Nonlinear hydroelastic FSI model for stability analysis of foam sandwich beams under viscous water flow

• A nonlinear hydroelastic FSI model is presented for buckling and postbuckling analysis of axially loaded foam sandwich beams under viscous water flow. • For the first time, the nonlinear pressure distribution of viscous water flow is developed in order to take into account the moderately large deformation of contact surface. • Closed-form expressions of static equilibrium paths, buckling compressive load ( N a , c r ) , and critical upstream speed ( U ∞ , c r ) are obtained. • Linear hydroelastic FSI model is inadequate for predicting the instability behavior. • The critical upstream speeds can increase significantly with the decay rate of viscous flow. Within the framework of an equivalent single-layer beam theory incorporating moderately large deformations at contact surface, a nonlinear hydroelastic fluid-structure interaction (FSI) model is developed to investigate the buckling and postbuckling behavior of foam sandwich beams in viscous flow. The sandwich beam is assumed to consist of two orthotropic face sheets and a metal foam core, with a symmetric porosity distribution along the thickness direction. For the first time, the nonlinear pressure distribution of incompressible viscous flow along the beam length is derived based on the exponential variation of velocity components through the thickness, the nonlinear impermeability condition, the continuity equation, and the Navier–Stokes equation. Then, Timoshenko beam equations with von Kármán’s geometric nonlinearity are solved via the Galerkin method, to present the closed-form expressions of static equilibrium paths (in both prebuckling and postbuckling regimes), buckling compressive load ( N a , c r ) , and critical upstream speed ( U ∞ , c r ) . The numerical results indicate that the critical values are highly sensitive to the decay rate, therefore its accurate determination is crucial for understanding the effect of viscous flow on the mechanical behavior of foam sandwich beams. Furthermore, the findings reveal that the linear hydroelastic FSI model by neglecting the geometric nonlinearities is inadequate for predicting the buckling behavior.