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Description of a variable step incremental procedure for the solution of nonlinear equations in finite element structural analysis. The proposed procedure is effective in improving the accuracy of the basic incremental technique and in providing, in addition, an accurate estimate of the discretization error. The proposed approach is highly appropriate for solving problems for which the user has no a priori estimate of the step size to use.
Techniques for defining a finite element model (FEM) for analysis of nonlinear vibrations in beam structures subjected to harmonic excitation are presented. The resulting model covers longitudinal deformation and inertial effects. The nonlinear oscillations of a beam element under forced excitation are modeled by a harmonic force matrix based on first order approximations of the Jacobian elliptic forcing function. Harmonic force and nonlinear stiffness matrices are derived and the nonlinear forced responses of beams are calculated under various boundary conditions. The results of FEM computations for simply-supported and clamped beams show that midplane stretching caused by large deflections increases the nonlinearity. Axially-restrained beams experience only hardening nonlinearity, while axially-free beams have reduced nonlinearity in deformation and inertia and an increase in linearity due to large deflection.
Computer architecture is investigated in conjunction with the algorithmic structures of nonlinear finite-element analysis. To help set the stage for this goal, the development is undertaken by considering the wide-ranging needs associated with the analysis of rolling tires which possess the full range of kinematic, material and boundary condition induced nonlinearity in addition to gross and local cord-matrix material properties.
This paper presents several current topics in rotary wing aeroelasticity and concludes by attempting to anticipate future trends and developments. These topics are: (1) the role of geometric nonlinearities; (2) structural modeling, and aeroelastic analysis of composite rotor blades; (3) aeroelastic stability and response in forward flight; (4) modeling of coupled rotor/fuselage aeromechanical problems and their active control; and (5) the coupled rotor-fuselage vibration problem and its alleviation by higher harmonic control. Selected results illustrating the fundamental aspects of these topics are presented. Future developments are briefly discussed.
Recent enhancements to the NLPAN computer code are presented. NLPAN is a finite strip method for the geometrically nonlinear static analysis of prismatic composite structures subjected to in-plane and pressure loading. Refinements to the original approach of NLPAN are noted, and the modifications necessary to model clamped ends, eccentrically loaded ends, and ends with rotationally elastic support are discussed. Analytical predictions for axially loaded stiffened panels with various types of end support are compared with experimental measurements. Overall there is good agreement between analytical results and test results. The method is successful in modelling key mechanisms which can cause elastic collapse.
Aircraft-based observations of turbulence fields of velocity, moisture, and temperature are used to study coherent turbulent structures that dominate turbulent transfer of moisture and heat above three different eco-systems. Flux traces are defragmented, to reconstruct the presumed full size (along the sampled transect) of these structures, and flux traces are simplified by elimination of those that contribute negligibly to the flux estimate. Structures are analyzed in terms of size, spatial distribution, and contribution to the flux, in the four 'quadrant' modes of eddy-covariance transfer (excess up/down and deficit up/down). The effect of nonlinear detrending of moisture and temperature data on this 'structural analysis,' over surfaces with heterogeneous surface wetness, is also examined. Results over grassland, wetland, and moist and dry agricultural land, show that nonlinear detrending may provide a more physically realistic description of structures. Significant differences are observed between structure size and associated relative flux contribution, between moist and dry areas, with smaller structures playing a more important role over the moist areas. Structure size generally increases with height, as spatial reorganization from smaller structures into larger ones takes place. This coincides with a gradual loss of surface 'signature' (position and clustering of plumes above localized source areas). The data are expected to provide a basis for an eventual statistical description of boundary-layer transfer events , and help to interpret the link between boundary-layer transfer and hydrological surface conditions.
Unconstrained minimization algorithms have been critically evaluated for their effectiveness in solving structural problems involving geometric and material nonlinearities. The algorithms have been categorized as being zeroth, first, or second order depending upon the highest derivative of the function required by the algorithm. The sensitivity of these algorithms to the accuracy of derivatives clearly suggests using analytically derived gradients instead of finite difference approximations. The use of analytic gradients results in better control of the number of minimizations required for convergence to the exact solution.
The focus here is on one aspect of the Computational Structural Mechanics (CSM) Testbed: finite element technology. The approach involves a Generic Element Processor: a command-driven, database-oriented software shell that facilitates introduction of new elements into the testbed. This shell features an element-independent corotational capability that upgrades linear elements to geometrically nonlinear analysis, and corrects the rigid-body errors that plague many contemporary plate and shell elements. Specific elements that have been implemented in the Testbed via this mechanism include the Assumed Natural-Coordinate Strain (ANS) shell elements, developed with Professor K. C. Park (University of Colorado, Boulder), a new class of curved hybrid shell elements, developed by Dr. David Kang of LPARL (formerly a student of Professor T. Pian), other shell and solid hybrid elements developed by NASA personnel, and recently a repackaged version of the workhorse shell element used in the traditional STAGS nonlinear shell analysis code. The presentation covers: (1) user and developer interfaces to the generic element processor, (2) an explanation of the built-in corotational option, (3) a description of some of the shell-elements currently implemented, and (4) application to sample nonlinear shell postbuckling problems.
Design and construction of a structure on planetary surfaces requires addressing a host of issues not encountered on earth. A modular quilted inflatable structure consisting of thin membranes of composite material integrated with supporting columns and arches is proposed. An initial linear analysis of the structure is briefly reviewed. The actual response of an inflatable membrane is nonlinear and, hence, a nonlinear numerical analysis of the stresses and displacements was undertaken. Results based on the loadings on a lunar structure clearly indicate that an inflatable structure is a feasible concept and is ideally suited for a planetary surface structure.
Design and construction of a structure on the moon requires addressing a host of issues not encountered on earth. A modular quilted inflatable structure consisting of thin membranes of composite material integrated with supporting columns and arches is proposed. An initial linear analysis of the proposed structure is briefly reviewed. The actual response of an inflatable membrane is nonlinear and, hence, a nonlinear numerical analysis for the stresses and displacements was undertaken. Initial results clearly indicate that an inflatable structure is a feasible concept and is ideally suited for a lunar structure.
System identification or mathematical modelling is utilised in the aerospace community for the development of simulation models for robust control law design. These models are often described as linear, time-invariant processes and assumed to be uniform throughout the flight envelope. Nevertheless, it is well known that the underlying process is inherently nonlinear. The reason for utilising a linear approach has been due to the lack of a proper set of tools for the identification of nonlinear systems. Over the past several decades the controls and biomedical communities have made great advances in developing tools for the identification of nonlinear systems. These approaches are robust and readily applicable to aerospace systems. In this paper, we show the application of one such nonlinear system identification technique, structure detection, for the analysis of F-15B QuietSpike(TradeMark) aeroservoelastic flight test data. Structure detection is concerned with the selection of a subset of candidate terms that best describe the observed output. This is a necessary procedure to compute an efficient system description which may afford greater insight into the functionality of the system or a simpler controller design. Structure computation as a tool for black-box modelling may be of critical importance for the development of robust, parsimonious models for the flight-test community. Moreover, this approach may lead to efficient strategies for rapid envelope expansion which may save significant development time and costs. The objectives of this study are to demonstrate via analysis of F-15B QuietSpike(TradeMark) aeroservoelastic flight test data for several flight conditions (Mach number) that (i) linear models are inefficient for modelling aeroservoelastic data, (ii) nonlinear identification provides a parsimonious model description whilst providing a high percent fit for cross-validated data and (iii) the model structure and parameters vary as the flight condition is altered.
The deployable sunshield is an example of a gossamer structure envisioned for use on future space telescopes. The basic structure consists of multiple layers of pretensioned, thin-film membranes supported by deployable booms. The prediction and verification of sunshield dynamics has been identified as an area in need of technology development due to the difficulties inherent in predicting nonlinear structural behavior of the membranes and because of the challenges involved. in ground testing of the full-scale structure. This paper describes a finite element analysis of a subscale sunshield that has been subjected to ground testing in support of the Next Generation Space Telescope (NGST) program. The analysis utilizes a nonlinear material model that accounts for wrinkling of the membranes. Results are presented from a nonlinear static preloading analysis and subsequent dynamics analyses to illustrate baseline sunshield structural characteristics. Studies are then described which provide further insight into the effect of membrane. preload on sunshield dynamics and the performance of different membrane modeling techniques. Lastly, a comparison of analytical predictions and ground test results is presented.
Composite loads spectra (CLS) were applied to generate probabilistic loads for use in the PSAM nonlinear evaluation of stochastic structures under stress (NESSUS) finite element code. The CLS approach allows for quantifying loads as mean values and distributions around a central value rather than maximum or enveloped values typically used in deterministic analysis. NESSUS uses these loads to determine mean and perturbation responses. These results are probabilistically evaluated with the distributional information from CLS using a fast probabilistic integration (FPI) technique to define response distributions. The main example discussed describes a method of obtaining load descriptions and stress response of the second-stage turbine blade of the Space Shuttle Main Engine (SSME) high-pressure fuel turbopump (HPFTP). Additional information is presented on the on-going analysis of the high pressure oxidizer turbopump discharge duct (HPOTP) where probabilistic dynamic loads have been generated and are in the process of being used for dynamic analysis. Example comparisons of load analysis and engine data are furnished for partial verification and/or justification for the methodology.
Underintegrated methods are investigated with respect to their stability and convergence properties. The focus was on identifying regions where they work and regions where techniques such as hourglass viscosity and hourglass control can be used. Results obtained show that underintegrated methods typically lead to finite element stiffness with spurious modes in the solution. However, problems exist (scalar elliptic boundary value problems) where underintegrated with hourglass control yield convergent solutions. Also, stress averaging in underintegrated stiffness calculations does not necessarily lead to stable or convergent stress states.
System identification or mathematical modeling is used in the aerospace community for development of simulation models for robust control law design. These models are often described as linear time-invariant processes. Nevertheless, it is well known that the underlying process is often nonlinear. The reason for using a linear approach has been due to the lack of a proper set of tools for the identification of nonlinear systems. Over the past several decades, the controls and biomedical communities have made great advances in developing tools for the identification of nonlinear systems. These approaches are robust and readily applicable to aerospace systems. In this paper, we show the application of one such nonlinear system identification technique, structure detection, for the analysis of F-15B Quiet Spike(TradeMark) aeroservoelastic flight-test data. Structure detection is concerned with the selection of a subset of candidate terms that best describe the observed output. This is a necessary procedure to compute an efficient system description that may afford greater insight into the functionality of the system or a simpler controller design. Structure computation as a tool for black-box modeling may be of critical importance for the development of robust parsimonious models for the flight-test community. Moreover, this approach may lead to efficient strategies for rapid envelope expansion, which may save significant development time and costs. The objectives of this study are to demonstrate via analysis of F-15B Quiet Spike aeroservoelastic flight-test data for several flight conditions that 1) linear models are inefficient for modeling aeroservoelastic data, 2) nonlinear identification provides a parsimonious model description while providing a high percent fit for cross-validated data, and 3) the model structure and parameters vary as the flight condition is altered.
A three-dimensional nonlinear finite element model of a representative open spelter socket termination was developed to examine the underlying mechanics of load transfer from a structural cable through the termination, the sensitivity of the joint design to wire brooming, zinc material nonlinearity, contact friction between the zinc and socket, voids within the zinc, and, finally, the effects of repeated loading on the joint. Primary factors affecting open spelter socket design are cast zinc plastic flow, depth of zinc slug seating, and quality of wire brooming. Zinc plasticity and proper brooming allows for efficient load transfer by developing confining pressure on the broomed wires in the narrow part of the socket, which keep the wires from pulling out of the zinc and shift failure to occur outside the socket. Highest wire stresses in the cable occur in the outer ring adjacent to the termination. While industry use of stay cables are typically designed to carry less than half the rated breaking force in aggregate, the constituent stresses within the zinc and the wires have the potential to exceed their respective allowable in operation and should be evaluated for fatigue- and creep-critical applications.
Space station requirements for power have resulted in a need for photovoltaic solar arrays possessing large blanket surface area. However, due to the limited shuttle payload volume solar array designers have been driven to a deployable concept that by nature is extremely flexible. The principal support for this array system is the Folding Articulating Square Truss Mast (FASTMast). In order to accomodate service loads the FASTMast is expected to exhibit nonlinear behavior which could possibly result in structural instability. Presented herein are the results of the Lewis Research Center test and analysis efforts performed in an effort to characterize the FASTMast structural behavior in terms of stability. Results include those obtained from recent nonlinear testing and analysis involving a 1/10 segment of the FASTMast flight article. Implications of these results as they relate to expected behavior of the flight unit will also be discussed.
Space Station requirements for power have resulted in a need for photovoltaic solar arrays possessing large blanket surface area. However, due to the limited Shuttle payload volume solar array designers have been driven to a deployable concept that by nature is extremely flexible. The principal support for this array system is the Folding Articulating Square Truss Mast (FASTMast). In order to accommodate service loads the FASTMast is expected to exhibit nonlinear behavior which could possibly result in structural instability. Presented herein are the results of the Lewis Research Center test and analysis efforts performed in an effort to characterize the FASTMast structural behavior in terms of stability. Results include those obtained from recent nonlinear testing and analysis involving a 1/10 segment of the FASTMast flight article. Implications of these results as they relate to expected behavior of the flight unit will also be discussed.