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DOE OSTI2020

Eigenfrequency constrained topology optimization of finite strain hyperelastic structures

This paper incorporates hyperelastic materials, nonlinear kinematics, and preloads in eigenfrequency constrained density–based topology optimization. The formulation allows for initial finite deformations and subsequent small harmonic oscillations. The optimization problem is solved by the method of moving asymptotes, and the gradients are calculated using the adjoint method. Both simple and degenerate eigenfrequencies are considered in the sensitivity analysis. A well-posed topology optimization problem is formulated by filtering the volume fraction field. Numerical issues associated with excessive distortion and spurious eigenmodes in void regions are reduced by removing low volume fraction elements. The optimization objective is to maximize stiffness subject to a lower bound on the fundamental eigenfrequency. Numerical examples show that the eigenfrequencies drastically change with the load magnitude, and that the optimization is able to produce designs with the desired fundamental eigenfrequency.

42 ENGINEERING↗

NASA NTRS1989

Nonlinear response of a blade-stiffened graphite-epoxy panel with a discontinuous stiffener: Work in progress

The problem of calculating detailed stress distributions around discontinuities in buckled, composite structural components for use with the various analytical failure prediction techniques has not been thoroughly explored. The purpose here is the application of computational methods to the detailed stress analysis problem which is the focus of this session of the workshop. One approach to uncovering the difficulties of this type of analysis and to providing specific directions for future research in this area is a direct attack on the problem using currently available analysis tools. A candidate problem has been selected and experiences from calculating its structural response are described.

Knight, Norman F., Jr.↗

NASA NTRS2002

Structural Analysis of a Magnetically Actuated Silicon Nitride Micro-Shutter for Space Applications

Finite element models have been created to simulate the electrostatic and electromagnetic actuation of a 0.5gm silicon nitride micro-shutter for use in a spacebased Multi-object Spectrometer (MOS). The micro-shutter uses a torsion hinge to go from the closed, 0 degree, position, to the open, 90 degree position. Stresses in the torsion hinge are determined with a large deformation nonlinear finite element model. The simulation results are compared to experimental measurements of fabricated micro-shutter devices.

Loughlin, James P.↗

NASA NTRS1981

Sensitivity of optimum solutions to problem parameters

In an aircraft configuration optimization, the information of interest is the sensitivity of optimal block fuel consumption and wing aspect ratio and area, to variations of required range and payload. The objectives of this study are: (1) to show how the equations capable of yielding the sensitivity derivatives (the sensitivity equations) can be obtained for a constrained optimum regardless of the type of optimization algorithm that was used to arrive at the optimum point, (2) to review the solvability of the sensitivity equations and (3) to report on applications on structural optimization. Numerical examples, which demonstrate the sensitivity analysis, include a tubular column and a three-bar truss for which closed form solutions are obtained, a ten-bar truss that requires the use of a finite element analysis, and a thin-walled beam characterized by strongly nonlinear constraints for local buckling. It is concluded that a practically significant extrapolation accuracy may be obtained for a reasonably broad range of parameter changes; and that accuracy does not depend strongly on the degree of convergence of the optimum solution from which the sensitivity derivatives are obtained.

Sobieszczanski-Sobieski, J.↗

NASA NTRS1981

Determination of airplane model structure from flight data by using modified stepwise regression

The linear and stepwise regressions are briefly introduced, then the problem of determining airplane model structure is addressed. The MSR was constructed to force a linear model for the aerodynamic coefficient first, then add significant nonlinear terms and delete nonsignificant terms from the model. In addition to the statistical criteria in the stepwise regression, the prediction sum of squares (PRESS) criterion and the analysis of residuals were examined for the selection of an adequate model. The procedure is used in examples with simulated and real flight data. It is shown that the MSR performs better than the ordinary stepwise regression and that the technique can also be applied to the large amplitude maneuvers.

Klein, V.↗

NASA NTRS1988

Compression strength of composite primary structural components

The geometrically nonlinear response and failure of thin-walled structural components made from advanced composite materials is discussed. The materials involved are structural components in flight vehicle structures that are laminated from graphite-epoxy unidirectional tape. The investigation involves the buckling, postbuckling, and failure of structures subject to axial compression. The structural analysis was performed using the Structural Analysis of General Shells (STAGS) computer code. Experimental and theoretical methods are used to study the fundamental mechanisms limiting the load-carrying capacity of these components.

Johnson, Eric R.↗

NASA NTRS1990

HITCAN: High temperature composite analyzer

A computer code, HITCAN (High Temperature Composite Analyzer) was developed to analyze/design metal matrix composite structures. HITCAN is based on composite mechanics theories and computer codes developed at NASA LeRC over the last two decades. HITCAN is a general purpose code for predicting the global structural and local stress-strain response of multilayered (arbitrarily oriented) metal matrix structures both at the constituent (fiber, matrix, and interphase) and the structure level and including the fabrication process effects. The thermomechanical properties of the constituents are considered to be nonlinearly dependent on several parameters including temperature, stress, and stress rate. The computational procedure employs an incremental iterative nonlinear approach utilizing a multifactor-interaction material behavior model. HITCAN features and analysis capabilities (static, load stepping, modal, and buckling) are demonstrated through typical example problems.

Singhal, Surendra N.↗

NASA NTRS2003

Interface Finite Elements for the Analysis of Fracture Initiation and Progression

Progressive failure analyses (PFA) are important for the prediction of residual strength and damage tolerance of vehicle structures, and to predict the energy absorbing capability of vehicle structures under crash-type loads. Typically continuum damage mechanics (CDM) and fracture mechanics (FM) are the methods used for PFA. The method of interfacial damage mechanics (IDM) is used for PFA in this research. IDM has capabilities intermediate between CDM and FM, and is used to numerically model the initiation, growth, and arrest of cracks. IDM smooths the stress singularity at the crack tip, and is easily adaptable with other nonlinearties such as plasticity and material damage. IDM is implemented by user-defined interface elements in the ABAQUS/ Standard structural analysis software package. The structural components selected to demonstrate the effectiveness PFA using interface elements are, for the most part, those with published test data. These structural components were subjected to quasi-static loading in the tests. Thus, the ABAQUS analyses are used to predict geometrically and materially nonlinear equilibrium states. Impact loading, dynamic fracture, reflected stress waves, inertia, and time dependent material behavior are not considered.

Ambur, Damodar R.↗

NASA NTRSDate not supplied

Development of a Full-Scale Finite Element Model of the Fokker F28 Fellowship Aircraft and Crash Simulation Predictions

In June 2019, a full-scale crash test of a Fokker F28 Fellowship aircraft was conducted as part of a joint National Aeronautics and Space Administration/Federal Aviation Administration (NASA/FAA) project to investigate the performance of transport aircraft under realistic crash conditions. The test objectives were to provide data for assessment of transport aircraft crashworthiness under realistic impact conditions and to generate test data for model validation. The test article was loaded with transport aircraft seats in a 3+2 configuration. A total of 24 instrumented ATDs were placed in the seats and restrained. The test article weighed 33,306-lb. (15,107.3-kg) and, during the crash test, impacted a 2-ft. (0.61-m) high soil bed at 65.3-ft/s (19.9-m/s) forward and 31.8-ft/s (9.7-m/s) vertical velocity. The full-scale aircraft crash test was simulated using the commercial nonlinear explicit transient dynamic finite element code, LS-DYNA. This paper will provide a description of the test article and the crash test conditions, document the F28 full-scale model development, and present test-analysis comparisons. The test-analysis comparisons include inertial properties, kinematic responses, structural acceleration responses, and structural deformation and failure.

Karen E Jackson↗

NASA NTRS2004

Neural network uncertainty assessment using Bayesian statistics: a remote sensing application

Neural network (NN) techniques have proved successful for many regression problems, in particular for remote sensing; however, uncertainty estimates are rarely provided. In this article, a Bayesian technique to evaluate uncertainties of the NN parameters (i.e., synaptic weights) is first presented. In contrast to more traditional approaches based on point estimation of the NN weights, we assess uncertainties on such estimates to monitor the robustness of the NN model. These theoretical developments are illustrated by applying them to the problem of retrieving surface skin temperature, microwave surface emissivities, and integrated water vapor content from a combined analysis of satellite microwave and infrared observations over land. The weight uncertainty estimates are then used to compute analytically the uncertainties in the network outputs (i.e., error bars and correlation structure of these errors). Such quantities are very important for evaluating any application of an NN model. The uncertainties on the NN Jacobians are then considered in the third part of this article. Used for regression fitting, NN models can be used effectively to represent highly nonlinear, multivariate functions. In this situation, most emphasis is put on estimating the output errors, but almost no attention has been given to errors associated with the internal structure of the regression model. The complex structure of dependency inside the NN is the essence of the model, and assessing its quality, coherency, and physical character makes all the difference between a blackbox model with small output errors and a reliable, robust, and physically coherent model. Such dependency structures are described to the first order by the NN Jacobians: they indicate the sensitivity of one output with respect to the inputs of the model for given input data. We use a Monte Carlo integration procedure to estimate the robustness of the NN Jacobians. A regularization strategy based on principal component analysis is proposed to suppress the multicollinearities in order to make these Jacobians robust and physically meaningful.

Neural Networks (Computer)↗

DOE OSTI2022

Grassmannian Diffusion Maps--Based Dimension Reduction and Classification for High-Dimensional Data

This work introduces the Grassmannian diffusion maps (GDMaps), a novel nonlinear dimensionality reduction technique that defines the affinity between points through their representation as low-dimensional subspaces corresponding to points on the Grassmann manifold. Here, the method is designed for applications, such as image recognition and data-based classification of constrained high-dimensional data where each data point itself is a high-dimensional object (i.e., a large matrix) that can be compactly represented in a lower-dimensional subspace. The GDMaps is composed of two stages. The first is a pointwise linear dimensionality reduction wherein each high-dimensional object is mapped onto the Grassmann manifold representing the low-dimensional subspace on which it resides. The second stage is a multipoint nonlinear kernel-based dimension reduction using diffusion maps to identify the subspace structure of the points on the Grassmann manifold. To this end, an appropriate Grassmannian kernel is used to construct the transition matrix of a random walk on a graph connecting points on the Grassmann manifold. Spectral analysis of the transition matrix yields low-dimensional Grassmannian diffusion coordinates embedding the data into a low-dimensional reproducing kernel Hilbert space. Further, a novel data classification/recognition technique is developed based on the construction of an overcomplete dictionary of reduced dimension whose atoms are given by the Grassmannian diffusion coordinates. Three examples are considered. First, a "toy" example shows that the GDMaps can identify an appropriate parametrization of structured points on the unit sphere. The second example demonstrates the ability of the GDMaps to revealing the intrinsic subspace structure of high-dimensional random field data. In the last ex- ample, a face recognition problem is solved considering face images subject to varying illumination conditions, changes in face expressions, and occurrence of occlusions. The technique presented high recognition rates (i.e., 95% in the best case) using a fraction of the data required by conventional methods.

42 ENGINEERING↗

NASA NTRS1974

Stability region maximization by decomposition-aggregation method

This work is to improve the estimates of the stability regions by formulating and resolving a proper maximization problem. The solution of the problem provides the best estimate of the maximal value of the structural parameter and at the same time yields the optimum comparison system, which can be used to determine the degree of stability of the Skylab. The analysis procedure is completely computerized, resulting in a flexible and powerful tool for stability considerations of large-scale linear as well as nonlinear systems.

Siljak, D. D.↗

NASA NTRS1976

Extended Lyapunov stability criterion using a nonlinear algebraic relation with application to adaptive control

A new nonlinear stability criterion is developed by use of a class of Lyapunov functionals for model-reference adaptive systems (MRAS). Results are compared with traditional results, and a comparative design technique is used to illustrate its function in improving the transient response of an MRAS controller. For a particular system structure and class of input signals, the new stability criterion is shown to include traditional sufficiency stability conditions as a special case. An example is cited to illustrate the use of the nonlinear criterion and its definite advantages in helping improve the adaptive error transient response of a system. Analysis of results is effected by use of a linearization technique on the resulting adaptive equations.

Colburn, B. K.↗

NASA NTRS1982

Development of a rotorcraft. Propulsion dynamics interface analysis, volume 2

A study was conducted to establish a coupled rotor/propulsion analysis that would be applicable to a wide range of rotorcraft systems. The effort included the following tasks: (1) development of a model structure suitable for simulating a wide range of rotorcraft configurations; (2) defined a methodology for parameterizing the model structure to represent a particular rotorcraft; (3) constructing a nonlinear coupled rotor/propulsion model as a test case to use in analyzing coupled system dynamics; and (4) an attempt to develop a mostly linear coupled model derived from the complete nonlinear simulations. Documentation of the computer models developed is presented.

Hull, R.↗

NASA NTRS1988

Recent developments in structural sensitivity analysis

Recent developments are reviewed in two major areas of structural sensitivity analysis: sensitivity of static and transient response; and sensitivity of vibration and buckling eigenproblems. Recent developments from the standpoint of computational cost, accuracy, and ease of implementation are presented. In the area of static response, current interest is focused on sensitivity to shape variation and sensitivity of nonlinear response. Two general approaches are used for computing sensitivities: differentiation of the continuum equations followed by discretization, and the reverse approach of discretization followed by differentiation. It is shown that the choice of methods has important accuracy and implementation implications. In the area of eigenproblem sensitivity, there is a great deal of interest and significant progress in sensitivity of problems with repeated eigenvalues. In addition to reviewing recent contributions in this area, the paper raises the issue of differentiability and continuity associated with the occurrence of repeated eigenvalues.

Haftka, Raphael T.↗

NASA NTRS1989

On finite element implementation and computational techniques for constitutive modeling of high temperature composites

The research work performed during the past year on finite element implementation and computational techniques pertaining to high temperature composites is outlined. In the present research, two main issues are addressed: efficient geometric modeling of composite structures and expedient numerical integration techniques dealing with constitutive rate equations. In the first issue, mixed finite elements for modeling laminated plates and shells were examined in terms of numerical accuracy, locking property and computational efficiency. Element applications include (currently available) linearly elastic analysis and future extension to material nonlinearity for damage predictions and large deformations. On the material level, various integration methods to integrate nonlinear constitutive rate equations for finite element implementation were studied. These include explicit, implicit and automatic subincrementing schemes. In all cases, examples are included to illustrate the numerical characteristics of various methods that were considered.

Saleeb, A. F.↗

NASA NTRS1989

Explicit modeling of composite plates and beams in the dynamics of multibody systems

The state of the art dynamic response analysis of flexible multibody systems is currently restricted to elastic bodies with homogeneous materials. The requirements for high speed operation has made it necessary to use lightweight multi layered composite bodies in robotic systems and space structure applications. Dynamic modeling and analysis of such systems are particularly important since the effects of body flexibility to the performance are likely to be more pronounced. The eight-noded isoperimetric quadrilateral element with independent rotational and displacement degrees of freedom is extended to laminated composite elements. The element includes an arbitrary number of bonded layers, each of which may have a different thickness. The transverse shear deformation which is a predominant factor in the analysis of laminated composite structures is taken into account in developing the stiffness and mass matrices. The corresponding 3-D mode shapes are then incorporated to the multibody system dynamical equations. Floating body reference frames allow the selection of different boundary conditions, and the dynamical equations contain all the nonlinear interactions between the rigid and elastic motion. Example simulations are presented to illustrate the methods proposed.

Amirouche, F. M. L.↗

NASA NTRS1989

Incorporation of a progressive failure analysis method in the CSM testbed software system

Analysis of the postbuckling behavior of composite shell structures pose many difficult and challenging problems in the field of structural mechanics. Current analysis methods perform well for most cases in predicting the postbuckling response of undamaged components. To predict component behavior accurately at higher load levels, the analysis must include the effects of local material failures. The CSM testbed software system is a highly modular structural analysis system currently under development at Langley Research Center. One of the primary goals of the CSM testbed is to provide a software environment for the development of advanced structural analysis methods and modern numerical methods which will exploit advanced computer architecture such as parallel-vector processors. Development of a progressive failure analysis method consists of the design and implementation of a processor which will perform the ply-level progressive failure analysis and the development of a geometrically nonlinear analysis procedure which incorporates the progressive failure processor. Regarding the development of the progressive failure processor, two components are required: failure criteria and a degradation model. For the initial implementation, the failure criteria of Hashin will be used. For a matrix failure which typically indicates the development of transverse matrix cracks, the ply properties will be degraded. Work to date includes the design of the progressive failure analysis processor and initial plans for the controlling geometrically nonlinear analysis procedure. The implementation of the progressive failure analysis has begun. Access to the model database and the Hashin failure criteria are completed. Work is in progress on the input/output operations for the processor related data and the finite element model updating procedures. In total the progressive failure processor is approximately one-third complete.

Arenburg, Robert T.↗