Application of Reduced-Order Models for Thermoelastic Trajectory Simulation

Hollkamp, Joseph J.; Gordon, Robert W.; Afb, Wright-Patterson

doi:10.2514/6.2012-1550

Cited by 11 publications

(6 citation statements)

References 12 publications

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“…21 The Newton-Raphson approach is well known and widely used within the nonlinear finite element community, 13 but is not typically used with NLROMs.…”

Section: Tangent-stiffness-based Solution Methods For Nlromsmentioning

confidence: 99%

Improved Solution of Nonlinear Reduced-Order Models for Static and Dynamic Response Prediction

O׳Hara

Hollkamp

2015

56th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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Nonlinear reduced-order models (NLROMs) have been used recently to predict the response of stiffened shell structures subjected to extreme acoustic loading and aerodynamic heating. The NLROMs are essentially modal models augmented with nonlinear terms to capture the large amplitude, nonlinear geometric effects. Temperature dependent linear stiffness terms can be added to capture thermal effects. Numerical stability issues have risen for quasi-static and dynamic simulations using the NLROMs. Most of these issues have been solved through the use of very high sample rates. However, these stability issues are more severe with thermal models of curved structures with softening effects. In this paper, the nonlinear terms of the reduced-order models will be re-cast in an alternate form that allows for more robust solution techniques. An example problem with a curved panel subjected to a thermal loading shows the benefits of the improved solution procedures.

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“…21 The Newton-Raphson approach is well known and widely used within the nonlinear finite element community, 13 but is not typically used with NLROMs.…”

Section: Tangent-stiffness-based Solution Methods For Nlromsmentioning

confidence: 99%

Improved Solution of Nonlinear Reduced-Order Models for Static and Dynamic Response Prediction

O׳Hara

Hollkamp

2015

56th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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“…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][9][10][11][12].…”

Section: Background and Objectivesmentioning

confidence: 99%

“…The generalized coordinates ( ) (3) and (4) are determined by solving the structural and thermal governing equations (see [12,13]) provide the influence of thermal loading on the structural response, thereby coupling the thermal and structural problem, see [7,8,10,11]. The symbols ij B and ij K represent the elements of the capacitance and conductance matrices, which may depend on temperature, and therefore, on time.…”

Section: Rom Formulationmentioning

confidence: 99%

“…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].…”

Section: Background and Objectivesmentioning

confidence: 99%

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Panel Response Prediction Through Reduced Order Models with Application to Hypersonic Aircraft

Matney

Mignolet

Culler

et al. 2015

56th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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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.

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“…The nonlinear ROM's have been used primarily as dynamic models but could be used for the quasi-static thermoelastic structural response which will occur throughout most of the flight trajectory. 6 The general modeling approach is to augment a normal modes model with nonlinear terms. The coefficients of the nonlinear terms can be determined by several methods.…”

Section: Ia Nonlinear Reduced-order Modelsmentioning

confidence: 99%

A Coupled Approach for Modeling Damage within a Reduced-OrderModel Framework

O'Hara

Hollkamp

2013

54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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Future high-speed flight vehicles will be exposed to extreme environments with aerodynamic heating, static, and dynamic loading. The resulting structural response can exhibit significant nonlinear deformation. As a consequence, detailed simulations of long portions of the vehicle's trajectory must be performed to account for path-dependent structural response. Recent developments in nonlinear reduced-order models (ROMs) have demonstrated orders-of-magnitude reductions in computation time for acoustic response prediction simulations. These models are relatively insensitive to small imperfections. Conversely, the generalized finite element method (GFEM) provides a framework to model local effects such as stress risers and cracks without geometric dependency on the finite element (FE) mesh. A more general version of the GFEM, with numerically-built enrichment functions provides a multi-scale modeling capability through a simple, direct coupling of global and local FE models. Replacing the component FE model with a ROM will allow for efficient computation of dynamic response while providing the necessary information to drive local, solid analyses which can zoom in on regions containing stress risers, as deemed necessary. This paper describes the coupling of these two approaches (ROM/GFEM). NomenclatureA i jk r = cubic stiffness coefficients B i j r = quadratic stiffness coefficients E = Young's Modulus f f f = external force vector G = energy release rate H 1 (ω α )= first order Hilbert space defined on ω α K K K = linear stiffness matrix K I , K II , K III = mode 1,2 and 3 stress intensity factors K K K1 1 1, , , K K K2 2 2 = quadratic and cubic stiffness matrices L αi = enrichment function defined on ω α M M M = mass matrix M = number of patches x x x belongs to m α = number of enrichment functions used for node α N = number of degrees-of-freedom in FE model n = number of modes q q q = vector of modal coordinates S GFEM = generalized FE approximation space t = time u u u = displacement field u u u hp = FE approximation of u u u w w w = displacement vector x x x = point in space α = index of node in FE mesh Γ Γ Γ = modal damping matrix θ θ θ = nonlinear function vector θ = angle along crack front Λ Λ Λ = modal stiffness matrix ν = Poisson's ratio Ψ Ψ Ψ = mode shape matrix ϕ α = FE partition of unity function φ αi = generalized FE shape function χ α = local approximation space on ω α Ω = solid, FE domain ω α = set of elements connected to node α

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Application of Reduced-Order Models for Thermoelastic Trajectory Simulation

Cited by 11 publications

References 12 publications

Improved Solution of Nonlinear Reduced-Order Models for Static and Dynamic Response Prediction

Improved Solution of Nonlinear Reduced-Order Models for Static and Dynamic Response Prediction

Panel Response Prediction Through Reduced Order Models with Application to Hypersonic Aircraft

A Coupled Approach for Modeling Damage within a Reduced-OrderModel Framework

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