A simple class of finite elements for plate and shell problems. I: Elements for beams and thin flat plates
Abstract
Rigorous analysis shows that the spin synchronous mode fluid motion inside a nutation fluid damper on board of a spinning satellite can be modeled as an incompressible, laminar pulsatile flow in a circular straight pipe. The pipe rotates with constant angular velocity ω_ about an axis perpendicular to its own axis. The distance between the rotation axis and the pipe axis is much greater than a, the pipe's radius. The flow is driven by a threedimensional harmonic oscillation of the pipe wall with frequency Ω and amplitude w^{'}_{0}, and is governed by threedimensionless parameters: R_{Ω}(=Ωa^{2}/ν), Δ(=ω/Ω), and A( = w^{'}_{0}/Ωa), where ν is the kinematic viscosity of the fluid. Both the asymptotic analysis and the numerical calculation have been carried out for R_{Ω}=0.11000 and Δ=02 under A≪1. It is found that the rotating effect increases the energy dissipation significantly in comparison with the result of the pulsatile straight pipe flow in an inertia frame (the previous theory for the nutation damper). For Δ=1.5, the energy dissipation in a rotating pipe flow is 5.43 times that in a ``stationary'' pipe flow for large R_{Ω}, which agrees with the previous experiment. A steady stream is induced by the convective effect for finite values of A. Such steady motion is consisted of axial counter flows together with pairs of counterrotating vortices in the crosssectional plane.
 Publication:

International Journal for Numerical Methods in Engineering
 Pub Date:
 September 1992
 DOI:
 10.1002/nme.1620350502
 Bibcode:
 1992IJNME..35..955P
 Keywords:

 Bending Moments;
 Finite Element Method;
 Flat Plates;
 Shells (Structural Forms);
 Stiffness Matrix;
 Boundary Conditions;
 Degrees Of Freedom;
 Mathematical Models;
 Plates (Structural Members);
 Structural Mechanics