S. Michael Spottswood

Progressive failure analysis of a composite shell

Abstract The objective of this research is to determine the physical response including material failure of a thin, curved composite panel designed to resist transverse loading. The cause of the material failure, in the form of fiber, matrix and/or delamination failure, will be determined through failure criterion based on nonlinear movement using a finite element analysis technique. The finite element analysis technique known as the simplified large displacement/rotation (SLR) theory allows for large displacements but assumes small to moderate rotations (A.N. Palazotto, S.T. Dennis, Nonlinear Analysis of Shell Structures, American Institute of Aeronautics and Astronautics, Inc., Washington, DC, 1992). Third-order shell kinematics, defined relative to the shell mid-surface, allow for the characterization of in-plane and transverse shear effects, while neglecting the direct transverse effects. Data generated using the SLR theory both with and without the addition of progressive failure criteria, will be compared with previously published experimental data, noting where the SLR theory diverges from the experimental results. The inclusion of the Hashin failure criterion will provide a more realistic representation of the total physical response of the shell (Z. Hashin, J. Appl. Mech. 47 (1980) 329–334). The criterion will investigate the shell, from initial loading, to further progressive composite failures. As the composite shell fails, the constitutive relations, or shell stiffness will be reduced. Results of the analytic comparison with the experimental data indicate that the SLR theory overpredicts the stiffness of the shell whether considering or not considering failure criteria. Results generated for the case incorporating a progressive failure criterion are closer to the experimental data because of the reduced stiffness due to failure as the deflection increases.

NONLINEAR REDUCED ORDER MODELING OF CURVED BEAMS: A COMPARISON OF METHODS

The accurate prediction of the response of aircraft panels subjected to strong acoustic excitation and high temperatures has been and remains an important requirement for the design of supersonic/hypersonic vehicles. One of the key challenges to achieving this prediction is the computationally efficient modeling of the complex physical processes taking place when the acoustic excitation is strong enough to induce a large, nonlinear geometric response of the panel. Even for a flat beam or plate, there exists a subtle energy exchange between the large transverse displacements resulting directly from the acoustic excitation and the much smaller in-plane motions nonlinearly induced by the change of geometry. The transverse displacements exhibit a stiffening behavior which is softened by the in-plane motions. Curved and buckled panels exhibit an even more complex behavior as they can “snap” through an unstable region leading to deformations that are drastically nonlinear, i.e. of the order of 10-100 thicknesses. The interplay of the curvature, acoustic excitation, and temperature leads to an occurrence of snap-through events varying from very rare, to frequent, to continuous. The present study demonstrates that reduced-order model can capture the complex snap-through behavior of shallow curved beams. Successful displacement comparisons are made for two different reduced-order modeling methods, for a single curved beam geometry considering combinations of thermal effects and loading.

Thermal reduced order model adaptation to aero-thermo-structural interactions

The application of reduced order modeling (ROM) techniques to hypersonic structures has gained significant momentum in recent years owing to its ability to deliver accurate structural-thermal response predictions with reduced computational costs relative to full order methods. Accurate response prediction is dependent on the selection of an appropriate basis which is relatively straightforward for single discipline problems. For structural problems, the basis is comprised of the natural mode shapes of the structure and duals, which are modes constructed to capture the nonlinear membrane stretching effect. Similarly, eigenvectors of the generalized conductance-capacitance eigenvalue problem have been shown to provide an adequate basis for thermal ROMs. Selecting a basis for multidisciplinary problems may be significantly more difficult because of the unexpected behavior that may result from the interactions between the disciplines. It is proposed here that reduced order models first be developed as above on single discipline arguments, then be adapted, specifically their bases, to account for the interaction as the computations proceed. An adaptive model is most likely needed for the thermal problem, since the corresponding eigenvalues are more densely clustered than for the structural problem, resulting in significant contributions from more modes as the thermal loading conditions change. To investigate these concepts, a representative hypersonic panel is considered here and a thermal reduced order model of it is first developed and validated under single discipline conditions. The applicability of this basis to represent the temperature distribution resulting from a fully coupled aero-thermo-structural interaction is then assessed and a methodology to adapt the thermal basis is proposed and discussed.

Experimental nonlinear response of tapered ceramic matrix composite plates to base excitation

The United States Air Force is interested in the development of hypersonic and reusable space vehicles. A significant factor in the pursuit of that goal is to develop the critical materials and structures necessary to withstand the expected aerodynamic heating, as well as the aeroacoustic and engine induced acoustic loading. This study focused on the geometric nonlinear response of these fully clamped, tapered CMC panels to stationary Gaussian random base excitation. The taper of the selected CMC panel was asymmetric resulting in an expected coupling of the axial and bending response. The power spectral densities (PSDs), amplitude, peak and rainflow probability density functions (PDFs), time-history response, and axial, bending and total strain contributions to narrowband random vibration testing were investigated, noting the effects of the geometric nonlinearities. Several interesting phenomenon resulted from the study. First, the effects of the coupling between the axial and bending strain on the response PSDs were highlighted. Next, the study indicated a distinct asymmetry in the narrow-band response PDFs due to the increasing significance the axial strain played in the total response. Finally, the mean total, bending and axial strain response were noted to exhibit a quadratic relationship with respect to the excitation level.

Panel response prediction through reduced order models with application to hypersonic aircraft

The present work is the culmination of a series of investigations by the authors on the construction and validation of structural, thermal, and coupled structural-thermal reduced order models (ROMs) for the prediction of the displacements and temperature fields on a representative panel of a hypersonic aircraft during a particular trajectory. The focus of the present paper is first on the development and validation of an efficient strategy for enriching the thermal ROM basis to reflect the temperature distribution induced by the structural deformations through changes of the aerodynamics. Next, the assembly of the thermal and structural ROM bases and the identification of their coefficients is revisited for both cases of constant and temperature dependent coefficient of thermal expansion. The coupled ROM predictions are finally compared to those obtained from full structural and thermal finite element models and it is seen that the ROMs perform overall very well over the large temperature change during the trajectory, from room temperature to 2300F. The only exception to the accuracy of the ROMs is a mode switching event occurring for one of the finite element models but not for the ROMs. This issue is under continued investigation. Background and Objectives There have been several attempts in the past to develop reusable, manned, hypersonic aircraft, but all attempts have so far been called off prior to accomplishing their goal. One of the challenges with developing such a vehicle has been the lack of accurate, predictive models [1]. Consider for example a panel of such a hypersonic vehicle. Its structural response is expected to be both highly nonlinear due to the extreme loading environment and the result of multidisciplinary interactions, involving aerodynamics, structural dynamics and heat transfer [26]. Further complicating the issue is the need to perform long duration analyses for fatigue life prediction. Taken together, these factors constitute a computational task that is extremely demanding even with current computational resources when utilizing full order analyses, i.e. finite element and CFD capabilities. As such, reduced order modeling has emerged as a promising tool to provide accurate structural-thermal predictions while reducing time and computational requirements for simulations. The consideration of nonlinear geometric effects in a reduced order model format has initially focused on isothermal conditions, e.g. see [7] for a recent extensive review. However, the inclusion of thermal effects with the temperature itself represented in a reduced order form has recently been developed and validated [8-12]. The structure considered here is a representative hypersonic panel of [2], see Fig. 1, of which structural and thermal finite element models were developed while the aerodynamic pressure and aerodynamic heating were modeled using piston theory and Eckert’s reference enthalpy method, respectively. The vehicle was accelerated from Mach 2 to Mach 12 over 300 seconds, while the dynamic pressure was held constant at 2,000 psf. The structural, thermal and aerodynamic solutions were marched in time in a process described in detail in [2]. Two different options for this time marching were considered: the one-way and two-way coupling scenarios. One-way coupling refers to an analysis in which the thermal problem is carried out in the absence of structural deformations. The temperature field is thus obtained directly from the aeroheating and heat conduction on the rigid structure, i.e. as a two-discipline (aerodynamics-thermal) problem. Then, the structural deformations are determined for the obtained temperatures distributions as the result of the interaction with the aerodynamics, i.e. another two-discipline problem (aerodynamics-structural). Two-way coupling refers to analyses in which the heating on the panel is influenced by the structural displacement through the aerodynamics, i.e. a three-discipline problem. It is this latter format that more closely resembles reality, and is the subject of the present reduced order model based investigation. Figure 1. Representative hypersonic ramp panel. The present work is the culmination of a series of investigations by the authors. A purely structural, isothermal reduced order model of the panel of Fig. 1 was first developed and validated using uniform static pressure loads and acoustic loading in [11]. Next, a basis for the thermal reduced order model was determined [12] that captures the temperature fields occurring in the one-way coupled trajectory analysis of [2]. The structural responses induced by these temperature distributions and an external loading were then determined using both Nastran and the reduced order models in [13]. A very good to excellent match of these two sets of responses demonstrated the applicability of the structural-thermal reduced order modeling to the one-way coupled scenario. The consideration of two-way coupling was initiated in [14] in which a methodology was proposed to construct a thermal basis for the two-way coupled temperature field. More specifically, an adaptive approach was presented in which a linear, auxiliary problem was utilized to obtain a very fast first estimate of the temperature fields resulting from the full interaction. Appropriate enrichments to the thermal basis were then determined from these Skin

Implicit large eddy simulation of acoustic loading in supersonic turbulent boundary layers

This paper investigates the accuracy of implicit large eddy simulation in the prediction of acoustic phenomena associated with pressure fluctuations within a supersonic turbulent boundary layer. We assess the accuracy of implicit large eddy simulation against direct numerical simulation and experiments for attached turbulent supersonic flow with zero-pressure gradient, and further analyze and discuss the effects of turbulent boundary layer pressure fluctuations on acoustic loading both at the high and low frequency regimes. The results of high-order variants of the simulations show good agreement with theoretical models, experiments, as well as previously published direct numerical simulations.

Design Sensitivities of Components Using Nonlinear Reduced-Order Models and Complex Variables

This work-in-progress paper explores the use of complex variables to define the design sensitivities of high-speed aircraft components modeled by nonlinear reduced-order models (NLROMs). Extreme conditions are expected to be seen by high-speed flight vehicles and it is anticipated that portions of the structure are likely to exhibit significant nonlinearity in their response. Accurate prediction of the path-dependent response requires direct time-integration of nonlinear models. Large finite element models of the structural components would require prohibitively large amounts of computer time to properly simulate. Methodologies have been proposed that use NLROMs to model the component level, dynamic response. The nonlinear ROMs are linear modal models that have been coupled through the addition of nonlinear modal stiffness terms. The nonlinearity in these models is sensitive to the connectivity of the components with the assembly. Recent work has investigated the use of complex variables to update NLROMs based on the boundary stiffness of the adjoining structure. This paper will explore complex methods to determine component design sensitivities to the thermal expansion and stiffness of the surrounding structure.