Search NASA⌕ Search

SEARCH · Search NASA

Results for “stiffness matrix”

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.

At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

An exact zooming method for finite element analyses

An exact zooming technique which employs static condensation and exact structural reanalysis methods was developed. Successive application of static condensation reduces the system to one that is only associated with the degrees of freedom (dof) of the original model. Application of an exact static reanalysis technique permits the displacements at the dof of the original model that are contained in the zoomed portion of the structure to be obtained first. The response external to the zoom, as well as the response of additional dof within various levels of zooming, is computed. With the triangular factor of the stiffness matrix of the original system available, this approach involves only the solution of a system of equations of small order.

Hirai, I.↗
NASA NTRS1982

A finite element approach for shells of revolution with a local deviation

A finite element model that is suitable for the static analysis of shells of revolution with arbitrary local deviations is presented. The model employs three types of elements: rotational, general, and transitional shell elements. The rotational shell elements are used in the region where the shell is axisymmetric. The general shell element are used in the local region of the deviation. The transitional shell elements connect these two distinctively different types of elements and make it possible to combine them in a single analysis. The form of the global stiffness matrix resulting when different forms of nodal degrees of freedom are combined is illustrated. The coupling of harmonic degrees of freedom due to the locally nonaxisymmetric geometry was studied. The use of a substructuring technique and separate partial harmonic analysis is recommended.

Han, K. J.↗
NASA NTRS1981

Problems encountered with conventional fiber-reinforced composites

Preparational, computational, and operational problems associated with fiber-reinforced composites (FRC) are reviewed. Initial preparation of FRCs is shown to involve consideration of the type of prepreg, the setting time, cure conditions and cycles, and cure temperatures. The effects of the choice of bonding agents, the fiber transfer length, and individual fiber responses to bonding agents are noted to have an impact on fiber strength, moisture uptake, and fatigue resistance. The deformation prior to failure and the failure region are modeled through models of mini-, micro- and macro mechanics formulations employing a stiffness matrix, failure criterion, or fracture mechanics. The detection, evaluation, and repair of defects comprises the operational domain, and it is stressed that no good repair techniques exist for FRCs.

Landel, R. F.↗
NASA NTRS1982

Improvement of a large dynamic analytical model using ground vibration test data

A method has been developed which uses measured normal modes and natural frequencies to improve an analytical mass and stiffness matrix model of a structure. The method directly identifies, without iteration, a set of minimum changes in the analytical matrices which force the eigensolutions to agree with the test measurements. An application is presented in which the analytical model had 508 degrees of freedom and 19 modes were measured at 101 locations on the structure. The resulting changes in the model are judged to be small compared to expectations of errors in the analysis. Thus the improved model is accepted as a reasonable model of the structure with improved dynamic response characteristics. In addition, it is shown that the procedure may be a useful tool in identifying apparent measured modes which are not true normal modes of the structures.

Berman, A.↗
NASA NTRS1982

Analytical and experimental vibration and buckling characteristics of a pretensioned stayed column

Modal vibration tests to determine lateral modes of vibration of a stayed column and static axial compression tests to determine the column's buckling and postbuckling behavior have been performed. Effects of stay tension levels and vibration-load interaction are presented. Two finite element models are used to analyze the column, a three-dimensional frame using NASTRAN and an equivalent two-dimensional frame using an exact dynamic stiffness matrix. Both analyses correlated well with the linear vibration and buckling experimental data. Results indicate premature buckling of the column due to vibration-load interaction and nonlinear oscillations due to stay slackening. Postbuckling behavior of the column is unusual because of stay slackening and results in a postbuckling restoring force of less than the bifurcation buckling load. Guidelines for design of pretensioned structures are presented which consider buckling, postbuckling and vibration behavior.

Belvin, W. K.↗
NASA NTRS1983

Research on the control of large space structures

The research effort on the control of large space structures at the University of Houston has concentrated on the mathematical theory of finite-element models; identification of the mass, damping, and stiffness matrix; assignment of damping to structures; and decoupling of structure dynamics. The objective of the work has been and will continue to be the development of efficient numerical algorithms for analysis, control, and identification of large space structures. The major consideration in the development of the algorithms has been the large number of equations that must be handled by the algorithm as well as sensitivity of the algorithms to numerical errors.

Denman, E. D.↗
NASA NTRS1983

Nonlinear structural dynamics analysis using a modified modal method

The procedure for predicting the nonlinear dynamic response of structural components subjected to a step loading is presented. The procedure is a modified modal method that involves a change of dependent variables from the unknown nodal degrees of freedom of the finite element model of the structure to a smaller set of generalized coordinates. This change of dependent variables uses a combination of the nonlinear static solution and some selected vibration mode shapes. The vibration mode shapes correspond to the eigenvectors obtained by solving a standard free vibration eigenvalue problem wherein the stiffness matrix is expanded about the nonlinear static solution. A strategy is also presented for determining which and how many vibration mode shapes to include in the transformation. The effect of inaccurate representation of the spatial distribution of the applied load on the nonlinear dynamic response is discussed for two classes of structural behavior. Application of the procedure to structures which exhibit a stiffening behavior and to those with a softening behavior is presented.

Knight, N. F., Jr.↗
NASA NTRS1984

Modeling material failure with a vectorized routine

The computational aspects of modelling material failure in structural wood members are presented with particular reference to vector processing aspects. Wood members are considered to be highly orthotropic, inhomogeneous, and discontinuous due to the complex microstructure of wood material and the presence of natural growth characteristics such as knots, cracks and cross grain in wood members. The simulation of strength behavior of wood members is accomplished through the use of a special purpose finite element/fracture mechanics routine, program STARW (Strength Analysis Routine for Wood). Program STARW employs quadratic finite elements combined with singular crack tip elements in a finite element mesh. Vector processing techniques are employed in mesh generation, stiffness matrix formation, simultaneous equation solution, and material failure calculations. The paper addresses these techniques along with the time and effort requirements needed to convert existing finite element code to a vectorized version. Comparisons in execution time between vectorized and nonvectorized routines are provided.

Cramer, S. M.↗
NASA NTRS1985

A Structural Dynamics Approach to the Simulation of Spacecraft Control/Structure Interaction

A relatively simple approach to the analysis of linear spacecraft control/structure interaction problems is presented. The approach uses a commercially available structural system dynamic analysis package for both controller and plant dynamics, thus obviating the need to transfer data between separate programs. The unilateral coupling between components in the control system block diagram is simulated using sparse matrix stiffness and damping elements available in the structural dynamic code. The approach is illustrated with a series of simple tutorial examples of a rigid spacecraft core with flexible appendages.

Young, J. W.↗
NASA NTRS1985

Parametric Stiffness Control of Flexible Structures

An unconventional method for control of flexible space structures using feedback control of certain elements of the stiffness matrix is discussed. The advantage of using this method of configuration control is that it can be accomplished in practical structures by changing the initial stress state in the structure. The initial stress state can be controlled hydraulically or by cables. The method leads, however, to nonlinear control equations. In particular, a long slender truss structure under cable induced initial compression is examined. both analytical and numerical analyses are presented. Nonlinear analysis using center manifold theory and normal form theory is used to determine criteria on the nonlinear control gains for stable or unstable operation. The analysis is made possible by the use of the exact computer algebra system MACSYMA.

Moon, F. C.↗
NASA NTRS1984

Analysis of hourglass instabilities and control in underintegrated finite element methods

Belytschko et al. (1981, 1984) has developed stabilization methods for the treatment of underintegrated FEM problems; these methods involve the computation of an underintegrated stiffness matrix, which is rank-deficient, and the addition of a stabilization matrix which effectively eliminates the spurious modes. An attempt is presently made to give this a priori stabilization method a mathematical means of support. Attention is also given to an a posteriority stabilization method for hourglass control, in which an approximate solution of the underintegrated system is obtained and then subjected to a special projection in order to eliminate the hourglass modes. A proof is obtained for the convergence of this stabilized underintegrated approximation to the exact solution of a model problem at almost the same rate (as the mesh is refined) as the fully integrated solutions.

Jacquotte, O.-P.↗
NASA NTRS1984

Natural frequencies of twisted rotating plates

A detailed comparison is presented of the predicted eigenfrequencies of twisted rotating plates as obtained by using two different shape functions. Primarily, rotating twisted plates of two different aspect ratios and two different thickness ratios are considered. The effects of rotation are included by using a 'stress smoothing' technique when calculating the augmented stiffness matrix. In addition, the effects of Coriolis acceleration, contributions from membrane behavior, setting angle and sweep angle are considered. The effects of geometric nonlinearity are briefly discussed. Finally, results of a brief study of cambered plates are presented.

Ramamurti, V.↗
NASA NTRS1985

Model-size reduction technique for the analysis of symmetric anisotropic structures

A two-step computational procedure is presented for reducing the size of the analysis model for an anisotropic symmetric structure to that of the corresponding orthotropic structure. The key elements of the procedure are: (1) decomposition of the stiffness matrix into the sum of an orthotropic and nonorthotropic (anisotropic) parts; and (2) successive application of the finite element method and the classical Rayleigh-Ritz technique. The finite element method is first used to generate few global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the Rayleigh-Ritz technique. The global approximation vectors are selected to be the solution corresponding to zero nonorthotropic matrix and its various-order derivatives with respect to an anisotropic tracing parameter (identifying the nonorthotropic material coefficients). The size of the analysis model used in generating the global approximation vectors is identical to that of the corresponding orthotropic structure. The effectiveness of the proposed technique is demonstrated by means of numerical examples and its potential for solving other quasi-symmetric problems is discussed.

Noor, A. K.↗
NASA NTRS1986

Inclusion of elastically connected members in exact buckling and frequency calculations

A standard stiffness matrix procedure which permits any combination of rigid, elastic, pinned or sliding connections of the degrees of freedom at the ends of a member to the nodes of its parent structure is described, in order to show how easily it can be extended to allow an existing algorithm to be used to ensure that no eigenvalues of the parent structure can be missed even when 'exact' member theory is used. The eigenvalues are the natural frequencies of undamped free vibration analyses or the critical load factors of buckling problems. The method preserves the exactness of the member theory and an efficient method for computer application is indicated. The theory also permits any combination of rigid, elastic, pinned or sliding connections between the freedoms of a substructure and those of its parent structure.

Williams, F. W.↗
NASA NTRS1986

BUNVIS-RG - An exact buckling and vibration program for lattice structures, with repetitive geometry and substructuring options

The exact FORTRAN computer program BUNVIS-RG which uses an exact stiffness matrix method to find eigenvalues and modes of three-dimensional planes, is presented in detail. It is shown that BUNVIS-RG solution times can be predicted fairly accurately from two computer dependent constants, the number of nodes and members in the frame, and the maximum node number difference of any pair of connected nodes. The program's use of repetitive geometry, stayed column substructures and nonuniform member options was found to enhance efficiency and range of application.

Anderson, M. S.↗
NASA NTRS1986

Model-size reduction for the buckling and vibration analyses of anisotropic panels

A computational procedure is presented for reducing the size of the model used in the buckling and vibration analyses of symmetric anisotropic panels to that of the corresponding orthotropic model. The key elements of the procedure are the application of an operator splitting technique through the decomposition of the material stiffness matrix of the panel into the sum of orthotropic and nonorthotropic (anisotropic) parts and the use of a reduction method through successive application of the finite element method and the classical Rayleigh-Ritz technique. The effectiveness of the procedure is demonstrated by numerical examples.

Noor, A. K.↗
NASA NTRS1986

Experimental study of unsteady hydrodynamic force matrices on whirling centrifugal pump impellers

An experimental facility was constructed and instrumented. A set of centrifugal flow pumps whose impellers were made to follow a controlled circular whirl motion were studied. The aim was to characterize the steady and unsteady fluid forces measured on the impeller under various pump operating conditions. The postulation was that the unsteady lateral forces result from interactions between the impeller and the surrounding diffuser and/or volute (via the working fluid), and that under certain flow regimes these forces can drive unstable lateral motions of the pump rotor. The lateral hydrodynamic forces were decomposed into their steady and unsteady parts, the latter being further expressed in terms of a generalized fluid stiffness matrix. Conclusions regarding the effect of impeller geometry could not be reached given the similarity of the tested designs. However, other results on phenomena such as skin friction and leakage flow are presented. Some of the findings are compared to experimental and theoretical data from other sources. Finally, the rotordynamic consequences of the results are discussed as the present data were applied to the case of the Space Shuttle Main Engine (SSME) High Pressure Oxidizer Turbopump (HPOTP).

Belgacem, Jery↗
NASA NTRS1987

Hub flexibility effects on propfan vibration

The significance of hub flexibility in the nonlinear static and dynamic analyses of advanced turboprop blades is assessed. The chosen blade is the 0.175 scale model of the GE-A7-B4 unducted fan blade. A procedure for coupling the effective hub stiffness matrix to an MSC/NASTRAN finite element model is defined and verified. A series of nonlinear static and dynamic analyses are conducted on the blade for both rigid and flexible hug configurations. Results indicate that hub flexibility is significant in the nonlinear static and dynamic analyses of the GE-A7-B4. In order to insure accuracy in analyses of other blades, hub flexibility should always be considered.

Ernst, Michael A.↗