Boron nitride (BN) nanomaterials such as boron nitride graphenes, boron nitride nanotubes, and boron nitride nanocones are attracting attention among the most promising nanomaterials due to their physical, chemical, and electronic properties when compared to other nanomaterials. BN nanomaterials suggest many exciting potential applications in various fields. Joining between BN nanostructures gives new enhanced structures with outstanding properties and potential applications for design of probes for scanning tunnelling microscopy and other nanoscale devices. This paper uses calculus of variations to model the joining between BN graphene with other BN nanostructures: BNNTs and BNNCs. Furthermore, during the joining between these BN nanostructures, this research examines two models which are depending on the curvature of the join profile. For the first case, Model I refers to when the join profile only includes positive curvature where for the second case, Model II is considered for both positive and negative curvatures. Thus, the purpose of this research is to formulate the basic underlying structure to present simple models based on joining BN graphene to other BN nanostructures.

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氮化硼石墨烯与其他BN纳米结构连接的数学模型

氮化硼（BN）纳米材料，例如氮化硼石墨烯，氮化硼纳米管和氮化硼纳米锥，由于与其他纳米材料相比的物理，化学和电子特性，因此在最有前途的纳米材料中引起了人们的注意。BN纳米材料建议在各个领域有许多令人兴奋的潜在应用。BN纳米结构之间的连接提供了具有出色性能的新型增强结构，并在设计用于扫描隧道显微镜和其他纳米级设备的探针方面具有潜在的应用前景。本文使用变化演算来模拟BN石墨烯与其他BN纳米结构（BNNT和BNNC）之间的连接。此外，在这些BN纳米结构之间的连接过程中，这项研究检查了两种取决于连接轮廓曲率的模型。对于第一种情况，模型I指的是连接轮廓仅包含正曲率，而对于第二种情况，模型II是指正曲率和负曲率。因此，本研究的目的是制定基本的基础结构，以提出基于将BN石墨烯与其他BN纳米结构连接的简单模型。