Since the first report of graphdiyne nanomembranes synthesis in 2010, different novel graphdiyne nanosheets have been fabricated. In a latest experimental advance, triphenylene-graphdiyne (TpG), a novel two-dimensional (2D) material was fabricated using the liquid/liquid interfacial method. In this study, we employed extensive first-principles simulations to investigate the mechanical/failure, thermal stability, electronic and optical properties of single-layer TpG. In addition, we predicted and explored the properties of nitrogenated-, phosphorated-and arsenicated-TpG monolayers. Our results reveal that TpG, N-TpG, P-TpG and As-TpG nanosheets can exhibit outstanding thermal stability. These nanomembranes moreover were found to yield linear elasticity with considerable tensile strengths. Notably, it was predicted that monolayer TpG, As-TpG, P-TpG and N-TpG show semiconducting electronic characters with direct band-gaps of 1.94 eV, 0.88 eV, 1.54 eV and 1.91 eV, respectively, along with highly attractive optical properties. We particularly analyzed the application prospect of these novel 2D materials as anodes for Li-ion batteries. Remarkably, P-TpG and N-TpG nanosheets were predicted to yield ultrahigh charge capacities of 1979 mAh/g and 2664 mAh/g, respectively, for Li-ions storage. The acquired results by this work suggest TpG based nanomembranes as highly promising candidates for the design of flexible nanoelectronics and energy storage devices.Corresponding authors: *bohayra.mortazavi@gmail.com, # timon.rabczuk@uni-weimar.de; Ι These authors contributed equally. nanoelectronics and optoelectronics, presenting a band-gap is a critical requirement. Among the aforementioned experimentally synthesized monoelemental 2D materials, only the phosphorene is well-understood to exhibit semiconducting electronic character and the other members show either metallic or zero band-gap electronic nature. Nevertheless, other families of 2D materials with inherent semiconducting electronic characters have garnered remarkable attentions. In this regard, 2D materials families of transition metal dichalcogenides, like MoS 2 and WS 2 [11,12], and carbon-nitride nanosheets, like graphitic carbon nitride g-C 3 N 4 [13,14], nitrogenated holey graphene, C 2 N [15] and 2D polyaniline, C 3 N [16] have been experimentally realized and extensively studied in the literature. A couple of decades before the rise of graphene [2], graphdiyne family, which includes full carbon 2D allotropes, with hybrid sp and sp 2 covalently bonded atoms arranged in various crystal lattices were theoretically predicted [17]. First-principles calculations notably confirm semiconducting electronic character for different graphdiyne family members [18][19][20][21][22][23][24][25], desirable for post-silicon nanoelectronics. Besides that, graphdiyne family members were also theoretically proven to exhibit outstanding properties, suitable for various applications, such as; anode materials for rechargeable batteries [26][27][28][29], hydrogen storage [30-33], catalyst...