We generalize the known collision results for a solid in a 3D compressible Newtonian fluid to compressible non-Newtonian ones, and to Newtonian fluids with temperature-depending viscosities.

This paper investigates the dynamics of an underwater vehicle-manipulator system (UVMS) consisting of a two-link flexible-joint manipulator affixed to an autonomous underwater vehicle. The quasi-Lagrange formulation is utilized in deriving a realistic mathematical model of the UVMS considering joints’ friction, hysteretic coupling between the joints and links, and the nonlinear hydrodynamic forces acting on the system, such as added mass, viscous damping, buoyancy, drag, and vortex-induced forces. Numerical simulations are performed to demonstrate the effects of hydrodynamic forces and system coupling between the vehicle and the manipulator and the joints and the links on the precise positioning of the end effector.

Given an open set with finite perimeter $\Omega \subset {\open R}^n$, we consider the space $LD_\gamma ^{p}(\Omega )$, $1\les p<\infty $, of functions with pth-integrable deformation tensor on Ω and with pth-integrable trace value on the essential boundary of Ω. We establish the continuous embedding $LD_\gamma ^{p}(\Omega )\subset L^{pN/(N-1)}(\Omega )$. The space $LD_\gamma ^{p}(\Omega )$ and this embedding arise naturally in studying the motion of rigid bodies in a viscous, incompressible fluid.

In this study, an improved fluid–structure interaction (FSI) analysis method is developed for a flapping wing. A co-rotational (CR) shell element is developed for its structural analysis. Further, a relevant non-linear dynamic formulation is developed based on the CR framework. Three-dimensional preconditioned Navier–Stokes equations are employed for its fluid analysis. An implicit coupling scheme is employed to combine the structural and fluid analyses. An explicit investigation of a 3D plunging wing is conducted using this FSI analysis method. A further investigation of this plunging wing is performed in relation to its operating condition. In addition, the relation between the wing’s aerodynamic performance and plunging motion is investigated.

Lubrication flows appear in many applications in engineering, biophysics and nature. Separation of surfaces and minimisation of friction and wear is achieved when the lubricating fluid builds up a lift force. In this paper we analyse soft lubricated contacts by treating the solid walls as viscoelastic: soft materials are typically not purely elastic, but dissipate energy under dynamical loading conditions. We present a method for viscoelastic lubrication and focus on three canonical examples, namely Kelvin–Voigt, standard linear and power law rheology. It is shown how the solid viscoelasticity affects the lubrication process when the time scale of loading becomes comparable to the rheological time scale. We derive asymptotic relations between the lift force and the sliding velocity, which give scaling laws that inherit a signature of the rheology. In all cases the lift is found to decrease with respect to purely elastic systems.