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<p>A topologically interlocked material (TIM) system belongs to a class of architectured materials and is known to perform outstanding mechanical properties such as stiffness, strength, and toughness. TIM systems are assemblies of polyhedral or building blocks, where individual elements constrain each other on inclined sides of building blocks. This thesis first focuses on developing novel designs of TIM plates composed of building blocks that interact with each other. The resulting TIM systems can be characterized concerning their periodicity and symmetry. Consequently, this study investigates how the proposed geometric features enhance mechanical properties and contribute to emerging properties. Specifically, four research questions provide a clear direction and framework for the investigation. For efficient analysis, finite element calculations are employed, and physical validation methods are used to verify them.</p> <p>The first research question is how the mechanical properties of aperiodic systems differ from those of periodic systems. Aperiodic systems offer diverse possibilities in terms of forms and arrangements. In this thesis, aperiodicity is further divided into two aspects: disrupting symmetry and preserving symmetry. In the approach that disrupts symmetry, the shapes of the tiles are randomly generated. An aperiodic system does not necessarily possess inherently superior or inferior mechanical properties compared to a periodic system. However, the flexibility of aperiodic systems allows for numerous forms and arrangements, presenting promising alternatives to identify factors or patterns that contribute to improved mechanical performance. To simplify these complex configurations, network theory is employed.</p> <p>Each building and its contact interfaces are represented as nodes and links. By utilizing network theory, a focused analysis of the links is conducted, enabling a comprehensive understanding of force propagation across TIM systems. The quantification of the significance of each link assists in reinforcing critical links while potentially sacrificing less critical ones.</p> <p>This approach not only simplifies the research problem but also facilitates the creation of customized design systems by adjusting the links.</p> <p>The other approach to achieve aperiodicity while preserving symmetry utilizes quasicrystal structures. This is based on another research question: What are the benefits of creating TIM systems with quasi-crystal tilting? Quasi-crystals possess a unique characteristic of maintaining 5-fold rotational symmetry while breaking away from periodic patterns observed in traditional systems. The arrangement of elements in quasi-crystal structures extends in a non-repetitive pattern from the center outward, offering a multitude of potential possibilities for TIM systems. By incorporating quasi-crystal tiling, TIM systems are expected to open up exceptional mechanical properties and unconventional behaviors.</p> <p>The third research question investigates whether the influence on mechanical performance varies based on the symmetry level of TIM systems. Despite using identical unit blocks, the arrangement of an assembly can lead to different levels of symmetry. Furthermore, it is possible to modify the symmetry of the unit block, thereby impacting the overall symmetry of the assembly. To achieve this, the symmetry of a unit block is adjusted by modifying the angles of side faces, transitioning from larger angles to smaller angles or vice versa. This modification introduces directionality (rotational symmetry) to the unit block and creates a greater variety of symmetry levels depending on the arrangements of these blocks. By implementing a broader range of symmetry levels that conventional TIM systems cannot achieve, this research aims to investigate the relationship between these symmetries and mechanical properties.</p> <p>The fourth research question is about what emerging properties could be present in TIM systems. While the primary application of TIMs is to enhance the damage tolerance of brittle materials against an external load, there have been ongoing attempts to research emerging properties like negative stiffness, sound absorption, and chirality. Chirality, in particular, serves as a valuable geometric property to describe a circulation of force propagation. Generally, the ability of TIM systems to carry transverse loads is explained through equivalent Mises truss along x− and y − axis. However, chirality enables the representation of not only axial force paths but also circulations of forces within TIM systems. In addition, a rich variety of geometric patches are observed in quasi-crystal structures. In crystal structures, a limited number of patches are repetitively arranged, resulting in a restricted range of properties. However, quasi-crystals like Penrose are non-periodic and possess a greater capacity to generate diverse patches, allowing for the selection of various mechanical properties.</p>

The aim of this study is to investigate means of efficiently assessing the effects of distributed structural modification on the dynamic properties of a complex structure. The helicopter structure is normally designed to avoid resonance at the main rotor rotational frequency. However, very often military helicopters have to be modified (such as to carry a different weapon system or an additional fuel tank) to fulfill operational requirements. Any modification to a helicopter structure has the potential of changing its resonance frequencies and mode shapes. The dynamic properties of the modified structure can be determined by experimental testing or numerical simulation, both of which are complex, expensive and time-consuming. Assuming that the original dynamic characteristics are already established and that the modification is a relatively simple attachment such as beam or plate modification, the modified dynamic properties may be determined numerically without solving the equations of motion of the full-modified structure. The frequency response functions (FRFs) of the modified structure can be computed by coupling the original FRFs and a delta dynamic stiffness matrix for the modification introduced. The validity of this approach is investigated by applying it to several cases, 1) 1D structure with structural modification but no change in the number of degree of freedom (DOFs). A simply supported beam with double thickness in the middle section is treated as an example for this case; 2) 1D structure with additional DOFs. A cantilever beam to which a smaller beam is attached is treated as an example for this case, 3) 2D structure with a reduction in DOFs. A four-edge-clamped plate with a cut-out in the centre is treated as an example for this case; and 4) 3D structure with additional DOFs. A box frame with a plate attached to it as structural modification with additional DOFs and combination of different structures. The original FRFs were obtained numerically and experimentally except for the first case. The delta dynamic stiffness matrix was determined numerically by modelling the part of the modified structure including the modifying structure and part of the original structure at the same location. The FRFs of the modified structure were then computed. Good agreement is obtained by comparing the results to the FRFs of the modified structure determined experimentally as well as by numerical modelling of the complete modified structure.