A review of indirect/non-intrusive reduced order modeling of nonlinear geometric structures

H YPERSONIC flight began in February 1949 when a WAC Corporal rocket was ignited from a U.S.-captured V-2 rocket [1]. In the six decades since this milestone, there have been significant investments in the development of hypersonic vehicle technologies. The NASA X-15 rocket plane in the early 1960s represents early research toward this goal [2,3]. After a lull in activity, the modern era of hypersonic research started in the mid-1980s with the National Aerospace Plane (NASP) program [4], aimed at developing a single-stage-to-orbit reusable launch vehicle (RLV) that used conventional runways. However, it was canceled due mainly to design requirements that exceeded the state of the art [1,5]. A more recent RLV project, the VentureStar program, failed during structural tests, again for lack of the required technology [5]. Despite these unsuccessful programs, the continued need for a low-cost RLV, as well as the desire of the U.S. Air Force (USAF) for unmanned hypersonic vehicles, has reinvigorated hypersonic flight research. An emergence of recent and current research programs [6] demonstrate this renewed interest. Consider, for example, the NASA Hyper-X experimental vehicle program [7], the University of Queensland HyShot program [8], the NASA Fundamental Aeronautics Hypersonics Project [9], the joint U.S. Defense Advanced Research Projects Administration (DARPA)/USAF Force Application andLaunch fromContinentalUnited States (FALCON) program [10], the X-51 Single Engine Demonstrator [11,12], the joint USAF Research Laboratory (AFRL)/Australian Defence Science and Technology Organisation Hypersonic International Flight Research Experimentation project [13], and ongoing basic hypersonic research at the AFRL (e.g., [14–20]). The conditions encountered in hypersonic flows, combined with the need to design hypersonic vehicles, have motivated research in the areas of hypersonic aeroelasticity and aerothermoelasticity. It is evident from Fig. 1 that hypersonic vehicle configurations will consist of long, slender lifting body designs. In general, the body, surface panels, and aerodynamic control surfaces are flexible due to minimum-weight restrictions. Furthermore, as shown in Fig. 2, these

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Aeroelastic and Aerothermoelastic Analysis in Hypersonic Flow: Past, Present, and Future

Christian Soize presents the main concepts, formulations, and recent advances in the use of a mathematical-mechanical modeling process to predict the responses of a real structural system in its environment.

Stochastic Models of Uncertainties in Computational Mechanics

Nonintrusive Structural Dynamic Reduced Order Modeling for Large Deformations: Enhancements for Complex Structures

The impact of flow induced loads on snap-through behavior of acoustically excited, thermally buckled panels

Response of a panel to shock impingement: Modeling and comparison with experiments - part 2

The focus of this investigation is on the development and validation of thermoelastic reduced order models for the geometrically nonlinear response and temperature of heated structures. The reduced order modeling approach is based on a modal-type expansion of both displacements and temperatures in the undeformed, unheated configuration. A set of coupled nonlinear differential equations governing the time varying generalized coordinates of the response and temperature expansion are derived from finite thermoelasticity using a Galerkin approach. Further, the selection of the basis functions to be used in these reduced order models is discussed and the numerical evaluation of the model coefficients is addressed. This approach is validated first on an isotropic beam subjected to both thermal effects and external loads. The thermal effects are large enough to induce a significant buckling of the panel while the time varying loads lead to snap-throughs ranging in frequency from infrequent to continuous. Validation to a functionally graded (FGM) panel in similar conditions is then performed. In both cases, the reduced order modeling predicted temperatures and responses are found to very closely match their full finite element counterparts.

Nonlinear reduced order models for thermoelastodynamic response of isotropic and fgm panels

This paper focuses on the extension and continued validation of coupled thermal-structural reduced order models for the prediction of the nonlinear geometric response of heated panels of hypersonic aircraft. The large spatial and temporal variations of temperature expected in such structures imply similar variations of the material properties, most notably elastic properties and coefficient of thermal expansion, which must be captured for an accurate response prediction. Accordingly, earlier reduced order models are first extended to include linear variations with local temperature of the elasticity tensor and coefficients of thermal expansion. The validation of these concepts is achieved on a beam structural model. A representative 3-D hypersonic panel is considered next in isothermal conditions to extend the validation of nonlinear reduced order modeling methods to complex structural models. Key in the reduced order model construction is the basis selection and the combination of linear and dual modes introduced and validated in prior efforts is once again found to capture well the structural response, although an additional set of functions, referred to as the tangent duals is introduced to complete the structural response modeling. The corresponding predictions of the forced static and dynamic responses are found to match full Nastran results very well.

X. Q. Wang

Papers

Response of a panel to shock impingement: Modeling and comparison with experiments - part 2

Nonlinear reduced order models for thermoelastodynamic response of isotropic and fgm panels

Nonlinear structural reduced order modeling methods for hypersonic structures

Prediction of displacement and stress fields of a notched panel with geometric nonlinearity by reduced order modeling

Timoshenko beam theory: A perspective based on the wave-mechanics approach