Generic Modal Design Variables for Efficient Aerodynamic Optimization

Orthogonal modes are an effective method for aerodynamic shape optimization due to their excellent design space compactness; however, all existing methods are generated from a database of representative geometry. Moreover, application to high-fidelity design spaces is not possible because high-frequency shape components are insufficiently bounded, leading to nonsmooth and oscillatory geometries. In this work, a new generic methodology for generating orthogonal shape modes is presented based on a purely geometric derivation, eliminating the need for geometric training data. The new method is a further development of the gradient-limiting method developed previously for constraining the design space in a geometrically meaningful way to reduce the effective degrees of freedom and improve optimization convergence rate and final result. Here, the gradient-limiting methodology is reformulated by transforming the constraints directly onto design variables to produce orthogonal shape modes with equivalent constraints for ensuring smooth and valid iterates. The new generic methodology requires no training data, can be applied to arbitrary topologies using different boundary conditions, and naturally includes translational modes as part of the orthogonal basis. When applied to two standard aerodynamic test cases, the new method has superior performance compared to library-derived modes. Importantly, the optimization convergence rate is independent of the number of design variables, and the optimized objective at high design fidelities is greatly improved by avoiding local minima corresponding to spurious geometries. A nonstandard test case is demonstrated, for which traditional library modes are not useable due to nontrivial topology, and it is shown to benefit from the high-fidelity design space and translational mode made possible with the novel methodology. </jats:p

Optimisation of Multi-Modal Aerodynamic Shape and Topology Problems

Kako i sam naslov kaže, tema ovog završnog rada jesu metode koje se koriste pri određivanju sila u štapovima rešetkastih nosača. Na samom početku krenut ćemo od podjele tehničkih konstrukcija i spomenuti nešto općenito o njima. Definirat ćemo pojmove statičke određenosti i neodređenosti rešetke te pojmove ravninske i prostorne rešetke. Obradit ćemo sveukupno četiri metode, od kojih su dvije analitičke, a dvije grafičke. Svaku od metoda razradit ćemo teorijski, a zatim prikazati princip provođenja kroz odabrani primjer. Problematika određivanja sila u štapovima rešetkastih nosača bit će bazirana isključivo na problemima koji se odnose na statički određene ravninske rešetkaste nosače. Problem određivanja sila u štapovima prostornih rešetkastih nosača neće biti obrađen u ovome radu.As the title itself, the subject of this final work are methods which are used to determine the forces in the rods of truss girders. At the begining the division and general classification of technical constructions will be explained and mentioned. The definitions of static determinateness and indeterminateness of the grid and terms of plane and spacial gird will be defined. Four methods will be analyzed of which two are analytical and the other two are graphical. Each of this methods will be elaborated in theory and afterwards the principle of implementation will be shown by using selected example. The issue of determining forces in the rods of truss girders will be based exclusively upon problems which are referred to statically detirmined planar truss girders. The issue of determining forces in the rods of spacial truss girders will not be adressed in this final work