A projection-based SPH framework for shell-related fluid coupling and contact interactions

A projection-based Smoothed Particle Hydrodynamics (SPH) framework is proposed for interaction dynamics involving thin shells represented by a reduced-dimensional, single-layer particle discretization, in contrast to full-dimensional SPH solid discretizations. The framework addresses one-sided fluid-shell coupling, where the fluid is present on only one side of the shell, as well as solid-shell, shell-shell, and shell-self contact. The study introduces a projected imaginary-particle treatment for single-layer shell boundaries, in which auxiliary quadrature points are generated from real shell particles along the local normal direction within the cut-off radius of nearby fluid particles. These projected points do not possess independent material dynamics; instead, they reconstruct an effective volumetric kernel support for the reduced-dimensional shell. Their area/volume weights are assigned according to the local shell curvature, which provides a geometrically consistent reconstruction of the shell-side kernel contribution while leaving the standard SPH fluid-solid coupling algorithm unchanged. In addition, a particle-level density/pressure-like repulsive model is employed for solid–solid interactions, in which a contact density is evaluated in a manner analogous to SPH density summation and the corresponding repulsive force is written in a momentum-equation-like form. Combined with the projected imaginary-particle treatment, the same contact formulation can be effectively applied to solid-shell, shell-shell, and shell-self contact without introducing an additional surface mesh or segment-based contact search. The proposed framework is assessed using a series of benchmark tests, demonstrating that the projection-based shell treatment can recover the shell-side kernel support, transmit fluid loading consistently, and handle shell-related contact interactions with stable and accurate performance. A complex industrial oil-tank collision case is further presented to demonstrate the applicability of the proposed framework to practical scenarios involving coupled fluid motion, large shell deformation, and contact events.