Multibody dynamic analysis using a rotation-free shell element with corotational frame

Rotation-free shell formulation is a simple and effective method to model a shell with large deformation. Moreover, it can be compatible with the existing theories of finite element method. However, a rotation-free shell is seldom employed in multibody systems. Using a derivative of rigid body motion, an efficient nonlinear shell model is proposed based on the rotation-free shell element and corotational frame. The bending and membrane strains of the shell have been simplified by isolating deformational displacements from the detailed description of rigid body motion. The consistent stiffness matrix can be obtained easily in this form of shell model. To model the multibody system consisting of the presented shells, joint kinematic constraints including translational and rotational constraints are deduced in the context of geometric nonlinear rotation-free element. A simple node-to-surface contact discretization and penalty method are adopted for contacts between shells. A series of analyses for multibody system dynamics are presented to validate the proposed formulation. Furthermore,the deployment of a large scaled solar array is presented to verify the comprehensive performance of the nonlinear shell model.

Corotational nonlinear analyses of laminated shell structures using a 4-node quadrilateral flat shell element with drilling stiffness

A new 4-node quadrilateral flat shell element is developed for geometrically nonlinear analyses of thin and moderately thick laminated shell structures. The fiat shell element is constructed by combining a quadrilateral area co- ordinate method （QAC） based membrane element AGQ6- II, and a Timoshenko beam function （TBF） method based shear deformable plate bending element ARS-Q12. In order to model folded plates and connect with beam elements, the drilling stiffness is added to the element stiffness matrix based on the mixed variational principle. The transverse shear rigidity matrix, based on the first-order shear deformation theory （FSDT）, for the laminated composite plate is evaluated using the transverse equilibrium conditions, while the shear correction factors are not needed. The conventional TBF methods are also modified to efficiently calculate the element stiffness for laminate. The new shell element is extended to large deflection and post-buckling analyses of isotropic and laminated composite shells based on the element independent corotational formulation. Numerical re- sults show that the present shell element has an excellent numerical performance for the test examples, and is applicable to stiffened plates.

A recursive formulation based on corotational frame for flexible planar beams with large displacement

A forward recursive formulation based on corotational frame is proposed for flexible planar beams with large displacement.The traditional recursive formulation has been successfully used for flexible mutibody dynamics to improve the computational efficiency based on floating frame,in which the assumption of small strain and deflection is adopted.The proposed recursive formulation could be used for large displacement problems based on the corotational frame.It means that the recursive scheme is used not only for adjacent bodies but also for adjacent beam elements.The nodal relative rotation coordinates of the planar beam are used to obtain equations with minimal generalized coordinates in present formulation.The proposed formulation is different from absolute nodal coordinate formulation and the geometrically exact beam formulation in which the absolute coordinates are used.The recursive scheme and minimal set of dynamic equations lead to a high computational efficiency in numerical integration.Numerical examples are carried out to demonstrate the accuracy and validity of this formulation.For all of the examples,the results of the present formulation are in good agreement with results obtained using commercial software and the published results.Moreover,it is shown that the present formulation is more efficient than the formulation in ANSYS based on GEBF.

STUDY ON THE GENERALIZED PRANDTL-REUSS CONSTITUTIVEEQUATION AND THE COROTATIONALRATES OF STRESS TENSOR

In this paper, the generalized Prandtl-Reuss (P-R) constitutive equations of elastic-plastic material in the presence of finite deformations through a new approach are studied. It analyzes the generalized P-R equation based on the material corotational rate and clarifies the puzzling problem of the simple shear stress oscillation mentioned in some literature. The paper proposes a modified relative rotational rate with which to constitute the objective rates of stress in the generalized P-R equation and concludes that the decomposition of total deformation rate into elastic and plastic parts is not necessary in developing the generalized P-R equations. Finally, the stresses of simple shear deformation are worked out.

Efficient Mesh Updating Scheme for the ALE Corotational Formulation of an Arbitrarily Curved Beam

This paper presents an efficient mesh updating scheme(MUS)for the arbitrary Lagrangian-Eulerian(ALE)formulation of an arbitrarily curved beam based on the corotational method.By discretizing the beam using both Lagrangian elements and ALE elements,the proposed MUS can take full advantage of the simple expression form of the Lagrangian formulation and the accurate moving-load description of the ALE node.The deleting-node and adding-node procedures of the MUS can avoid the negative influence of the variation of the ALE element length on the element accuracy and stiffness matrix singularity.In contrast to the adding-node procedure for Lagrangian elements,interpolation cannot be used directly.Inserting a Lagrangian node in an ALE element is investigated,and the displacement,velocity,and acceleration of the newly added node are evaluated accurately based on the corotational method.Three examples are investigated to verify the validity,computational accuracy and computational efficiency of the proposed MUS by comparing the results of the MUS with those from literature that utilized traditional ALE formulation.These examples show that the proposed MUS has significant advantages in terms of computational time and computer memory.

Finite element corotational formulation for geometric nonlinear analysis of thin shells with large rotation and small strain

Based on the consistent symrnetrizable equilibrated （CSE） corotational formulation, a linear triangular flat thin shell element with 3 nodes and 18~ of freedom, constructed by combination of the optimal membrane element and discrete Kirchhoff trian- gle （DKT） bending plate element, was extended to the geometric nonlinear analysis of thin shells with large rotation and small strain. Through derivation of the consistent tangent stiffness matrix and internal force vector, the corotational nonlinear finite element equations were established. The nonlinear equations were solved by using the Newton-Raphson iteration algorithm combined with an automatic load controlled technology. Three typical case studies, i.e., the slit annular thin plate, top opened hemispherical shell and cylindrical shell, validated the accuracy of the formulation established in this paper.

Energy conserving and decaying algorithms for corotational finite element nonlinear dynamic responses of thin shells

On the basis of the finite element corotational formulation for geometric nonlinear static analysis of thin shells with large rota- tion and small strain established before and from the generalized-a time integration algorithm, the energy conserving and de- caying algorithms for corotational formulation nonlinear dynamic response analysis of thin shells are established in this paper. Responses are solved by means of a predictor-corrector procedure. In the case of ignoring the structural damping, the conserv- ing or decaying total energy of structure and the controllable numerical damping for high frequency responses can ensure the numerical stability of the algorithm. The inertial parts are linearly interpolated directly in the fixed global coordinate system by using the element nodal displacement in the global coordinate system for obtaining the constant mass matrix, while the elastic parts adopt the corotational formulation. Hence, the whole formulation obtained in this paper is element independent. Through three typical numerical examples, the performances of the algorithm in this paper were compared with those of the classical Newmak and HHT-a algorithms to indicate that the algorithm in this paper could accurately solve nonlinear dynamic respons- es of thin shells with large displacements and large rotations.

Solar energetic particles intensity variations associated with a tilted-dipole 3D corotating interaction region

The effect of a tilted-dipole three-dimensional corotating interaction region(CIR)on the transport and acceleration of solar energetic particles(SEPs)is studied.In this work,we discussed how the particle intensity longitudinal and radial dependence might be influenced by the background structures.Moreover,we investigate how the spectral index distribution is modulated by the CIR structure We use the focused transport equation(FTE)to describe the propagation and acceleration of SEPs in a tilt-dipole 3D CIR,generated by the high-resolution 3D magnetohydrodynamic(MHD)model.The forward stochastic differential method is used to solve the FTE.The protons with theE~(-4.4)spectrum from 0.5 to 15 MeV are injected uniformly at the heliographic equator of 0.15 AU.Physical quantities are extracted along each interplanetary magnetic field(IMF)line to show the results.In the tilted-dipole CIR background,if injected from the solar equator at the inner boundary,particles in the slow flow are transported to higher latitudes due to the extension of the IMF lines to higher latitudes.The longitudinal patterns of the particles are dominated by the density of IMF lines.The focusing effect modulates the longitudinal variation of the particle intensity and gives rise to new longitudinal intensity peaks.The adiabatic effect largely increases the intensity fluctuation along the longitude.The structure of the solar wind can also lead to the difference of the indexαin the empirical functionI_(max)=kR~(-α),describing the radial variation of peak intensity according to our simulation.Under the influence of the CIR structure,the indexαvaries from 1.9 to 3.4 at 0.3-1.0 AU.The variation of the solar wind speed should be considered when estimating the radial dependence of the SEP peak intensity.The spectra indices rise near the CIR boundaries and drop near the stream interface(SI).The adiabatic effect makes the spatial variability of the spectral index larger.The spectral index could be similar at different radial distances in the CIR structure.

A URI 4-NODE QUADRILATERAL ELEMENT BY ASSUMED STRAIN METHOD FOR NONLINEAR PROBLEMS

In this paper one-point quadrature'assumed strain'mixed element formulation based on the Hu-Washizu variational principle is presented.Special care is taken to avoid hourglass modes and volumetric locking as well as shear locking.The assumed strain fields are constructed so that those portions of the fields which lead to volumetric and shear locking phenomena are eliminated by projection,while the implementation of the proposed URI scheme is straightforward to suppress hour- glass modes.In order to treat geometric nonlinearities simply and efficiently,a corotational coordinate system is used.Several numerical examples are given to demonstrate the performance of the suggested formulation,including nonlinear static/dynamic mechanical problems.

Distribution of O^(+)and O_(2)^(+) fluxes and their escape rates in the near-Mars magnetotail:A survey of MAVEN observations

Tailward ion outflows in the Martian-induced magnetotail are known to be one of the major channels for Martian atmospheric escape.On the basis of nearly 6.5 years of observations from the Mars Atmosphere and Volatile EvolutioN(MAVEN)mission,we investigate the statistical distribution of tailward and Marsward fluxes of heavy ions(i.e.,O^(+),and O_(2)^(+))in the near-Mars magnetotail and explore their characteristic responses to the corotating interaction region(CIR),solar wind dynamic pressure,and local magnetic field intensity.Our results show that the tailward fluxes of oxygen ions and molecular oxygen ions in the magnetotail are significantly greater than their Marsward fluxes and that the tailward flux of molecular oxygen ions is generally larger than that of oxygen ions.Furthermore,the tailward ion flux distribution exhibits dependence on the CIR,solar wind dynamic pressure,and local magnetic field strength in a manner stronger than the Marsward ion flux distribution.According to the distribution of tailward ion fluxes,we calculate the corresponding escape rates of heavy ions and show that when the CIR occurs,the total escape rates of oxygen ions and molecular oxygen ions increase by a factor of~2 and~1.2,respectively.We also find that the escape rates of heavy ions increase with the enhancement of solar wind dynamic pressure,whereas the overall effect of the local magnetic field is relatively weak.Our study has important implications for improved understanding of the underlying mechanisms responsible for the Martian atmospheric escape and the evolution of the Martian atmospheric climate.

人类首颗研究太阳系外行星的卫星COROT升空

法国制造的COROT卫星在哈萨克斯坦境内的拜科努尔发射场升空,这是人类发射的首颗专门用于研究太阳系外行星的卫星。

Real-Time Deformation Simulation of Kidney Surgery Based on Virtual Reality

Virtual reality-based surgery simulation is becoming popular with the development of minimally invasive abdominal surgery,where deformable soft tissue is modelled and simulated.The mass-spring model(MSM)and finite element method(FEM)are common methods used in the simulation of soft tissue deformation.However,MSM has an issue concerning accuracy,while FEM has a problem with efficiency.To achieve higher accuracy and efficiency at the same time,we applied a co-rotational FEM in the simulation of a kidney with a tumour inside,achieving a real-time and accurate deformation simulation.In addition,we set a multi-model representation for mechanical simulation and visual rendering.The implicit Euler method and conjugate gradient method were adopted for setting and solving the linear system.For a realistic simulation of surgery,constraints outside the kidney and between the kidney and tumour were set with two series of mechanical properties for the two models.Experiments were conducted to validate the accuracy and real-time performance.

Geometric nonlinear analysis of large rotation behavior of a curved SWCNT

Nanotubes form clusters and are found in curved bundles in nano-tube films and nanocomposites.Separation phenomenon is sus-pected to occur in these curved bundles.In this study,the deformation of a single-wall carbon nanotube(SWCNT)interacting with curved bundle nanotubes is analyzed.It is assumed that the bundle is rigid and only van der Waals force acts between the nanotube and the bundle of nanotubes.A new method of model-ing geometric nonlinear behavior of the nanotube due to finite rotation and the corresponding van der Waals force is developed using co-rotational finite element method(CFEM)formulation,combined with small deformation beam theory,with the inclusion of axial force.Current developed CFEM method overcomes the limitation of linear Finite Element Method(FEM)formulation regarding large rotations and deformations of carbon nanotubes.This study provides a numerical tool to identify the critical curvature influence on the interaction of carbon nanotubes due to van der Waals forces and can provide more insight into studying irregula-rities in the electronic transport properties of adsorbed nanotubes in nanocomposites.