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The computational budget for designing and optimizing engineering systems has been tightened by the growth in the number of technology alternatives to satisfy the increasingly demanding goals in modern systems and the use of sophisticated, but also computationally burdensome, simulation tools to quantitatively choose the best technology alternative more accurately. This paper develops a new Gaussian process metamodel, which leverages trends in engineering objectives that are similar across derivative concepts, as opposed to current approximation methods that handle concepts independently. This metamodel is based on a muitifidelity approach that enhances a new concept prediction with observations of a previous concept with similar trends. The influence of the sizes of the new and the old concept training sets in the performance of the proposed metamodel is explored in this paper. The proposed multifidelity metamodel is tested against traditional independent surrogates in approximating the engine shaft horsepower of a UH-60A modification with a Fenestron tail, where observations from the UH-60A with a conventional tail are available. The proposed metamodels are up to two times as accurate as independent concept modeling for small new concept training sets; then, a multiobjective efficient global optimization algorithm is applied to the proposed metamodel to search for minimal UH-60A power consumption in hover and cruise. This results in Pareto-optimal solutions that are 10% more efficient than the UH-60A baseline. [ABSTRACT FROM AUTHOR]

Nonlinearities can be present in an aeroelastic system because of some aerodynamic factors that occur in transonic flight regimes or at a large angle of attack. The sources are shock wave motions and separated flows. Complex aeroelastic problems due to the aerodynamic nonlinearity can be studied using high-fidelity computational fluid dynamics (CFD) codes. However, the computational cost may be very high. Hence, this kind of problem is conveniently solved using the reduced-order model (ROM) for unsteady aerodynamic analysis. Many studies have been done using reduced-order modeling for aeroelastic analysis. However, most of the reduced-order aerodynamic models are dynamic linear models and have loads proportional to the structural motions. In the current paper, a nonlinear unsteady reduced-order aerodynamic model is constructed using the radial basis function neural network model. This kind of ROM is used to analyze the limit cycle oscillation (LCO) for two linear structural models with large shock motions in transonic flow. Unlike the input signals in the traditional design method, the signals of the self-excited vibration of the aeroelastic system are designed as the input signals in the current paper. Coupling the structural equations of motion and nonlinear aerodynamic ROM, the system responses are determined by time marching the governing equations using a hybrid linear multistep algorithm. Then, the LCO change with velocities (dynamic pressure) was analyzed. The two transonic aeroelastic examples show that both the structural responses and the LCO characteristics simulated using the nonlinear ROM agree well with those obtained using the direct CFD method. Moreover, the computational efficiency of the nonlinear ROM-based method is improved by one to two orders of magnitude compared with that of the direct CFD method. [ABSTRACT FROM AUTHOR]

The study of a multidomain coupling algorithm of numerical methods applied to direct acoustic waves simulation is the focus of this paper. The idea is to be able to use meshing techniques and numerical methods of different natures, depending on the domain area, in order to meet the local requirements of the computation. Here, the linearized Euler equations are solved by carrying out a coupling between a discontinuous Galerkin method running on an unstructured mesh and a finite difference method running on a Cartesian grid. The aim is to take into account complex geometries by running a discontinuous Galerkin method and run a finite difference method away from the obstacles to reduce computational costs, in this paper, two different discontinuous Galerkin/finite difference coupling algorithms are presented, and some associated validation results in terms of precision and stability are discussed. An application of a hybrid solver in the framework of an acoustic benchmark dedicated to complex geometries is also presented. [ABSTRACT FROM AUTHOR]

Finite volume discretizations on unstructured grids that are more than second-order-accurate have not yet gained wide acceptance. This is due to the high computational cost and memory requirements of the proposed schemes and the technical difficulties in achieving a high-order-accurate solution. It is especially true when considering flows in complex geometries. In this paper, a third-order cell-centered finite volume discretization is detailed that is based on quadratic data recovery, which is computationally efficient and has optimal memory requirements. The density-based flow-solver discretization and solution algorithm are described briefly, followed by a detailed presentation of the least-squares-based multistep quadratic data-reconstruction methodology proposed here. The paper is concluded with numerical examples to verify the accuracy and numerical efficiency of this high-order finite volume discretization. [ABSTRACT FROM AUTHOR]

Because of their small size and flight regime, coupling of aerodynamics, structural dynamics, and flight dynamics are critical for micro aerial vehicles. This paper presents a computational framework for simulating structural models of varied fidelity and a Navier-Stokes solver, aimed at simulating flapping and flexible wings. The structural model uses either 1) the in-house developed UM/NLABS, which decomposes the equations of 3-D elasticity into cross-sectional and spanwise analyses for slender wings, or 2) MSC.Marc, which is a commercial finite-element solver capable of modeling geometrically nonlinear structures of arbitrary geometry. The flow solver employs a well-tested pressure-based algorithm implemented in STREAM. A NACA0012 cross-sectional rectangular wing of aspect ratio 3, chord Reynolds number of 3 x 104, and reduced frequency varying from 0.4 to 1.82, with prescribed pure plunge motion is investigated. Both rigid and flexible wing results are presented, and good agreement between experiment and computation are shown regarding tip displacement and thrust coefficient. Issues related to coupling strategies, fluid physics associated with rigid and flexible wings, and implications of fluid density on aerodynamic loading are also explored in this paper. [ABSTRACT FROM AUTHOR]

This paper reports on the SIMPLE-like solution algorithm that significantly improves velocity-pressure coupling, leading to the accelerated convergence. The algorithm is applicable to both incompressible and compressible flows. It is implemented within the framework of a cell centered finite volume method using colocated storage of flow variables on unstructured grids. The convergence acceleration is an outcome of the novel treatment of the pressure correction equation that accounts for two commonly neglected terms appearing in a general pressure correction equation. These terms, namely, the neighbor and nonorthogonal corrections, represent velocity corrections from neighboring cells and the cell-face pressure correction gradient associated with the grid nonorthogonality, respectively. Reminiscent of the PISO method, both neighbor and nonorthogonal corrections are taken into account by performing two or more correction steps. However, the full inclusion of neighbor velocity corrections can prevent the solution convergence. Following an analogy between time marching and a steady-state iterative approach, this problem has been resolved by introducing a pseudounsteady term into discretized velocity correction equations. Using this term, the contribution of neighbor corrections is underrelaxed, enabling a satisfactory convergence rate. The algorithm is applied to several benchmark test cases, covering laminar and turbulent, as well as incompressible and compressible, flows. For all test cases, the convergence rate can be significantly improved by performing two or more pressure correction steps. An optimal number of pressure corrections exists for which a meaningful reduction of computing time is possible. [ABSTRACT FROM AUTHOR]

The paper presents the developments of novel mesh generation algorithms over complex glaze-ice shapes containing multicurvature ice-accretion geometries, such as single/double ice horns. The twofold approaches tackle surface geometry discretization as well as field mesh generation. First, an adaptive curvilinear curvature control algorithm is constructed, solving a one-dimensional elliptic partial differential equation with periodic source terms. This method controls the arc length grid spacing, so that high convex and concave curvature regions around ice horns are appropriately captured, and is shown to effectively treat the grid shock problem. Second, a novel blended method is developed by defining combinations of source terms with two-dimensional elliptic equations. The source terms include two common control functions, Sorenson and Spekreijse, and an additional third source term to improve orthogonality. This blended method is shown to be very effective for improving grid quality metrics for complex glaze-ice meshes with Reynolds-averaged Navier-Stokes resolution. The performance in terms of residual reduction per nonlinear iteration of several solution algorithms (point-Jacobi, Gauss-Seidel, alternating direction implicit, point, and line Successive Over-Relaxation) are discussed within the context of a full multigrid operator. Details are given on the various formulations used in the linearization process. It is shown that this performance of the solution algorithm depends on the type of control function used. Finally, the algorithms are validated on standard complex experimental ice shapes, demonstrating the applicability of the methods. [ABSTRACT FROM AUTHOR]

This paper focuses on the development of a surface mesh movement algorithm suitable for computer-aided-design-based aerodynamic shape optimization. The algorithm interrogates the computer-aided-design system via the vendor-neutral application programming interface Computational Analysis Programming Interface and uses the Computational Analysis Programming Interface's watertight triangulation of a modified computer-aided-design geometry to guide the movement of the structured surface mesh as the geometry changes during the optimization process. A mapping procedure is introduced that not only preserves the characteristics of the original surface mesh but also guarantees that the new mesh points are on the computer-aided-design geometry. The deformed surface mesh is then smoothed in the parametric space before it is transformed back into three-dimensional space. The procedure is efficient, in that all the processing is done in the parametric space, incurring minimal computational cost. The mesh movement tool is integrated into a three-dimensional shape-optimization framework, with a linear-elasticity volume-mesh movement algorithm, a Newton-Krylov flow solver for the Euler equations, and a discrete-adjoint gradient-based optimizer. The accuracy of the computed gradients is verified through a number of examples. [ABSTRACT FROM AUTHOR]

A computational-fluid-dynamics-driven robust and accurate method for aerodynamic shape optimization, previously developed by the authors, is further enhanced by extending it to automatic multipoint design of wingbody- nacelle configurations. The shape is optimized for minimum drag at fixed lift subject to numerous geometrical and aerodynamical constraints. The method, which is driven by genetic algorithms and full Navier-Stokes computations combined with reduced-order models approach, is supported by massive multilevel parallelization. The applications include single- and multipoint aerodynamic designs for a transport-type aircraft configuration. For the considered class of shape optimizations, significant drag reduction in on- and off-design conditions has been achieved. It was also shown that the optimizations, which start from markedly different initial shapes, ultimately converge to optimum shapes very close one to one another. The paper demonstrates how automated techniques based on the developed method have now matured and provide an industrial strength solution. [ABSTRACT FROM AUTHOR]

Numerical algorithms and solutions of generalized nonlinear lifting-line theory over an elliptical wing are examined, with emphasis on near/poststall flows. First, a thorough analysis on the circulation-based and angle-ofattack- based correction methods (Γ and α methods, respectively) highlights their respective numerical poststall characteristics. The stability of the method is demonstrated, producing single and multiple solutions in the pre- and poststall regions, respectively. Second, artificial dissipation added to the a method is shown to be an effective means of controlling the poststall flow region. Finally, a strongly coupled algorithm is presented, allowing to bypass the interpolation phase via the use of Legendre polynomials. The model sheds light on poststall flow behavior, in agreement with several papers studying formation of stall cell patterns. [ABSTRACT FROM AUTHOR]

The interaction of vortical structures with a solid wall is studied numerically in this paper. The incompressible Navier--Stokes equations in their primitive variable formulation are solved on a staggered Cartesian grid using the fractional-step algorithm. The convective terms are marched in time using the Adams--Bashforth or Runge--Kutta schemes, while the viscous terms are treated implicitly using the trapezoidal scheme. An upwind reconstruction of the convective fluxes in their conservative form is proposed and compared against the nonconservative flux formulation, as differences are expected due to nonzero velocity divergence in the numerical solution. The performance of the algorithm is assessed on the convection of an isolated vortex. The algorithm is verified on benchmark incompressible flows and flows involving the convection, mutual interaction, and wall impingement of vortical structures. An attempt is made to simulate the impingement of two and multiple vortex rings against a solid wall to understand the effect of mutual interactions on the interactions with a solid wall. The effects of Reynolds number and initial separation between the rings are studied. These parameters are observed to affect the behavior of the vortical structures, thus affecting the formation and ejection of secondary vortices. [ABSTRACT FROM AUTHOR]

Computational fluid dynamics (CFD) based on the Navier-Stokes equations is by far the most useful predictive method available today for helicopter analysis and design. The main drawback of CFD, and perhaps the reason for its slow acceptance by design offices of helicopter manufacturers, is apparently due to the substantial requirements of CPU time and the relatively slow turnaround times in comparison to lower-order methods. However, progress with CFD algorithms and parallel computing has allowed CFD analyses to be used more routinely. Typical applications include computations of aerofoil data that feed rotor performance codes and analyses of rotors in hovering flight. The computation of unsteady flow cases is, however, still challenging. This paper presents alternative ways of tackling unsteady flow problems pertinent to rotorcraft using methods that aim to reduce the time-marching unsteady computations to more manageable steady-state solutions. The techniques investigated so far by the CFD laboratory of Liverpool include time-linearized and harmonic-balance methods. The details of the methods are presented along with their implementation in the framework of the helicopter multiblock CFD solver. Results were obtained for several flow cases, ranging from pitching/translating aerofoils to complete rotors. The results highlight some of the limitations of the time-linearized method and the potential of the harmonic-balance technique. It was found that the time-linearized method can provide adequate results for cases where the unsteady flow is a rather small perturbation of a known mean. The harmonic-balance method proved to have a larger range of applicability and provided adequate results for the analysis of unsteady flows. The required CPU time was reduced, and the required core computer memory was increased. Overall, the harmonic-balance method appears to be a possible alternative to time-marching CFD for a wide range of problems. [ABSTRACT FROM AUTHOR]

This paper presents a provably convergent multifidelity optimization algorithm for unconstrained problems that does not require high-fidelity gradients. The method uses a radial basis function interpolation to capture the error between a high-fidelity function and a low-fidelity function. The error interpolation is added to the low-fidefity function to create a surrogate model of the high-fidelity function in the neighborhood of a trust region. When appropriately distributed spatial calibration points are used, the low-fidelity function and radial basis function interpolation generate a fully linear model. This condition is sufficient to prove convergence in a trust region framework. In the case when there are multiple lower-fidelity models, the predictions of all calibrated lower-fidelity models can be combined with a maximum likelihood estimator constructed using kriging variance estimates from the radial basis function models. This procedure allows for flexibility in sampling lower-fidelity functions, does not alter the convergence proof of the optimization algorithm, and is shown to be robust to poor low-fidelity information. The algorithm is compared with a single-fidelity quasi-Newton algorithm and two first-order consistent multifidelity trust region algorithms. For simple functions the quasi-Newton algorithm uses slightly fewer high-fidelity function evaluations; however, for more complex supersonic airfoil design problems it uses significantly more. In all cases tested, our radial basis function calibration approach uses fewer high-fidelity function evaluations when compared with first-order consistent trust region schemes. [ABSTRACT FROM AUTHOR]

Based on the measured vibration information, a method for detecting reduction in stiffness parameters of a structure using generalized flexibility matrix and changes in natural frequencies is presented in this paper. For incomplete measured data of the first mode shape, dynamic expansion of mode shape is introduced. The generalized flexibility matrix is approximately constructed by using the measured first frequency and the extended mode shape only, and it is further used to detect the possible damaged elements. An iterative algorithm using the changes of the first several natural frequencies only is subsequently used to update the damage extent of these possible damaged elements, while the number of damage-extent parameters to be determined in the algorithm is remarkably reduced. Finally, two numerical examples concerning a two-span beam and a two-story frame are used to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Stacking-sequence optimization of laminated composite structures is a combinatorial problem involving discrete variables when ply angles are used as design variables. Such an optimization problem can be solved using genetic algorithms coupled with response surface methods to reduce the computational cost. Alternatively, the optimization problem can be formulated using lamination parameters as design variables, allowing efficient gradient-based optimization methods to be used. Nevertheless, practical stacking sequences have to be reconstructed in a second step, which can be problematic. A synthesis of the two-step approach and the response surface approach to composite design is proposed in this paper. The synthesis is effected by constructing a new multipoint structural approximation scheme based on an innovative use of the classical Shepard's method applied in the space of laminate stiffness. A distance measure in the stiffness space is proposed to adapt the method to composite design. The response surface genetic algorithm optimization is performed starting from a continuous optimum defined by prior continuous optimization. The method is first applied to single-laminate design example problems to demonstrate its efficiency and accuracy compared with known methods. The capacity of the optimization strategy to solve more complex problems is then demonstrated using two patch design examples. [ABSTRACT FROM AUTHOR]

This paper presents an unsteady discrete adjoint algorithm for high-order implicit discontinuous Galerkin discretizations in time-dependent inviscid flow problems. The major function of the adjoint approach is to obtain the sensitivity information in a time-dependent functional output, which in turn is used to drive an unsteady shape-optimization process to deliver a minimum of the objective functional. A gradient-based optimization strategy is investigated, in which the sensitivity derivatives of the objective functional with respect to input variables are formulated in the context of high-order discontinuous Galerkin discretizations, while special emphasis is given to the variations and linearizations of curvilinear boundary elements. Implicit temporal discretizations consisting of a second-order backward Euler scheme and a fourth-order implicit Runge-Kutta scheme are considered exclusively in this work, where the corresponding adjoint problem is required to be solved in a backward time-integration manner due to the associated transpose operation. Two numerical examples for the unsteady shape design techniques are presented to verify the derived sensitivity formulations and to demonstrate the performance of the adjoint approach; the first involves an inverse shape-optimization case by matching a time-dependent target pressure profile for a two-dimensional periodic vortical gust impinging on a RAE-2822 airfoil, and the second considers minimization of the acoustic noise produced by subsonic flow over a NACA0012 airfoil with a 0.03c thick blunt trailing edge. [ABSTRACT FROM AUTHOR]

Aeroelastic systems may exhibit vibrations that are induced by a forced periodic motion of their elements. For example, the forced periodic motion of an aileron on a deformable wing produces vibrations of this wing. Accurate numerical simulation of such problems is usually based on a time-marching scheme and a code-coupling strategy. Such computations are costly, since before the periodic-vibration cycles, a long transient has to be computed. A technique called time-harmonic balance has been developed in the field of computational fluid dynamics to accelerate the computation of unsteady periodic flows. This technique allows the periodic state of these flows to be computed directly without computing their transients. In this paper the time-harmonic-balance strategy is applied to an aeroelastic solver consisting of two coupled codes. The time-harmonic-balance technique allows the resulting aeroelastic solver to compute the periodic-vibration cycles caused by a periodic forced motion directly, without computing the long transients. The time-harmonic-balance-based aeroelastic solver is analyzed and validated on a two-dimensional aeroelastic pitch-plunge airfoil undergoing a forced pitching. Furthermore, application to an industrial case is considered, where the flexibility of an aircraft wing is taken into account in the computation of unsteady aerodynamic forces caused by an oscillating aileron. [ABSTRACT FROM AUTHOR]

In this paper an efficient general algorithm to calculate the Hessian of a steady or unsteady functional of interest in the context of computational fluid dynamics is outlined, verified, and applied to an aerodynamic optimization and to an extrapolation example. The successful extrapolation is then applied to approximate Monte Carlo simulations for artificial geometric uncertainty analysis. The presented optimization and extrapolation examples demonstrate that the combination of automatic differentiation and an adjoint method to calculate the Hessian of a steady or unsteady objective function, and thereby obtaining second-order information, can be an efficient tool for optimization and uncertainty quantification. [ABSTRACT FROM AUTHOR]

This paper develops a methodology for the optimum layout design of sensor arrays of structural health monitoring systems under uncertainty. This includes finite element analysis under transient mechanical and thermal loads and incorporation of uncertainty quantification methods. The finite element model is validated with experimental data, accounting for uncertainties in experimental measurements and model predictions. The structural health monitoring sensors need to be placed optimally in order to detect with high reliability any structural damage before it turns critical. The proposed methodology achieves this objective by combining probabilistic finite element analysis, structural damage detection algorithms, and reliability-based optimization concepts. [ABSTRACT FROM AUTHOR]

This paper deals with aerodynamic shape optimization using a high-fidelity solver. Because of the computational cost needed to solve the Reynolds-averaged Navier-Stokes equations, the performance of the shape must be improved using very few objective function evaluations, despite the high number of design variables. In our framework, the reference algorithm is a quasi-Newton gradient optimizer. An adjoint method inexpensively computes the sensitivities of the functions, with respect to design variables, to build the gradient of the objective function. As usual, aerodynamic functions show numerous local optima when the shape varies, and a more global optimizer is expected to be beneficial. Consequently, a kriging-based optimizer is set up and described. It uses all original sampling refinement process that adds up to three points per iteration by using a balancing between function minimization and error minimization. To efficiently apply this algorithm to high-dimensional problems, the same sampling process is reused to form a cokriging (gradient-enhanced model) based optimizer. A comparative study is then described on two drag-minimization problems depending on 6 and 45 design variables. This study was conducted using an original set of performance criteria, characterizing the strength and weakness of each optimizer in terms of improvement, cost, exploration, and exploitation. [ABSTRACT FROM AUTHOR]

In this paper, a new damage detection technique able to identify the location of a breathing crack in an isotropic rod, relying only on real-time measurements, is proposed. The detection algorithm exploits the phase information associated with the superharmonic components produced, in the Fourier spectrum, by the nonlinear dynamic response of this kind of defect under the influence of an external dynamic excitation. The validity of the proposed algorithm for a weakly nonlinear system is supported by an analytical solution for a cracked beam obtained through the harmonic balance approach. A numerical investigation is conducted by means of a finite element model of an isotropic beam integrating nonlinear contact elements in the damaged area and solved for the steady-state response. Three different postprocessing approaches, incorporating the proposed damage detection algorithm, are formulated and compared to assess the capability of the current methodology. Results from the cracked beam model clearly show the generation of the superharmonics as a result of the nonlinear dynamic behavior of the breathing crack. The phase associated with the superharmonic components is then processed through the detection algorithm and the predicted location is compared with the actual position of the defect to assess the performances of the methodology. [ABSTRACT FROM AUTHOR]

This paper presents the work done in designing a morphing wing concept for a small experimental unmanned aerial vehicle to improve the vehicle's performance over its intended speed range. The wing is designed with a multidisciplinary design optimization tool, in which an aerodynamic shape optimization code coupled with a structural morphing model is used to obtain a set of optimal wing shapes for minimum drag at different flight speeds. The optimization procedure is described as well as the structural model. The aerodynamic shape optimization code, that uses a viscous two-dimensional panel method formulation coupled with a nonlinear lifting-line algorithm and a sequential quadratic programming optimization algorithm, is suitable for preliminary wing design optimization tasks. The morphing concept, based on changes in wing-planform shape and wing-section shape achieved by extending spars and telescopic ribs, is explained in detail. Comparisons between optimized fixed wing performance, optimal morphing wing performance, and the performance of the wing obtained from the coupled aerodynamic-structural solution are presented. Estimates for the performance enhancements achieved by the unmanned aerial vehicles when fitted with this new morphing wing are also presented. Some conclusions on this concept are addressed with comments on the benefits and drawbacks of the morphing mechanism design. [ABSTRACT FROM AUTHOR]

In this paper, we present a technique for generating solution adaptive meshes that uses feature-aligned surfaces embedded in the computational domain. A feature-detection algorithm is first employed to identify features of interest. Surfaces associated with these features are then meshed, and a volume mesh that respects these embedded surface meshes is then generated. This approach is promising because it provides a mechanism for controlling local grid quality as well as automatically aligning cell faces with the feature. For flows that include topologically and/or geometrically complex features, we describe a mesh refinement technique that can be used in tandem with the embedded surface meshes to provide a mechanism for refining throughout the computational domain. We include results from two cases to illustrate how the method works. [ABSTRACT FROM AUTHOR]

Supersonic inlet buzz and, in particular, its onset were studied through the analysis of pressure records. These records are issued from an experimental study that was presented in a previous paper. The onset of buzz is a nonstationary phenomenon, and so the pressure signals could not be analyzed using classical signal-processing tools such as the Fourier transform, which does not take into account the possible evolutions in time. That is why time-frequency methods (spectrogram, wavelet transform, and Wigner-Ville distribution) were used. The evolution in time of the energy levels corresponding to buzz frequencies were studied. This analysis shows the existence of precursor phenomena that can appear several tenths of seconds before the onset of buzz. The detection of these precursors could, with the appropriate activation of a control device, allow the avoidance of buzz. Two change-detection algorithms (cumulative sum and generalized likelihood ratio) were tested on experimental pressure signals and proved their ability to successfully detect these precursors. [ABSTRACT FROM AUTHOR]

This paper presents a comparison between three continuum-based topology optimization methods: the hybrid cellular automaton method, the optimality criteria method, and the method of moving asymptotes. The purpose of the study is to highlight the differences between the three. The optimality criteria method and the method of moving asymptotes are well established in topology optimization. The hybrid cellular automaton method is a recently developed gradient-free technique that combines both local design rules based on the cellular automaton paradigm and the finite element analysis. The closed-loop controllers used in the hybrid cellular automaton method are used to modify the mass distribution in the design domain to find an optimum material layout. The hybrid cellular automaton and optimality criteria methods and the method of moving asymptotes are described and applied in a comparative study to three sample problems. The influence of different algorithm control parameters is shown in this work. The paper demonstrates that, for the sample problems presented, the hybrid cellular automaton method generally required the fewest number of iterations to converge to a solution compared with the optimality criteria method and the method of moving asymptotes. The final topologies generated using the hybrid cellular automaton method typically had the lowest compliance and exhibited the fewest number of intermediate densities at the solution. [ABSTRACT FROM AUTHOR]

This paper proposes a methodology for the analysis and design of systems subject to parametric uncertainty in which design requirements are specified via hard inequality constraints. Hard constraints are those that must be satisfied for all parameter realizations within a given uncertainty model. Uncertainty models given by norm-bounded perturbations from a nominal parameter value (i.e., hyperspheres) and by sets of independently bounded uncertain variables (i.e., hyperrectangles) are the focus of this paper. These models, which are also quite practical, allow for a rigorous mathematical treatment within the proposed framework. Hard-constraint feasibility is determined by sizing the largest uncertainty set for which the design requirements are satisfied. Assessments of robustness are attained by comparing this set with the actual uncertainty model. These assessments do not suffer from the numerical deficiencies of sampling-based methods. Strategies that enable the comparison of the robustness characteristics of competing design alternatives, the approximation of the robust design space, and the systematic search for designs with improved robustness are also proposed. Because the problem formulation is generic and the tools derived only require standard optimization algorithms for their implementation, this methodology is applicable to a broad range of engineering problems. [ABSTRACT FROM AUTHOR]

The objective of this paper is to examine nonlinear normal modes and their bifurcations in cyclic periodic structures. The nonlinear normal modes are computed using a numerical technique that combines shooting and pseudoarclength continuation. Unlike perturbation techniques, the resulting algorithm can investigate strongly nonlinear regimes of motion. This study reveals that modal interactions may occur without necessarily having commensurate natural frequencies in the underlying linear system. In addition, a countable infinity of such modal interactions are shown to exist in the system. [ABSTRACT FROM AUTHOR]

Many industrial applications involve flows periodic in time. Such flows are not simulated with enough efficiency when using classical unsteady techniques, as a transient regime must be bypassed. New techniques, dedicated to time- periodic flows and based on Fourier analysis, have been developed recently. Among these, the time spectral method casts a time-periodic flow computation in several coupled steady computations, corresponding to a uniform sampling of the period. Up until now, the steady states were reached using an explicit pseudotime algorithm. Thus, very small time steps were needed and the convergence rate slowed down when increasing the number of harmonics. In this paper, a block-Jacobi approach is presented to solve the stationary problems with an implicit algorithm. Numerical simulations show, on one hand, the good quality of the results and, on the other hand, the interest of the proposed method to reduce the sensitivity of computations to a large number of harmonics. [ABSTRACT FROM AUTHOR]

In this paper we present the application of a hyper radial basis function network as a topology description function. A hyper radial basis function network is used to parameterize the material distribution (density) for topology optimization. The density of each finite element in the continuum topology optimization domain is governed by a single network of hyper radial function bases. Thus, the topology optimization problem is to determine the parameters governing the hyper radial basis function network to satisfy certain design criteria. Here we present the solution to a minimum compliance topology design. A hyper radial basis function network is used to parameterize the material density during the finite element analysis stage. An efficient optimization algorithm that makes use of perturbation and sequential linear programming is developed to obtain the hyper radial basis function network parameters. Examples are presented to demonstrate the proposed approach and to compare it with the traditional solid isotropic microstructures with penalization topology optimization. Some of the advantages of the proposed approach are that it can yield checkerboard-free, manufacturable topologies using coarse-mesh finite element analysis models as opposed to the traditional approach, which requires fine meshes. This results in a reduction in the solution time for finite element analysis while conserving the ability to yield a smooth topology. [ABSTRACT FROM AUTHOR]

In this paper, the precise time-step integration method by step-response and impulsive-response matrices is further developed by expanding the dimension of the matrices so as to avoid computing the particular solutions separately. Two new precise time-step integration algorithms with excitations described by second-order and first-order differential equations are proposed. The first method is a direct extension of the existing algorithms. However, the extended system matrices are not symmetrical. In the second method, the Duhamel integrals are used as the particular solutions. As a result, the responses can be expressed in terms of the given initial conditions and the step-response matrix, the impulsive-response matrix and a newly derived Duhamel-response matrix. The symmetry property of the system matrices can be used in the computation. However, it will first require a calculation of the Duhamel-response matrix and its derivative. To reduce the computational effort, the relation between the Duhamel response matrix and its derivative is established. A special computational procedure for periodic excitation is also discussed. Numerical examples are given to illustrate the present highly efficient algorithms. [ABSTRACT FROM AUTHOR]

Engineering codes are powerful tools for the conceptual design stage. Use of these codes in early design stages enables higher fidelity computational fluid dynamics calculations or wind-tunnel tests to be performed on more mature configurations. Two widely used engineering tools for conceptual level supersonic/hypersonic aerodynamic prediction are tangent-wedge and tangent-cone methods. Unfortunately, these analysis tools lack the ability to systematically account for effects of real-gas flow across the oblique shock wave. This paper derives an extension to the classical oblique shock wave equations where the effects of real-gas flow changes are modeled using theoretical models borrowed from statistical mechanics. Using an enthalpy balance across the shock wave, the Einstein model for a diatomic gas is analytically integrated to give a relationship of temperature, ratio of specific heats, and velocity on the downstream side of the shock wave. This relationship replaces the energy equation used in the ideal-gas oblique shock analysis. This method is adapted to conical flowfield assuming an initial shock angle, and using the new oblique shock algorithm to compute properties immediately behind the conical shock. The resulting model is compared to equilibrium real-gas calculations and shown to give accurate results well into the hypersonic flow regime, approximately Mach 20. [ABSTRACT FROM AUTHOR]

This paper presents a method for computing the thermoacoustic modes in combustors. In the case of a nonisothermal reacting medium, the wave equation for the pressure fluctuations contains a forcing term related to the unsteady heat release. Depending on the phase relationship between the acoustics and the flame, certain linear modes may become unstable, leading to thermoacoustic instabilities. The relevant Helmholtz equation is derived and two approaches for solving the corresponding nonlinear eigenvalue problem are proposed. The first one is based on an asymptotic expansion of the solution, the baseline being the acoustic modes and frequencies for a steady (or passive) flame and appropriate boundary conditions. This method allows a quick assessment of any acoustic mode stability but is valid only for cases where the coupling between the flame and the acoustic waves is small in amplitude. The second approach is based on an iterative algorithm where a quadratic eigenvalue problem is solved at each subiteration. It is more central processing unit demanding but remains valid even in cases where the response of the flame to acoustic perturbations is large. Frequency-dependent boundary impedances are accounted for in both cases. A parallel implementation of the Arnoldi iterative method is used to solve the large eigenvalue problem that arises from the space discretization of the Helmholtz equation. Several academic and industrial test cases are considered to illustrate the potential of the method. [ABSTRACT FROM AUTHOR]

Analytical target cascading is a hierarchical multilevel multidisciplinary design methodology. In analytical target cascading, top-level design targets (i.e., specifications) are propagated to lower-level design problems in a consistent and efficient manner. In this paper, a modified Lagrangian dual formulation and coordination for analytical target cascading are developed to enhance a formulation and coordination proposed earlier in the literature. The proposed approach guarantees all the properties established earlier and additionally offers new significant advantages. As established previously for the convex case, the proposed analytical target cascading coordination converges to a global optimal solution with corresponding optimal Lagrange multipliers in the dual space. The Lagrange multipliers can be viewed as the weights for deviations in analytical target cascading formulations. Thus the proposed coordination algorithm finds the optimal solution and the optimal weights for the deviation terms simultaneously. The enhancement allows for target cascading between levels, for the use of augmented Lagrangian to improve convergence of the coordination algorithm, and for prevention of unboundedness. A guideline to set the step size for subgradient optimization when solving the Lagrangian dual problem is also proposed. [ABSTRACT FROM AUTHOR]

Direct aeroacoustic computations require nonreflective boundary conditions that allow disturbances to leave the domain freely without anomalous reflections. In the present paper we analyze a series of nonreflective boundary conditions already published in the literature and propose an improved outflow nonreflective boundary condition with reflection characteristic that is reduced greatly. For the solution of the linearized Euler equations, a sixth-order compact finite-difference algorithm is used together with a sixth-order explicit digital filter that suppresses the highfrequency spurious oscillations in the solution. A number of representative test cases are presented. The new outflow boundary condition is recommended for the simulation of sound produced by turbulence. [ABSTRACT FROM AUTHOR]