the present procedure and to test its applicability within a design environment, several real and large structures were solved. The results of the efficiency studies indicate that the break-even point of the procedure varies between 8% and 60% stiffness modifications, depending upon the structure's characteristics and the options employed.

Raibstein, A. I.↗
NASA NTRS1977

A multilevel approach for minimum weight structural design including local and system buckling constraints

A rational multilevel approach for minimum weight structural design of truss and wing structures including local and system buckling constraints is presented. Overall proportioning of the structure is achieved at the system level subject to strength, displacement and system buckling constraints, while the detailed component designs are carried out separately at the component level satisfying local buckling constraints. Total structural weight is taken to be the objective function at the system level while employing the change in the equivalent system stiffness of the component as the component level objective function. Finite element analysis is used to predict static response while system buckling behavior is handled by incorporating a geometric stiffness matrix capability. Buckling load factors and the corresponding mode shapes are obtained by solving the eigenvalue problem associated with the assembled elastic stiffness and geometric stiffness matrices for the structural system. At the component level various local buckling failure modes are guarded against using semi-empirical formulas. Mathematical programming techniques are employed at both the system and component level.

Schmit, L. A., Jr.↗
NASA NTRS1998

Progressive Failure And Life Prediction of Ceramic and Textile Composites

An engineering approach to predict the fatigue life and progressive failure of multilayered composite and textile laminates is presented. Analytical models which account for matrix cracking, statistical fiber failures and nonlinear stress-strain behavior have been developed for both composites and textiles. The analysis method is based on a combined micromechanics, fracture mechanics and failure statistics analysis. Experimentally derived empirical coefficients are used to account for the interface of fiber and matrix, fiber strength, and fiber-matrix stiffness reductions. Similar approaches were applied to textiles using Repeating Unit Cells. In composite fatigue analysis, Walker's equation is applied for matrix fatigue cracking and Heywood's formulation is used for fiber strength fatigue degradation. The analysis has been compared with experiment with good agreement. Comparisons were made with Graphite-Epoxy, C/SiC and Nicalon/CAS composite materials. For textile materials, comparisons were made with triaxial braided and plain weave materials under biaxial or uniaxial tension. Fatigue predictions were compared with test data obtained from plain weave C/SiC materials tested at AS&M. Computer codes were developed to perform the analysis. Composite Progressive Failure Analysis for Laminates is contained in the code CPFail. Micromechanics Analysis for Textile Composites is contained in the code MicroTex. Both codes were adapted to run as subroutines for the finite element code ABAQUS and CPFail-ABAQUS and MicroTex-ABAQUS. Graphic user interface (GUI) was developed to connect CPFail and MicroTex with ABAQUS.

Xue, David Y.↗
NASA NTRS1982

Semi-implicit transient analysis procedures for structural dynamics analysis

A semi-implicit direct time integration procedure is presented which avoids factorization of the implicit difference solution matrix. The procedure, if properly implemented, requires only vectorial calculations and hence needs the same computer core space as explicit integration procedures. Guidelines for splitting the stiffness matrix into upper and lower matrices are established, which among other things are designed to satisfy a correct transmission of rigid-body motions from element (or grid) to its adjacent elements.

Park, K. C.↗
NASA NTRS1984

Stability and Convergence of Underintegrated Finite Element Approximations

The effects of underintegration on the numerical stability and convergence characteristics of certain classes of finite element approximations were analyzed. Particular attention is given to hourglassing instabilities that arise from underintegrating the stiffness matrix entries and checkerboard instabilities that arise from underintegrating constrain terms such as those arising from incompressibility conditions. A fundamental result reported here is the proof that the fully integrated stiffness is restored in some cases through a post-processing operation.

Oden, J. T.↗
NASA NTRS1984

On reduced matrix inversion for operator splitting methods

The element-splitting heat-conduction algorithm of Hughes et al. (1983) is modified using the dual-basis approach of Flanagan and Belytschko (1981). The size of the system to be solved is reduced, and the formulation of a stiffness matrix is avoided. The 2D application is demonstrated, and the feasibility of a 3D implementation is indicated.

Belytschko, T.↗
NASA NTRS1981

Graph theory approach to the eigenvalue problem of large space structures

Graph theory is used to obtain numerical solutions to eigenvalue problems of large space structures (LSS) characterized by a state vector of large dimensions. The LSS are considered as large, flexible systems requiring both orientation and surface shape control. Graphic interpretation of the determinant of a matrix is employed to reduce a higher dimensional matrix into combinations of smaller dimensional sub-matrices. The reduction is implemented by means of a Boolean equivalent of the original matrices formulated to obtain smaller dimensional equivalents of the original numerical matrix. Computation time becomes less and more accurate solutions are possible. An example is provided in the form of a free-free square plate. Linearized system equations and numerical values of a stiffness matrix are presented, featuring a state vector with 16 components.

Reddy, A. S. S. R.↗
NASA NTRS1975

Mixed isoparametric elements for Saint-Venant torsion

Mixed isoparametric elements are presented for the Saint-Venant torsion problem of laminated and anisotropic bars. Both triangular and quadrilateral elements are considered. The 'generalized' element stiffness matrix is obtained by using a modified form of the Hellinger-Reissner mixed variational principle. Group-theoretic techniques are used in conjunction with computerized symbolic integration to obtain analytic expressions for the stiffness coefficients. The accuracy of the mixed isoparametric elements developed is demonstrated by means of numerical examples, and their advantages over commonly used stress and displacement elements are discussed.

Noor, A. K.↗
NASA NTRS1982

Alternative ways for formulation of hybrid stress elements

An element stiffness matrix can be derived by the conventional potential energy principle and, indirectly, also by generalized variational principles, such as the Hu-Washizu principle and the Hellinger-Reissner principle. The present investigation has the objective to show an approach which is concerned with the formulation of incompatible elements for solid continuum and for plate bending problems by the Hellinger-Reissner principle. It is found that the resulting scheme is equivalent to that considered by Tong (1982) for the construction of hybrid stress elements. In Tong's scheme the inversion of a large flexibility matrix can be avoided. It is concluded that the introduction of additional internal displacement modes in mixed finite element formulations by the Hellinger-Reissner principle and the Hu-Washizu principle can lead to element stiffness matrices which are equivalent to the assumed stress hybrid method.

Pian, T. H. H.↗
NASA NTRS2012

Macro Scale Independently Homogenized Subcells for Modeling Braided Composites

An analytical method has been developed to analyze the impact response of triaxially braided carbon fiber composites, including the penetration velocity and impact damage patterns. In the analytical model, the triaxial braid architecture is simulated by using four parallel shell elements, each of which is modeled as a laminated composite. Currently, each shell element is considered to be a smeared homogeneous material. The commercial transient dynamic finite element code LS-DYNA is used to conduct the simulations, and a continuum damage mechanics model internal to LS-DYNA is used as the material constitutive model. To determine the stiffness and strength properties required for the constitutive model, a top-down approach for determining the strength properties is merged with a bottom-up approach for determining the stiffness properties. The top-down portion uses global strengths obtained from macro-scale coupon level testing to characterize the material strengths for each subcell. The bottom-up portion uses micro-scale fiber and matrix stiffness properties to characterize the material stiffness for each subcell. Simulations of quasi-static coupon level tests for several representative composites are conducted along with impact simulations.

Blinzler, Brina J.↗
NASA NTRS1992

Iterative use of direct matrix updates - Connectivity and convergence

In this paper, optimal matrix adjustment was examined with a focus on connectivity and its preservation. To accomplish this, techniques which do not preserve the sparsity pattern were applied in an iterative approach that forces the preservation of the zero/nonzero pattern of the original stiffness matrix. This approach showed impressive results for locating damaged truss members. In addition, this approach also provides understanding of optimal updates in general.

Smith, Suzanne W.↗