This paper presents analysis of thin plates with holes within the context of XFEM. New integration techniques are developed for exact geometrical representation of the holes. Numerical and exact integration techniques are presented, with some limitations for the exact integration technique. Simulation results show that the proposed techniques help to reduce the solution error, due to the exact geometrical representation of the holes and utilization of appropriate quadrature rules. Discussion on minimum order of integration order needed to achieve good accuracy and convergence for the techniques presented in this work is also included.
Porous nanosheets have attracted significant attention as viable options for energy storage materials because of their exceptionally large specific surface areas. A recent study (Int. J. Hydrogen Energy, 2024, 66, 33-39) has demonstrated that Li/Na-metalized inorganic BP-biphenylene (b-B3P3) and graphenylene (g-B6P6) analogues possess suitable functionalities for hydrogen (H2) storage. Herein, we evaluate the H2 storage performance of alkaline earth metal (AEM = Be, Mg, Ca)-decorated b-B3P3 and g-B6P6 structures based on first-principles density functional theory (DFT) calculations. Our investigations revealed that individual Be and Mg atoms are not stable on pure b-B3P3 and g-B6P6 sheets, and the formation of aggregates is favored due to their low binding energy to these surfaces. However, the binding energy improves for Ca-decorated b-B3P3 (b-B3P3(mCa)) and g-B6P6 (g-B6P6(nCa)) structures, forming stable and uniform mCa(nCa) (m and n stand for the numbers of Ca atom) coverages on both sides. Under maximum hydrogenation, the b-B3P3(8Ca) and g-B6P6(16Ca) structures exhibited the ability to adsorb up to 32H2 and 48H2 molecules with average adsorption energy (E a) values of -0.23 eV per H2 and -0.25 eV per H2, respectively. Gravimetric H2 uptakes of 7.28 wt% and 5.56 wt% were found for b-B3P3(8Ca)@32H2 and g-B6P6(16Ca)@48H2 systems, exceeding the target of 5.50 wt% set by the US Department of Energy (DOE) to be reached by 2025. Our findings indicate the importance of these b-B3P3 and g-B6P6 sheets for H2 storage technologies.