Topological interlocking assemblies (TIA) are arrangements of blocks such that rigid-body motions of the blocks are fully constrained by their neighbours and a fixed frame. In this work, we investigate tubular interlocking structures derived from the sine curve and parametrised by several geometric design parameters. We analyse the behaviour of these parametrised tubular interlockings under various boundary conditions and examine how our proposed parameters influence the mechanical response. For this purpose, we first develop a simplified multibody dynamics formulation that enables an efficient exploration of how the design parameters of the block influence the load transfer within the assembly. To further corroborate these results, we perform several finite element simulations, which give insights into the mechanical behaviour of our proposed TIA. Our results show that the block geometry plays a decisive role in the mechanical performance of the corresponding TIA. We additionally discuss the problem of exploding TIAs and demonstrate that the TIA resulting from our Sine Block does not exhibit this behaviour. Lastly, we provide evidence that non-exploding TIAs possess better mechanical properties than exploding ones.

翻译：拓扑互锁装配（TIA）是由若干块体组成的结构，其中各块体的刚体运动完全受其相邻块体及固定框架约束。本研究探讨了基于正弦曲线并参数化于多个几何设计参数的管状互锁结构。我们分析了这些参数化管状互锁体在不同边界条件下的行为，并考察了所提参数对力学响应的影响机制。为此，我们首先建立了一种简化的多体动力学公式，以高效探索块体设计参数对装配体内载荷传递的影响。为进一步验证这些结果，我们开展了多项有限元模拟，深入解析所提出的TIA的力学行为。研究结果表明，块体几何构型对相应TIA的力学性能具有决定性影响。此外，我们探讨了TIA的爆裂问题，并证实基于正弦块设计的TIA不会呈现此类现象。最后，我们提供了非爆裂型TIA比爆裂型TIA具有更优力学性能的证据。