Design Methodologies of Aeronautical Structures with Acoustic Constraints

The aim of this thesis is to present a finite element methodology, based upon a three-dimensional extensions of the classical Hermite interpolation and of the Coons Patch, for the evaluation of the natural modes of vibration of the air inside cavities (interior acoustics) and of elastic structures (structural dynamics). This methodology is thought for acoustic applications within Multidisciplinary Desing and Optimization, where computational effectiveness is a key attribute, especially during iterative optimization. The distinguishing feature of the proposed technique is its high efficiency, with the possibility to capture relatively high spatial frequency modes (essential in acoustics) even using a limited number of degrees of freedom. Also, the element is quite flexible and may be used for modeling any three-dimensional geometry. For instance, thin-wall structures like shells and plates are treated with three-dimensional brick elements with a single element along the thickness. An additional advantage is related to the possibility of applying a quasi-static reduction, which allows one to eliminate those degrees of freedom associated with the derivatives while maintaining a high level of accuracy, so that to further improve the effectiveness of the element. The classical one-dimensional Hermite interpolation is an interpolating technique of order three that uses the function and its derivative at the end points of the element. The classical Hermite technique for one-dimensional domains can be extended to higher orders, by including higher derivatives as nodal unknowns, thereby increasing the class of the element. Then, the three-dimensional extension is obtained combining the Hermite polynomials in each direction. For example, in the three-dimensional third-order interpolation, the unknowns are the nodal values of the function, of its three partial derivatives, of its three mixed second derivatives, and of its third mixed derivative. Similarly to the one-dimensional approach, higher orders are then obtained by including higher derivatives at nodes. The Hermite element, even that of order three, is rarely used because of problems that arise whenever the domain is not topologically hexahedral, that is when the coordinate lines (and so the base vectors) of two adjacent blocks present a discontinuity. Specifically, as far as the first-order derivatives are concerned, the problem has been removed by assuming as unknowns the Cartesian coordinates of the gradient, since they are continuous across block boundaries. The problem remains for the higher-order derivatives: in order to express them in terms of Cartesian components, their set should be complete (in particular, we have only the mixed second derivatives and, hence, incomplete information on the Hessian matrix). The remedies to this issue are key features of the present thesis. In particular, two solutions have been proposed in this thesis: (1) the high-order derivatives relative to different blocks are treated as independent unknowns at the block boundaries; (2) a new 3-D high-order internal-nodes family of elements based upon the Coons Patch is used: these elements are defined so as to have only the function and the three derivatives as nodal unknowns (thereby, the higher the order of the element the higher the quantity of internal nodes needed for the interpolation). To be specific, the Coons Patch pertain the interpolation over a quadrilateral surface. Given the four edge lines, the Coons Patch is obtained as the sum of the two linear interpolations between opposite boundary lines, minus a bilinear interpolation through the four corner points. From this technique stems the idea of a new family of elements, which edges are generated using the Hermite interpolation. The objective is to extend the use of high-order elements based on a Hermite approach also to generically complicated geometries, so as to take advantage of their effectiveness. These elements will be referred to as Hybrid elements. The validation is based upon the evaluation of the natural eigenvalues (or natural frequencies) and modes of the air vibrating inside hexahedral cavities as well as of those of elastic thin plates (for each of this case exact or accurate solutions are available). Applications to quite complicated structures, such as curved domains (cylindrical cavities) or very simplified wing-boxes are presented. The results are compared with those obtained using commercial softwares (such as Ansys). Comparisons with the literature are also included

A Novel Highly Accurate Finite-Element Family

A novel Nth order finite element for interior acoustics and structural dynamics is presented, with N arbitrarily large. The element is based upon a three-dimensional extension of the Coons patch technique, which combines high-order Lagrange and Hermite interpolation schemes. Numerical applications are presented, which include the evaluation of the natural frequencies and modes of vibration of (1) air inside a cavity (interior acoustics) and (2) finite-thickness beams and plates (structural dynamics). The numerical results presented are assessed through a comparison with analytical and numerical results. They show that the proposed methodology is highly accurate. The main advantages however are (1) its flexibility in obtaining different level of accuracy (p-convergence) simply by increasing the number of nodes, as one would do for h-convergence, (2) the applicability to arbitrarily complex configurations, and (3) the ability to treat beam- and shell-like structures as three-dimensional small-thickness elements

A diastrophic dysplasia sulfate transporter (SLC26A2) mutant mouse: morphological and biochemical characterization of the resulting chondrodysplasia phenotype

Mutations in the diastrophic dysplasia sulfate transporter (DTDST or SLC26A2) cause a family of recessively inherited chondrodysplasias including, in order of decreasing severity, achondrogenesis 1B, atelosteogenesis 2, diastrophic dysplasia (DTD) and recessive multiple epiphyseal dysplasia. The gene encodes a widely distributed sulfate/chloride antiporter of the cell membrane whose function is crucial for the uptake of inorganic sulfate, which is needed for proteoglycan sulfation. To provide new insights in the pathogenetic mechanisms leading to skeletal and connective tissue dysplasia and to obtain an in vivo model for therapeutic approaches to DTD, we generated a Dtdst knock-in mouse with a partial loss of function of the sulfate transporter. In addition, the intronic neomycine cassette in the mutant allele contributed to the hypomorphic phenotype by inducing abnormal splicing. Homozygous mutant mice were characterized by growth retardation, skeletal dysplasia and joint contractures, thereby recapitulating essential aspects of the DTD phenotype in man. The skeletal phenotype included reduced toluidine blue staining of cartilage, chondrocytes of irregular size, delay in the formation of the secondary ossification center and osteoporosis of long bones. Impaired sulfate uptake was demonstrated in chondrocytes, osteoblasts and fibroblasts. In spite of the generalized nature of the sulfate uptake defect, significant proteoglycan undersulfation was detected only in cartilage. Chondrocyte proliferation and apoptosis studies suggested that reduced proliferation and/or lack of terminal chondrocyte differentiation might contribute to reduced bone growth. The similarity with human DTD makes this mouse strain a useful model to explore pathogenetic and therapeutic aspects of DTDST-related disorder

A Hermite High-Order Finite Element in Structural Dynamics

The paper presents a review of a recently developedfinite-element technique based upon a three-dimensional Hermite interpolation for the evaluation of the natural modes of vibration of elastic structures, with spacial frequencies as high as possible, so as to make the technique useful for instance for structural acoustics applications. The finite-element unknowns are the nodal values of the unknown function (displacement), of its three first-order partial derivatives, of its three second-order mixed second derivatives, and of its third-order mixed derivative. The test-case used for the validation is the eigenproblem of the Laplacian, for a cubic domain, for which an exact solution is available. Applications include the evaluation of the natural frequencies of elastic plates, which are treated as three--dimensional objects, with only one element along the normal. The results obtained for simple geometries are highly encouraging, as they show that the method has an excellent rate of convergence, higher than that in standard finite-element methods. Thus, the extension to complex geometriesappears warranted. Unfortunately, existing geometry processor are not structured so as to provide the kind of data necessary for the type of element addressed here. Thus, a novel user-friendly formulation to generate complex three-dimensional geometries is presented

Coons Patch, Hermite Interpolation, and High-Order Finite Elements in Structural Dynamics

The paper presents a novel finite element for the evaluation of the natural modes of vibrations of complex structures. The element is based upon a three-dimensional extension of the Coons patch technique, combined with the fact that the generating lines are obtained using the Hermite interpolation technique; the resulting finite-element unknowns are the nodal values of: (i) the unknownfunction (the displacement vector in our case), and (ii) the Cartesian components of its gradient. In addition, the paper presents a review of recent work by the authors on another closely related element, which is an extension to complex configurations of the Hermite element, which in turn is based upon the three-dimensional extension of the Hermite interpolation; in this case, the finite-elementunknowns are the nodal values of: (i) the unknown function, (ii) the Cartesian components of its gradient, (iii) its three second?order mixed derivatives, and (iv) its third-order mixed derivative. The objective of these methods is the user?friendly evaluation of natural modes of vibration of elastic structures, as used in multi-disciplinary optimization; accordingly, in order to validate and assess the two methods, numerical results for simple test cases are included; we concentrate on the natural frequencies of elastic plates (which are treated as three-dimensional structures, with only one elementalong the normal). In addition, in view of the fact that the ultimate objective is the applicability of the techniques for arbitrary geometries, results for a relatively complex structure (that is, a simplifiedmodel of a wing box) are included

A Hermite High-Order Finite Element for Aeroacoustic Analysis

In this paper we assess a finite--element technique based upon a three-dimensional Hermite interpolation for the evaluation of natural modes of vibration of the air inside a cavity (interior acoustics) and/or of elastic structures (structural dynamics), for frequency as high as possible, so as to make the technique useful for aeroacoustics applications, such as coupling of vibrating structures and air. The unknowns are the nodal values of the function (velocity potential for acoustics and displacement forstructural dynamics), of its three partial derivatives, of its three mixed second derivatives, and of its third mixed derivative. Applications include the evaluation of the natural frequencies of the air inside simple geometries, as well as shell-like elastic structures, which are treated as three--dimensional objects, with only one element along the normal (comparisons with commercial-code results are included). The generalization to complex geometries is outlined, with simple example provided. Thepotentiality of Guyan reduction is also assessed

Hermite High--Order Finite Elements for Aeroacoustic Analysis

The paper is motivated by the analysis of fluid-structure interaction inside an aircraft cabin. The analysis of this phenomenon requires the accurate evaluation of the natural modes of vibration of both: (1) the air inside the cavity (interior acoustics), and (2) the structure surrounding the cavity (structural dynamics). Finite-element methods for these types of problems typically fail for thosemodes that have moderate to high spatial frequencies, which however are quite relevant in structuralacoustics. The paper presents high-order finite elements for the evaluation of the natural modes ofvibrations of the air and surrounding structure. The elements are based upon a three-dimensional extensionof the Hermite interpolation technique. Specifically, both the third- and fifth-order Hermiteelements are presented. Numerical results for both schemes are included, with emphasis on high-spatial-frequency modes, so as to assess the techniques' usefulness for structural-acoustics applications.In addition, in view of the fact that the ultimate objective is the applicability of the techniquesfor arbitrary geometries, an analysis of the problems encountered in the use of Hermite elements forcomplex geometries is presented, and remedies for eliminating the problems are discussed

Cubesat Mission with technological demonstrator payload for high data-rate downlink and health monitoring

The HyperCube payload will be composed by two different technological experiment, an high data-rate C band antenna, and a demonstrator for a remote structural health monitoring system. The first one has been thought with the aim to give Cubesats the capability to download an high quantity of data; it could be useful either if the data requiring the high data-rate downlink is on-board generated or simply retransmitted. The applications for which this payload could be used are several; an example for the first category of application is to download the data generated by another payload; the high data-rate capability could be necessary due to the narrow visibility window with the ground station, affected also by the absence of an active AOCS subsystem, which makes difficult the alignment of the on board antenna with the ground one. But the C band antenna could also be used to act as a “space–repeater”, downloading up–linked information. The second payload is related to the need to take under strictly control the health of the structures (not only the ones strictly belonging to primary structures, but also that of any subsystem component). In order to do that, smart materials are integrated into the structural component that need to be monitored; in particular, piezoelectric patches are used as sensors. As the structure is stressed, and the integrated piezoelectric sensors are subjected to mechanical deformation, they produce an electric signal; acquiring and properly studying the produced signal it is possible to monitor the mechanical condition of the structures. The health monitoring system is completed by a MicroController Unit which acquires, samples and stores the signal produced, and a transmitting system, which could be the C band antenna, or the TT&C antenna which each satellite needs