Boundary Element Analysis of a Freestanding Sliding‐Mode Triboelectric Nanogenerator

Quantitative electrostatic modeling of freestanding sliding‐mode triboelectric nanogenerators (FS‐TENGs) is challenging when nonuniform conductor charge distributions and open‐domain interactions must be resolved repeatedly. Here, a two‐dimensional (2D) boundary element method (BEM) framework is developed for tribo‐charged‐layer and metal‐layer FS‐TENGs (TL‐ and ML‐FS‐TENGs). The formulation resolves distributed conductor charges, constructs the terminal voltage‐transferred–charge–displacement ( V – Q – z ) relation, and couples it to prescribed periodic motion and a resistive load. Numerical accuracy is assessed using canonical analytical benchmarks, independently converged finite element method (FEM) solutions, and BEM boundary‐refinement studies, while 2D finite‐thickness (2D FT) and finite‐width three‐dimensional (3D) FEM models separately assess the baseline idealization for the tribo‐charged‐layer FS‐TENG (TL‐FS‐TENG). For the examined electrostatic tasks, the self‐convergence‐selected BEM discretization requires substantially less workload time and peak memory than the corresponding converged FEM calculations. The TL‐FS‐TENG exhibits displacement‐independent capacitance, and its optimal electrical loading is nearly geometry‐independent and closely follows constant‐capacitance RC matching, whereas the displacement‐dependent capacitance of the metal‐layer FS‐TENG (ML‐FS‐TENG) produces geometry‐dependent optimal loading. Waveform changes affect instantaneous current more strongly than cycle‐averaged power. The baseline formulation is restricted to quasi‐electrostatic, 2D, zero‐thickness FS‐TENGs. It cannot be directly applied to configurations requiring finite dielectric domains, such as vertical contact–separation (VCS) and ordinary attached‐electrode sliding TENGs, while finite out‐of‐plane effects require an extended formulation or separate higher‐fidelity analysis.