No description available.

No description available.

No description available.

Sonic boom annoyance is an important technical showstopper for commercial supersonic aircraft operations. It has been proposed that aircraft can be shaped to alleviate sonic boom. Choosing the right aircraft shape reflecting the design requirements is a fundamental and most important step that is usually over simplified in the conceptual stages of design by resorting to a qualitative selection of a baseline configuration based on historical designs and designers perspective. Final aircraft designs are attempted by minor shape modifications to this baseline configuration. This procedure may not yield large improvements in the objectives, especially when the baseline is chosen without a rigorous analysis procedure. Traditional analyses and implementations tend to have a complex algorithmic flow, tight coupling between tools used and computational limitations. Some of these shortcomings are overcome in this study and a diverse mix of tools is seamlessly integrated to provide a simple, yet powerful and automatic procedure for sonic boom minimization. A shape optimization procedure for supersonic aircraft design using better geometry generation and improved analysis tools has been successfully demonstrated. The geometry engine provides dynamic reconfiguration and efficient manipulation of various components to yield unstructured watertight geometries. The architecture supports an assimilation of different components and allows configuration changes to be made quickly and efficiently because changes are localized to each component. It also enables an automatic way to combine linear and non-linear analyses tools. It has been shown in this study that varying atmospheric conditions could have a huge impact on the sonic boom annoyance metrics and a quick way of obtaining probability estimates of relevant metrics was demonstrated. The well-accepted theoretical sonic boom minimization equations are generalized to a new form and the relevant equations are derived to yield increased flexibility in aircraft design process. Optimum aircraft shapes are obtained in the conceptual design stages weighing in various conflicting objectives. The unique shape optimization procedure in conjunction with parallel genetic algorithms improves the computational time of the analysis and allows quick exploration of the vast design space. The salient features of the final designs are explained. Future research recommendations are made.

Recently, the use of permanent magnets as magnetic field sources in biomedical applications has become widespread. However, usage of permanent magnets in magnetic resonance imaging (MRI) is limited due to their inhomogeneous magnetic field distributions. In this thesis, shape and geometry optimization of a magnet is performed. Moreover, placement of more than one magnet is optimized to obtain desired magnetic field distribution in specific region of space. However, obtained magnetic field distribution can not be used in the conventional MRI image reconstruction techniques. Consequently, an image reconstruction technique for MRI in inhomogeneous magnetic fields is developed. Apart from these, since any reconstruction technique requires signal data, an MRI simulator in inhomogeneous magnetic fields is constructed as a part of this thesis. Obtained results show that the theory developed in this thesis is valid. Consequently, new MRI devices that have permanent magnets as magnetic field sources can be constructed in the future.

No description available.

Strides in modern computational fluid dynamics and leaps in high-power computing have led to unprecedented capabilities for handling large aerodynamic problem. In particular, the emergence of adjoint design methods has been a break-through in the field of aerodynamic shape optimization. It enables expensive, high-dimensional optimization problems to be tackled efficiently using gradient-based methods in CFD; a task that was previously inconceivable. However, adjoint design methods are intended for gradient-based optimization; the curse of dimensionality is still very much alive when it comes to design space exploration, where gradient-free methods cannot be avoided. This research describes a novel approach for reducing dimensionality in large, computationally expensive design problems to a point where gradient-free methods become possible. This is done using an innovative application of Principal Component Analysis (PCA), where the latter is applied to the gradient distribution of the objective function; something that had not been done before. This yields a linear transformation that maps a high-dimensional problem onto an equivalent low-dimensional subspace. None of the original variables are discarded; they are simply linearly combined into a new set of variables that are fewer in number. The method is tested on a range of analytical functions, a two-dimensional staggered airfoil test problem and a three-dimensional Over-Wing Nacelle (OWN) integration problem. In all cases, the method performed as expected and was found to be cost effective, requiring only a relatively small number of samples to achieve large dimensionality reduction.

Baigiamajame darbe atliktas tiltin÷s santvaros, iš metalinių profiliuočių, konstrukcijos formos ir strypų skerspjūvių optimizavimas, esant vienam ir dviems apkrovų variantams. Konstrukcija projektuota atsižvelgiant į STR reikalavimus. Tam buvo spręstas netiesinio programavimo uždavinys. Sudarytos nagrinėjamo modelio pagrindinės priklausomybės taikant pusiausviruosius baigtinius elementus. Jų pagrindu sudaryta konstrukcijos optimizavimo programa MATLAB aplinkoje. Naudojantis ją, nustatyta optimali konstrukcijos struktūra ir optimalūs strypų skerspjūviai, esant minimaliam konstrukcijos tūriui, taikant ir netaikant santvaros aukščio ribojimą. Suformuluotos išvados. Darbą sudaro 6 dalys: įvadas, santvaros skaičiuojamoji schema ir apkrovų deriniai, santvaros įtempių ir deformacijų būvio analizė taikant pusiausviruosius baigtinius elementus, konstrukcijos masės minimizavimo uždavinys,optimizavimo rezultatai, išvados, literatūros sąrašas. Darbo apimtis – 67 p. teksto be priedų, 19 iliustr., 11 lent., 26 bibliografiniai šaltiniai. Atskirai pridedami darbo priedai. / In the work bridge truss made of steel cross sections was optimized. There was both form of truss and cross sections optimized according to one, and two loads combinations. Construction was design by STR (Lithuanian national design codes). For the mathematical nonlinear programing problem was solved. The main equations inequality of structure analyze discrete model was made using finite elements method. Basing on them program for optimization in Matlab language was made. By that program, optimal truss form and cross sections was found by minimizing structure volume. Six projects were found including and not including limitation of truss high. Structure: introduction, truss analytical scheme and load combinations, truss analysis using finite element method, construction mass minimization, optimal structure results, conclusions and suggestions, references. Thesis consist of: 67 p. text without appendixes, 19 pictures, 11 tables, 26 bibliographical entries. Appendixes included.

Gradient-based aerodynamic shape optimization, based on Computational Fluid Dynamics analysis of the flow, is a method that can automatically improve designs of aircraft components. The prospect is to reduce a cost function that reflects aerodynamic performances. When the shape is described by a large number of parameters, the calculation of one gradient of the cost function is only feasible by recourse to techniques that are derived from the theory of optimal control. In order to obtain the best computational efficiency, the so called adjoint method is applied here on the complete mapping, from the parameters of design to the values of the cost function. The mapping considered here includes the Euler equations for compressible flow discretized on unstructured meshes by a median-dual finite-volume scheme, the primal-to-dual mesh transformation, the mesh deformation, and the parameterization. The results of the present research concern the detailed derivations of expressions, equations, and algorithms that are necessary to calculate the gradient of the cost function. The discrete adjoint of the Euler equations and the exact dual-to-primal transformation of the gradient have been implemented for 2D and 3D applications in the code Edge, a program of Computational Fluid Dynamics used by Swedish industries. Moreover, techniques are proposed here in the aim to further reduce the computational cost of aerodynamic shape optimization. For instance, an interpolation scheme is derived based on Radial Basis Functions that can execute the deformation of unstructured meshes faster than methods based on an elliptic equation. In order to improve the accuracy of the shape, obtained by numerical optimization, a moving mesh adaptation scheme is realized based on a variable diffusivity equation of Winslow type. This adaptation has been successfully applied on a simple case of shape optimization involving a supersonic flow. An interpolation technique has been derived based on a mollifier in order to improve the convergence of the coupled mesh-flow equations entering the adaptive scheme. The method of adjoint derived here has also been applied successfully when coupling the Euler equations with the boundary-layer and parabolized stability equations, with the aim to delay the laminar-to-turbulent transition of the flow. The delay of transition is an efficient way to reduce the drag due to viscosity at high Reynolds numbers.

Advances in numerical optimization have raised the possibility that efficient and novel aircraft configurations may be ``discovered'' by an algorithm. To begin exploring this possibility, a fast and robust set of tools for aerodynamic shape optimization is developed. Parameterization and mesh-movement are integrated to accommodate large changes in the geometry. This integrated approach uses a coarse B-spline control grid to represent the geometry and move the computational mesh; consequently, the mesh-movement algorithm is two to three orders faster than a node-based linear elasticity approach, without compromising mesh quality. Aerodynamic analysis is performed using a flow solver for the Euler equations. The governing equations are discretized using summation-by-parts finite-difference operators and simultaneous approximation terms, which permit nonsmooth mesh continuity at block interfaces. The discretization results in a set of nonlinear algebraic equations, which are solved using an efficient parallel Newton-Krylov-Schur strategy. A gradient-based optimization algorithm is adopted. The gradient is evaluated using adjoint variables for the flow and mesh equations in a sequential approach. The flow adjoint equations are solved using a novel variant of the Krylov solver GCROT. This variant of GCROT is flexible to take advantage of non-stationary preconditioners and is shown to outperform restarted flexible GMRES. The aerodynamic optimizer is applied to several studies of induced-drag minimization. An elliptical lift distribution is recovered by varying spanwise twist, thereby validating the algorithm. Planform optimization based on the Euler equations produces a nonelliptical lift distribution, in contrast with the predictions of lifting-line theory. A study of spanwise vertical shape optimization confirms that a winglet-up configuration is more efficient than a winglet-down configuration. A split-tip geometry is used to explore nonlinear wake-wing interactions: the optimized split-tip demonstrates a significant reduction in induced drag relative to a single-tip wing. Finally, the optimal spanwise loading for a box-wing configuration is investigated.