【正文】 is toLiquidtheusuati. Thegoodpaperreddisturbancerigid containersfew decades.andonater oscillationpoolsto both highway safety and the environment (Botkin,1970).Tank trucks employed in general purpose chemical transportation encounter partial fill conditions due to the varyingweight density of the products and the laws governing axle loads,while those employed in fuel transportation encounter partial fillApart from heavy vehicle design factors, the dynamic stabilitylimit of tank trucks are directly related to dynamic load shift. Thedynamic load transfer encountered during a braking or turningmanoeuvre is a plex function of fluid slosh, fill level, tankgeometry, vehicle weight and dimension, suspension and tireproperties. The study of the sloshing behaviour of liquids withina moving container involves highly plex dynamic modelingand analyses. Slibar and Troger (1977) have characterized thesloshing liquid cargo in the roll plane as two lumped masses* Corresponding author.Contents lists availableEuropean Journal ofEuropean Journal of Mechanics A/Solids 28 (2020) 1026–1034Email address: (M. Bouazara).limits of partially filled liquid cargo vehicles are known to besignificantly lower than those of conventional rigid cargo vehiclesduetotheuniquedynamicinteractionsbetweenthevehicleandthesloshing liquid cargo. The forces and moments arising from a directional manoeuvre yield considerable dynamic load shifts in the rolland pitch planes due to the sloshing of the liquid cargo within thepartially filled tank. The dynamic load shift affects the directionalstability of the partially filled tank trucks in an adverse manner.When dangerous goods are hauled it canpose an unreasonable riskturning, braking and lane change。 and liquidstructure dynamicinteractions. Various accident analysis studies have reported thattank vehicles are more frequently involved in single vehiclehighway accidents than rigid cargo vehicles. It has been reportedthat 40% of road accidents involving tank trucks were single vehicleaccidents (Matteson et al., 2020). Nearly 50% of the single vehicleaccidents and almost 80% of multiple vehicle accidents involved atleast one fatality. The majority of single vehicle accidents occurredduring cornering, 52% of which resulted in a rollover.1. IntroductionSloshing is a potential source ofcontainers. The motion of liquids insubject of many studies in the pastapplication in several engineering disciplines:carryingliquidfuelcargo,inaircraftsoscillation in large storage tanks。 wwatersloshinginnuclearfuelstorageproblem is plex and strongly nonlinear09977538/$ – see front matter Crown Copyright C211 20doi:in liquid storagehas been theIt has frequentsloshing in vehiclessuspensionbridges。oilin storage and. Directional stabilityconditions along delivery routes. Movement or sloshing of theliquid in the tank increases significantly when vehicle weights anddimensions increase. The liquid slosh coupled with heavy vehicledynamics can lead to a significant reduction in longitudinal andlateral stability and controllability, as well as to increased stresseson the container structure (Bauer,1975). The handling and stabilitylimits of tank trucks are thus dependent upon factors other thannormal trucking practices. These factors include tank geometry。height of the centre of gravity (cg)。 fill level。 lateral and longitudinal load shift during typical highway manoeuvres such asImpact of liquid sloshing on the behaviourM. Toumia, M. Bouazaraa,*, . RichardbaDepartment of Applied Sciences, University of Quebec at Chicoutimi, Quebec, CanadabDepartment of Mechanical Engineering, Laval University, Quebec, Canadaarticle infoArticle history:Received 25 September 2020Accepted 25 April 2020Available online 5 May 2020Keywords:Tank vehiclesNavier–Stokes equationsVolume of fluid technique and impact ofliquid sloshingabstractThe purpose of this papercarrying liquid fuel cargo.problems strongly related toliquid sloshing is developedplex Navier–Stokes eqsimplified analytical modelmodel. The results show aIn the second part for thissimulation result is paCrownjournal homepage: 09 Published by Elsevier Massonof vehicles carrying liquid cargostudy the stability and the behaviour of the dynamics of tank vehiclesforces and moments due to liquid sloshing is one of the most seriousinstability of tank vehicles. In this paper, a simplified analytical model ofing the Navier–Stokes equations. Simulation results obtained using the fullons modulated with numerical mercial software are pared to theparison highlights the validity assumptions used on the analyticalcorrelation under single or double lane change and turning manoeuvres., a full dynamic vehicle is coupled with the analytical liquid model. Thisto a rigid vehicle cargo.Copyright C211 2020 Published by Elsevier Masson SAS. All rights reserved.at ScienceDirectMechanics A/SolidsSAS. All rights reserved.0 188。C01rVP 254。Fr。 0 188。C01rvPvxi254。 ai。 ih240。x。 y。 z222。 (4)Starting from Eq. (4), the total derivative of the pressure will havethe following form:dP 188。C18vPvxC19dx 254。C18vPvyC19dy 254。C18vPvzC19dz 188。C0raxdx C0raydy C0razdz(5)where (x, y, z) and (ax, ay, az) are respectively, the coordinates andaccelerations of the liquid centre of mass.Thedynamicloadtransfercausedbythemovementof theliquidcargowithinapartiallyfilledtankisevaluatedfromtheverticalandlateral displacements of its centre of mass and the variation of theinertia matrix. The procedure used in this research is to calculateMechanics A/Solids 28 (2020) 1026–1034 1027coupled through a linear spring and a viscous damper. Abramson(1966) has investigated the fluid slosh in spacecraft fuel tankscaused by lateral motion using a similar mechanical