Reliability of initially compressed uncertain laminated plates in supersonic flow

Liaw, D. G.; Yang, Henry T. Y.

doi:10.2514/3.10685

Cited by 24 publications

(11 citation statements)

References 19 publications

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“…Optimal (deterministic) thickness distributions for increasing stiffness of the torsional edge springs. [15][16][17][18][19][20][21][22][23][24][25][26]to an initial violation in the frequency separation constraints (not shown). For the other cases, the optimizer is able to immediately decrease the volume and satisfy the frequency separation constraint simultaneously.…”

Section: Deterministic Optimizationmentioning

confidence: 92%

“…General perturbation methods for quantification of aeroelastic uncertainty are utilized by Liaw and Yang [16] (mean-centered second moment method) and Castravete and Ibrahim [17] (Karhunen-Love expansions), while FORM is specifically used by Yang and Nikolaidis [18] and Verhoosel et al [19]. FORM estimates the probability of failure P f by locating the most probable point (MPP) along a failure surface transformed into the independent standard normal random space.…”

Section: Introductionmentioning

confidence: 99%

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Minimum-mass panels under probabilistic aeroelastic flutter constraints

Stanford

Beran

2013

Finite Elements in Analysis and Design

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a b s t r a c tAeroelastic flutter is a dangerous failure mode, and aircraft structural components are designed under a deterministic flutter margin. Meeting this safety factor may result in overly-conservative structures, however, an alternative approach incorporates uncertainties into the computational models, and imposes a maximum allowable flutter probability during the optimization process. This technique is demonstrated for the variable-thickness design of an elastic panel subjected to supersonic flow. A performance measure approach based on the first-order reliability method incorporates probabilistic flutter constraints during the search for a minimum-mass panel. Optimization results are given for uncertainties in the panel's boundary conditions, and for non-deterministic thickness design variables.Published by Elsevier B.V.

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Section: Deterministic Optimizationmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Minimum-mass panels under probabilistic aeroelastic flutter constraints

Stanford

Beran

2013

Finite Elements in Analysis and Design

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“…15 The rectangular element possesses 12 DOF at each of the four corner nodes: u, u x , u y , u xy , v, v x , v y , v xy , w, w x , w y , and w xy , where w, v, and w are the displacements in the Cartesian coordinate system jc, y, z, respectively. The subscript indicates differentiation.…”

Section: Formulationmentioning

confidence: 99%

“…15 It is the intent of this study to extend this earlier formulation to include the thermal effect to study the thermal buckling and supersonic flutter of laminated plates simultaneously.…”

Section: Introductionmentioning

confidence: 99%

Supersonic flutter of laminated thin plates with thermal effects

Liaw¹

1993

Journal of Aircraft

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A 48 degree-of-freedom rectangular laminated thin plate finite element including the effects of thermal and aerodynamic loadings is formulated to study the buckling and supersonic flutter characteristics of thin plate structures. Interactive effects between the critical temperature difference and critical aerodynamic pressure for the plates are also studied. The element formulation is based on the classical lamination theory. The aerodynamic pressure due to supersonic potential flow is described by a two-dimensional steady supersonic theory. The element formulation and solution procedure are evaluated by comparing results of three examples with existing alternative solutions. The practical applicability is demonstrated by performing buckling and supersonic flutter analyses of laminated thin plates under various types of temperature distributions. Based on the numerical results, the effects of aspect ratio, ratio of thermal expansion coefficients, fiber orientation, type of temperature distribution, and flow angularity on these examples are discussed.

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“…Monte Carlo Simulation can be computationally expensive due to the large number of model runs required, and as such, it is common to use surrogate models in order to reduce the computation time. A perturbation method, based upon a linear Taylor series approximation, was used by Liaw and Yang (1991) to estimate the mean and variance of the flutter speed of a composite plate with uncertainty in the ply orientations, thickness, elastic moduli, and material and air densities. Polynomial Chaos Expansion (PCE), in which orthogonal polynomials are used as a surrogate model, was used by Pettit and Beran (2004) to model limit cycle oscillations of a two degree of freedom aerofoil with uncertain pitching stiffness and angle of attack.…”

Section: Introductionmentioning

confidence: 99%

Reliability-based aeroelastic design of composite plate wings using a stability margin

Scarth

Cooper

2017

Struct Multidisc Optim

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Reliability-based design is concerned with ensuring that constraints are enforced with acceptable probability under inherent variability in properties. In aircraft design, such a constraint may be that aeroelastic instability does not occur at velocities encountered by the aircraft. This approach can be complicated, as the aeroelastic instability speed is a discontinuous function of material properties, on account of particular modes only becoming unstable for some parameter values. In reliability analysis, it is common to use surrogate models due to the computational expense associated with Monte Carlo Simulation, however, such methods can be inaccurate when emulating discontinuous functions such as the aeroelastic instability speed. In this paper, an alternative approach is proposed in which Gaussian process surrogate models are fitted directly to each of the modal eigenvalues at the design air-speed, and used to emulate a stability margin based upon the most critical eigenvalue. Using this approach, it is shown that the reliability may be estimated for the aeroelastic stability using smooth emulators, thereby overcoming the problems associated with discontinuities. The method is demonstrated for layup optimisation of composite plate wings with uncertain ply angles, in which the probability of aeroelastic instability occurring is minimised for a prescribed air-speed. In uncertainty quantification, a good agreement is found with Monte Carlo Simulation with an order of two magnitudes reduction in model runs. Through reliability-based design, reductions in the probability of failure of up to 99.8% are achieved by increasing the stability margin at the design speed.

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Reliability of initially compressed uncertain laminated plates in supersonic flow

Cited by 24 publications

References 19 publications

Minimum-mass panels under probabilistic aeroelastic flutter constraints

Minimum-mass panels under probabilistic aeroelastic flutter constraints

Supersonic flutter of laminated thin plates with thermal effects

Reliability-based aeroelastic design of composite plate wings using a stability margin

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