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Beschreibung:
Metamaterials are artificial composites with micro-structures that are systematically designed such that the macroscopic behavior can accommodate particular functionalities or exhibit extraordinary properties, which are not commonly found in natural materials. Topology and geometry of micro-structures play an important role in characterizing the properties of the metamaterials. Inverse design of metamaterials via topology optimization methods offer new topological features and helps in achieving novel physical mechanism or high-performance functionalities. Inverse design is an iterative process, that involves numerical analysis and requires much computational resources. This dissertation proposes the methodology for designing metamaterials using topology optimization with level set functions and model order reduction methods. Level set method enables design with smooth boundaries, while the computational effort required in solving large linear system of equations is eliminated with reduced basis approximations. An example of the inverse design method from the dissertation is to find a unit cell structure that results in macroscopic properties with intended elastic modulus for instance, with negative Poisson's ratio. The other example is to enhance hydrophone performance in 1-3 piezoelectric composites. Numerical examples demonstrate that the methodology is computationally efficient and robust for designing metamaterials. Taking advantage of inverse design as a powerful tool in designing metamaterials, it is adopted in this dissertation for the waveguides design. The second part of this thesis aims to design phononic crystals that offer robust transport of mechanical waves on the interfaces. The propagating wave modes in plate-like structures are topologically protected edge states and are analogous to quantum valley hall effect and quantum spin hall effect in the electronic systems. The computational inverse design methodology adopted is through topology optimization using genetic algorithm to find optimized ...