Research On Sloshing Response In Curved Liquid-Filled Tanks Based On Rational ANCF Fluid Elements

The liquid sloshing phenomenon generally occurs in a liquid-filled container that is subjected to external motion or force.The force and moment caused by the sloshing have a negative impact on the structure or movement stability of the container.The shape of the container determines the law of sloshing response that occurs inside.Most existing research focuses on the sloshing problem in regular containers(such as cuboid),but most of the liquid-filled tanks used in engineering practice are mostly curved.Therefore,the study of nonlinear sloshing response in curved tanks has practical engineering research value.Liquid-filled storage tanks generally exist in multi-body systems.Existing research methods are difficult to model the liquid and multi-body systems uniformly.At the same time,it is difficult to accurately describe the configuration of liquid curved bodies.Therefore,this paper establishes rational absolute node coordinates The formula is the fluid element of the configuration description function,and the sloshing problem in the cylindrical and spherical tanks is simulated and analyzed.In order to establish the fluid element based on the rational absolute nodal coordinate formula,the modeling method of continuum mechanics is introduced,and the deformation gradient,strain tensor,Cauchy stress and other mechanical parameters are derived.At the same time,the rational Bézier function is introduced to replace the interpolation function of the traditional absolute nodal coordinate formula,and then the calculation of the shape function of the rational absolute nodal coordinate formula is derived.Based on the continuum balance equation,the virtual work equation in the generalized form of force is derived using the principle of virtual work.The penalty method is applied to incompressible fluids,and a continuity equation(conservation of mass)in the form of a generalized penalty force is proposed,and then the element dynamics equation composed of element node coordinates,generalized mass matrix,and generalized force is derived.The constraint equations formed by the constraint conditions are sorted out,and the system control equations of the fluid-multibody system are established by the Lagrange multiplier method.In order to establish the third-order and fifth-order rational absolute nodal coordinate fluid elements of the regular initial configuration,the 3 × 3 × 3 order rational Bézier entity and the 5 × 5 × 5 order rational Bézier entity are introduced respectively.The three-dimensional eight-node unit structure is established,and two types of unit node coordinate vector structures are designed respectively,and the control point position and weight coefficient setting plan of the regular initial configuration is given.Aiming at the required plane constraint conditions,the constraint equations and the Jacobian matrix establishment methods were deduced by the same design principles.A dam break simulation experiment was established,and the waterfront displacement was used as the evaluation index to verify the correctness and convergence of the third-order and fifth-order rational absolute nodal coordinate fluid elements.The sloshing simulation experiment of the rectangular parallelepiped liquid-filled storage tank is established,and the free liquid surface wave height is used as the evaluation index,which also verifies the correctness of the above unit.In order to establish a third-order rational absolute nodal coordinate fluid element with an initial configuration of a cylinder,the calculation results of the control point positions and weight coefficients of the third-order rational Bézier arc are introduced.In view of the difference in the placement of the storage tank,the initial configuration of the fluid unit is a vertical cylinder and a horizontal cylinder.Aiming at the required cylindrical constraint conditions,the constraint equations and Jacobi matrix are deduced respectively.For the vertical cylindrical fluid element,the collapse simulation experiment is used to verify the correctness of the element by using the radius of the waterfront loop as the evaluation index.For a horizontal cylindrical fluid unit,through sloshing simulation experiments,the effects of liquid filling depth,excitation frequency,and excitation direction on the sloshing response are analyzed: the same liquid filling depth,resonance excitation frequency,and the deviation of the liquid centroid trajectory in the direction of gravity when sloshing Larger,the greater the deviation of the trajectory of the liquid center of mass in the sloshing direction when the liquid is sloshing longitudinally.With the same filling depth,longitudinal excitation direction,and excitation frequency directly determine the shape of the free liquid surface wave height curve.Longitudinal excitation direction,resonance excitation frequency,low liquid filling depth,small free liquid surface sloshing amplitude,small deviation of the liquid center of mass in the direction of gravity,large deviation in the sloshing direction,and no liquid concentration at the symmetry axis of the front and rear bottom surfaces;liquid filling The depth is high,the free liquid surface sloshing amplitude is large,the liquid center of mass trajectory deviates greatly in the gravity direction,and the deflection is small in the sloshing direction,and the liquid concentration phenomenon occurs at the position of the symmetry axis of the front and rear bottom surfaces.In order to establish the fifth-order rational absolute nodal coordinate fluid element with the initial configuration of a sphere,the calculation results of the control point positions and weight coefficients of the 5 × 5 order "trilateral" rational Bézier spherical surface are introduced,and the initial configuration is constructed.The type is a hemispherical fluid unit.Aiming at the required spherical constraint conditions,the constraint equations and Jacobi matrix expressions are derived.Through the sloshing simulation experiment,the liquid surface wave height simulation curves of different methods are compared,and the simulation results are consistent.Also through the sloshing simulation experiment,the influence of the excitation frequency on the sloshing response is analyzed: when the excitation frequency is close to the resonance frequency,the peak and valley value of the free surface wave height will monotonously increase(decrease),when the excitation frequency and the resonance frequency have a certain deviation When the excitation frequency is much lower than the resonance frequency,the wave height curve will show a small regular vibration.