Semi-analytical analysis of nonlinear liquid sloshing in rectangular tanks with scaled boundary finite element method.

This article focuses on the development and validation of a novel semi-analytical scaled boundary finite element method (SBFEM) model for analyzing nonlinear liquid sloshing in two-dimensional (2D) liquid storage tanks. The model integrates potential flow theory with the semi-Lagrange method for free surface tracking and employs a fourth-order Runge–Kutta algorithm for time integration, requiring discretization only along the tank boundary and thus reducing computational complexity. Numerical examples—including free sloshing, forced sloshing under horizontal and vertical excitations, sloshing in a U-shaped aqueduct, and tanks with submerged obstacles—demonstrate the method's high accuracy, robustness, and computational efficiency compared to existing approaches. Key findings include the intensification of nonlinear effects with increased excitation amplitude, the influence of liquid depth on sloshing amplitude and frequency, and the significant impact of obstacle height (but not width) on suppressing sloshing dynamics. The study confirms the SBFEM's applicability to complex geometries and nonlinear sloshing phenomena relevant to engineering design and safety.