Luciano Demasi

Dynamic Aeroelasticity of Structurally Nonlinear Configurations Using Linear Modally Reduced Aerodynamic Generalized Forces

Steady state and time domain methods for integrating commonly used frequency-domain unsteady aerodynamic modeling based on a modal approach with full order flnite element models for structures with geometric nonlinearities are introduced. The methods are aimed at airplane conflgurations where geometric stifiness efiects are important but where deformations are moderate, ∞ow is attached, and linear unsteady aerodynamic modeling is adequate, such as joined-wing and strut-braced wings at small to moderate angles of attack or low aspect ratio wing. Results obtained using full order nonlinear structural modeling and full order aerodynamic modeling (including aerodynamic in∞uence coe‐cients for all aerodynamic panels) are compared to results obtained using full order structural modeling with generalized aerodynamic matrices obtained using a modal approach.

Two benchmarks to assess two-dimensional theories of sandwich, composite plates

Two-dimensional theories and e nite elements are assessed to analyze displacement and stress e elds in sandwich, composites plates. Two benchmarks are used to conduct the assessment. The e rst benchmark is a sandwich plate loaded by harmonic distribution of transverse pressure for which a three-dimensional closed-form solution exists in the literature. The second benchmark is a rectangular sandwich plate loaded by a transverse pressure located at the center. More than 20 plate theories and e nite elements were implemented in a unie ed formulation recently proposed by the authors. Classical theories based on displacement assumptions are compared to advanced mixed modelsformulatedonthebasisofReissner’ smixedvariationaltheorem.Bothequivalentsingle-layermodelsaswell as layerwise models are considered. Analytical closed-form solutions and e nite elements are given. The considered benchmarks highlight both the performance and limitations of the considered two-dimensional theories. The convenience of layerwisedescription and advanced mixed theorieshas been demonstrated. Thesecond benchmark especially proved the need for layerwise models to capture the local effects.

2D, Quasi 3D and 3D Exact Solutions for Bending of Thick and Thin Sandwich Plates

A previous authors work related to the exact solution of a single layer isotropic plate is extended to the case of multilayered plate structures composed of isotropic layers. The method solves a first order linear system of differential equations in the unknown amplitudes of the displacements and stresses. An eigenvalue problem, in which analytical expressions for the basis of eigenvectors and generalized eigenvectors are available, is then formulated. This makes the coding of exact solution of multilayered structures very simple and effective compared with other exact methods present in the literature. The paper is mainly concerned about the analysis of sandwich structures made of isotropic layers. Challenging cases of thick and moderately thick plates (a/h = 1, 4, 10) and thin plates (a/h = 100) are analyzed in detail and the displacements and stresses are found and plotted through the thickness of the plate. An extensive study of the ratio between the elastic modulus of the skins and the elastic modulus of the core, as well as the change in the displacements and stresses with that parameter, is conducted. The exact three-dimensional results are also validated with quasi-3D results obtained by adopting a mixed assiomatic theory of order 9 presented here for the first time. Twenty three two-dimensional theories are assessed, five of which are presented here for the first time. The use of Murakamis zig—zag function and the consequent improvement of the ESL theories is also analyzed and discussed. All the results of this work are an useful tool to test and compare approximated methods, such as Finite Element Method.

Exploratory Studies of Joined Wing Aeroelasticity

Interest in Joined Wing configurations has been growing recently especially with the appearance of new possible applications such as the sensorcraft and advanced aerial tanker. The aeroelastic behavior of Joined Wings is the focus of this work. Particular attention is given to the eect of structural nonlinearity on the divergence and linearized flutter predictions for such configurations. In a typical flight condition, significant compressive loads are present in the rear wing (which supports the main wing) and its eective stiness (linear + geometric) varies. As a consequence, the aeroelastic behavior of the wing system changes significantly and a nonlinear structural analysis is required. The paper reports the results of a study based on linear aerodynamic theory and a nonlinear Updated Lagrangian Formulation for the structural part. The goal is to demonstrate an approach to the evaluation of aeroelastic characteristics in the early design stages.

Invariant Formulation for the Minimum Induced Drag Conditions of Nonplanar Wing Systems

Under the hypotheses of linear potential flow and rigid wake aligned with the freestream, a configuration-invariant analytical formulation for the induced drag minimization of single-wing nonplanar systems is presented. Following a variational approach, the resulting Euler–Lagrange integral equation in the unknown circulation distribution is obtained. The kernel presents a singularity of the first order, and an efficient computational method, ideal for the early conceptual phases of the design, is proposed. Munk’s theorem on the normalwash and its relation with the geometry of the wing under optimal conditions is naturally obtained with the present method. Moreover, Munk’s constant of proportionality, not provided in his original work, is demonstrated to be the ratio between the freestream velocity and the optimal aerodynamic efficiency. The augmented Munk’s minimum induced drag theorem is then formulated. Additional induced drag theorems are demonstrated following the derivations of this invariant proced...

Investigation on conditions of minimum induced drag of closed wing systems and C-wings

A theoretical method for predicting minimum induced-drag conditions in a nonplanar lifting systems is presented in this paper. The procedure is based on lifting line theory and the small perturbation acceleration potential. Under the hypotheses of linearity and rigid wake aligned with the freestream, optimality conditions are formulated using the Euler-Lagrange integral equation with constraints on fixed total lifting force and wing span. Particular attention is paid to analysis and numerical treatment of the Hadamard finite-part integrals involved in the solution process. The minimum induced-drag problem is then formulated and solved numerically and analytically. In the case of annular wings, closed-form expressions for the optimal circulation distribution, the normalwash, the induced-drag coefficient, and the efficiency are presented. Optimal annular wings and C-wings are extensively analyzed

Vibration Analysis of Anisotropic Simply Supported Plates by Using Variable Kinematic and Rayleigh-Ritz Method

This work deals with accurate free-vibration analysis of anisotropic, simply supported plates of square planform. Refined plate theories, which include layer-wise, equivalent single layer and zig-zag models, with increasing number of displacement variables are take into account. Linear up to fourth N-order expansion, in the thickness layer-plate direction have been implemented for the introduced displacement field. Rayleigh-Ritz method based on principle of virtual displacement is derived in the framework of Carreras unified formulation. Regular symmetric angle-ply and cross-ply laminates are addressed. Convergence studies are made in order to demonstrate that accurate results are obtained by using a set of trigonometric functions. The effects of the various parameters (material, number of layers, and fiber orientation) upon the frequencies and mode shapes are discussed. Numerical results are compared with available results in literature.

Improved Response of Unsymmetrically Laminated Sandwich Plates by Using Zig-zag Functions

This article shows the advantages of using the zig-zag function (-1) kξk (ZZF) in the bending analysis of unsymmetrically laminated sandwich flat panels with a soft core. Higher order theories are developed by adding ZZF to displacement fields of known theories. From linear to seventh order cases in displacement are considered. The main advantage of ZZF lies in the fact that it introduces a discontinuity in the first derivative (so called zig-zag effect) of the displacement distribution corresponding to the core-face interfaces. Results including and discarding ZZF are compared in the bending response of sandwich plates loaded by an harmonic distribution of transverse pressure at the top surface. Different values of face-to-core stiffness ratio (FCSR) as well as length-to-thickness ratio (LTR) have been analyzed. It is concluded that: (1) ZZF is highly recommended in the bending analysis of unsymmetrically laminated sandwich plates; (2) the use of ZZF makes the error almost independent of the FCSR parameter; (3) ZZF is easy to implement and its use should be considered with respect to other theories.

Minimum Induced Drag Theorems for Joined Wings, Closed Systems, and Generic Biwings: Theory

An analytical formulation for the induced drag minimization of closed wing systems is presented. The method is based on a variational approach, which leads to the Euler–Lagrange integral equation in the unknown circulation distribution. It is shown for the first time that the augmented Munk’s minimum induced drag theorem, formulated in the past for open single-wing systems, is also applicable to closed systems, joined wings and generic biwings. The quasi-closed C-wing minimum induced drag conjecture discussed in the literature is addressed. Using the variational procedure presented in this work, it is also shown that in a general biwing, under optimal conditions, the aerodynamic efficiency of each wing is equal to the aerodynamic efficiency of the entire wing system (biwing’s minimum induced drag theorem). This theorem holds even if the two wings are not identical and present different shapes and wingspans; an interesting direct consequence of the theorem is discussed. It is then verified (but yet not demonstrated) that in a closed path, the minimum induced drag of the biwing is identical to the optimal induced drag of the corresponding closed system (closed system’s biwing limit theorem). Finally, the nonuniqueness of the optimal circulation for a closed wing system is rigorously addressed, and direct implications in the design of joined wings are discussed.

Assess the Accuracy of the Variational Asymptotic Plate and Shell Analysis (VAPAS) Using the Generalized Unifled Formulation (GUF)

The accuracy of the Variational Asymptotic Plate and Shell Analysis (VAPAS) is assessed against several higher order, zig zag, and layerwise theories generated by using the invariant axiomatic framework denoted as Generalized Unified Formulation (GUF). These theories are also compared against the elasticity solution developed for the case of a sandwich structure with high Face to Core Stiffness Ratio. GUF allows to use an infinite number of axiomatic theories (Equivalent Single Layer theories with or without zig-zag effects and Layerwise theories as well) with any combination of orders of the displacements and it is an ideal tool to precisely assess the range of applicability of the Variational Asymptotic Plate and Shell Analysis or other theories in general. In fact, all the axiomatic theories generated by GUF are obtained from the kernels or fundamental nuclei of the Generalized Unified Formulation and changing the order of the variables is “naturally” and systematically done with GUF. It is demonstrated that VAPAS achieves accuracy comparable to a fourth (or higher) order zig-zag theory or lower-order layerwise theories with the least number of Degrees of Freedom. The differences between the axiomatic zig-zag models and VAPAS are also assessed. Range of applicability of VAPAS will be discussed in detail and guidelines for new developments based on GUF and VAPAS are provided.