Hamed Haddad Khodaparast

Transonic Aeroelastic Stability Predictions Under the Influence of Structural Variability

DOI: 10.2514/1.46971 Flutter prediction as currently practiced is almost always deterministic in nature, based on a single structural model that is assumed to represent a fleet of aircraft. However, it is also recognized that there can be significant structural variability, even for different flights of the same aircraft. The safety factor used for flutter clearance is in part meant to account for this variability. Simulation tools can, however, represent the consequences of structural variability in the flutter predictions, providing extra information that could be useful in planning physical tests and assessing risk. The main problem arising for this type of calculation when using high-fidelity tools based on computational fluid dynamics is the computational cost. The current paper uses an eigenvalue-based stability method together with Euler-level aerodynamics and different methods for propagating structural variability to stability predictions.The propagation methodsare Monte Carlo,perturbation, andinterval analysis. Thefeasibility of this type of analysis is demonstrated. Results are presented for the Goland wing and a generic fighter configuration.

A spectral approach for fuzzy uncertainty propagation in finite element analysis

Abstract Uncertainty propagation in complex engineering systems with fuzzy variables constitutes a significant challenge. This paper proposes a Polynomial Chaos type spectral approach based on orthogonal function expansion. A fuzzy variable is represented as a set of interval variables via the membership function. The interval variables are further transformed into the standard interval [ − 1 , 1 ] . Smooth nonlinear functions of standard interval variables are projected in the basis of Legendre polynomials by exploiting its orthogonal properties over the interval [ − 1 , 1 ] . The coefficients associated with the basis functions are obtained by a Galerkin type of error minimisation. The method is first illustrated using scalar functions of multiple fuzzy variables. Later the method is proposed for elliptic type finite element problems where the technique is extended to vector valued functions with multiple fuzzy variables. The response of such systems can be expressed in the complete basis of multivariate Legendre polynomials. The coefficients, obtained by Galerkin type of error minimisation, can be calculated from the solution of an extended set of linear algebraic equations. An eigenfunction based model reduction technique is proposed to obtain the coefficient vectors in an efficient way. A numerical example of axial deformation of a rod with fuzzy axial stiffness is considered to illustrate the proposed methods. Linear and nonlinear membership functions are used and the results are compared with direct numerical simulation results.

Finite-element modelling and updating of laser spot weld joints in a top-hat structure for dynamic analysis

Abstract Spot welds made by resistance spot welding are used extensively in automotive engineering. However, owing to increasing demands in the use of advanced and lightweight materials, laser welding has become a popular alternative for producing spot welds. Because of the complexity and uncertainties of laser welds and thus formed structures, the finite-element (FE) modelling of the welds for dynamic analysis is a research issue. This article first outlines some of the existing modelling works of spot welds. Then, a hat-plate structure used for this study is described and its FE representations are explained. The welds are modelled using CWELD elements in MSC/NASTRAN and their feasibility for representing laser spot welds is investigated. Numerical results for the initial FE model differ considerably from that of their experimental counterparts; hence, a model updating procedure is carried out to minimize the discrepancy between the two sets of results. In this work, the updating is posed as an optimization problem and is performed using the structural optimization capability (SOL 200) in MSC/NASTRAN. Two stages of updating are conducted, that is (a) updating FE models of individual components and (b) updating an FE model of the welded structure. Crucial steps in updating are explained. It is found that by selecting the right updating parameters, the CWELD element can be used to represent laser spot welds with good accuracy.

The design of a coated composite corrugated skin for the camber morphing airfoil

One of the critical components of a morphing wing is the anisotropic skin, which has to be stiff to withstand the aerodynamic loads and flexible to enable the morphing deformations. This work presents the design of an elastomer coated composite corrugated skin for the camber morphing airfoil. The good in-plane strain capability and highly anisotropic behaviour of composite corrugated panels make them very effective in morphing wing applications. The behaviour of these corrugated skins must be investigated comprehensively and optimized in terms of aero-elastic effects and the boundary conditions arising from the internal wing structure. In this article, the geometric parameters of the coated composite corrugated panels are optimized to minimize the in-plane stiffness and the weight of the skin and to maximize the flexural out-of-plane stiffness of the corrugated skin. A finite element code for thin beam elements is used with the aggregate Newton’s method to optimize the geometric parameters of the coated corrugated panel. The advantages of the corrugated skin over the elastomer skin for the camber morphing structure are discussed. Moreover, a finite element simulation of the internal structure with the corrugated skin is performed under typical aerodynamic and structural loadings to check the design approach.

Calculating the Influence of Structural Uncertainty on Aeroelastic Limit Cycle Response

Previous work by the authors has considered the impact on aeroelastic stability of uncertainty in structural parameters. Particular consideration has been given to how large dimensional systems like those arising from computational fluid dynamics can be made tractable for the stability analysis. There is considerable practical interest in evaluating the impact of structural parameter variability on limit cycle responses. This is a demanding task since nonlinearity must be involved in some form (which tends to render model reduction through methods like proper orthogonal decomposition less effective than for linear problems). The best current approach seems to be that described in reference, which contains a good review of the current state of the art. The current paper has the objective of reconsidering the (nonlinear) model reduction presented in references 6 for application to parametric variability studies. The approach is to calculate the critical eigenspace of the linearised system and use this as a basis for model reduction. The full order system is manipulated using a Taylor expansion which is then projected onto the critical eigenspace basis. The extra step here is to add the influence of an uncertain parameter to the Taylor Series. This allows the reduced model (two degrees-of-freedom) to be precomputed, and then exploited for the variability analysis. The feasibility of this approach was demonstrated in a recent paper, where the application was made to a two degree of freedom system with a structural nonlinearity, and a linear model for the aerodynamics. Results showed that the nonlinear reduced model was effective for computing the LCO probability density function when a distribution for one of the structural parameters was assumed. In the current paper this work is extended to a three dimensional case with a nonlinearity introduced into the structural model of a wing/tip store test case.

How Structural Model Variability Influences Transonic Aeroelastic Stability

This paper considers the ways in which structural model parameter variability can influence aeroelastic stability. Previous work on formulating the stability calculation (with the Euler equations providing the aerodynamic predictions) is exploited to use Monte Carlo, interval, and perturbation calculations to allow this question to be investigated. Three routes are identified. The first involves variable normal-mode frequencies only. The second involves normal-mode frequencies and shapes. Finally, the third, in addition to normal-mode frequencies and shapes, also includes their influence on the static equilibrium. Previous work has suggested only considering the first route, which allows significant gains in computational efficiency if reduced-order models can be built for the aerodynamics. However, results in the current paper show that neglecting the mode-shape variation can give misleading results for the flutter-onset prediction, complicating the development of reduced aerodynamicmodels for variability analysis.

FE Model Updating for Damage Detection – Application to a Welded Structure

Finite Element (FE) model updating is initially developed to update numerical models of structures to match their experimentally measured modal properties (i.e., natural frequencies and modes). In FE model updating, uncertain physical parameters of a structure are modified so that the discrepancies between the numerically estimated and experimentally measured modal properties are minimized. The process of updating is employed not only in parameter identification; it can also be developed for structural damage identification. In this work, a welded structure that is intended to represent a common configuration used in automotive body construction is investigated. It is known that presence of any damage in the welds of such a structure could affect its dynamic behavior. So, in theory modal test data can allow damage to be assessed accurately. As a typical automotive body contains thousands of welds, the effects of damage in the welds could be influential. The FE model updating process using experimental data is presented. It is carried out using NASTRAN optimization code. The procedure aims to adjust the uncertain properties of the FE model (from the weld joints) by minimizing the differences between the measured modal properties and the corresponding numerical predictions. The initial parameter values used in the numerical model are the nominal values. The procedure brings the numerical results of the structure as close as possible to the experimental ones, according to an objective function, therefore altering some of the FE model parameters of the structure. It may be concluded that when the identified values of certain parameters deviates from the nominal values to certain extent, there is a fault or damage at that particular joint.

Modal testing and finite element model updating of laser spot welds

Spot welds are used extensively in automotive engineering. One of the latest manufacturing techniques for producing spot welds is Laser Welding. Finite element (FE) modelling of laser welds for dynamic analysis is a research issue because of the complexity and uncertainty of the welds and thus formed structures. In this work, FE model of the welds is developed by employing CWELD element in NASTRAN and its feasibility for representing laser spot welds is investigated. The FE model is updated based on the measured modal data of hat-plate structures and cast as a structural minimisation problem by the application of NASTRAN codes.

FE model updating of welded structures for identification of defects

A non-destructive evaluation procedure for identifying defects using finite element (FE) model updating based on natural frequencies is presented in this paper. Welded structures that are intended to represent a common configuration used in automotive body construction are investigated. The first procedure is to find the measured natural frequencies of both benchmark and defective structures, by carrying out the experimental modal analysis (EMA). Then, the FE model of the benchmark structure is developed and updated by modifying some design parameters from their initial values. FE modelling is accomplished with MSC NASTRAN and the FE model updating procedure is performed using the NASTRAN optimisation code (SOL200). Next, appropriate defects on the defective structure are observed by performing a visual inspection. Information from the visual inspection and the updated benchmark model is incorporated when modelling the defective structure, followed by the FE model updating procedure to identify the defect parameters.

CFD based aeroelastic stability predictions under the influence of structural variability.

Flutter prediction as currently practised is almost always deterministic in nature, based on a single structural model that is assumed to represent a fleet of aircraft. However, it is also recognised that there can be significant variability, even for different flights of the same aircraft. The safety factor used during flutter clearance is in part meant to account for this variability. Simulation tools can however represent the consequences of structural variability in the flutter predictions, providing extra information which could be useful in planning physical tests and assessing risk. The main problem arising for this type of calculation when using high fidelity tools based on Computational Fluid Dynamics (CFD) is the computational cost. The current paper uses an eigenvalue based stability method together with CFD level aerodynamics and different methods for propagating structural variability to stability predictions. The propagation methods are Monte Carlo, perturbation and interval analysis. The feasibility of this type of analysis is demonstrated. Results are presented for the Goland wing and for a generic fighter configuration.