A new subregion mesh method for the investigation of the elastic-plastic impact in flexible multibody systems

Impact processes between flexible bodies often lead to local stress concentration and wave propagation of high frequency. Therefore, the modeling of flexible multibody systems involving impact should consider the local plastic deformation and the strict requirements of the spatial discretization. Owing to the nonlinearity of the stiffness matrix, the reduction of the element number is extremely important. For the contact-impact problem, since different regions have different requirements regarding the element size, a new subregion mesh method is proposed to reduce the number of the unnecessary elements. A dynamic model for flexible multibody systems with elastic-plastic contact impact is established based on a floating frame of reference formulation and complete Lagrange incremental nonlinear finite-element method to investigate the effect of the elastic-plastic deformation as well as spatial discretization. Experiments on the impact between two bodies are carried out to validate the correctness of the elastic-plastic model. The proposed formulation is applied to a slider-crank system with elastic-plastic impact.

A VIRTUAL MESH METHOD FOR THE OPTIMIZED DESIGN OF COMPLEX STRUCTURES

Concepts for a virtual 3D space and a hyper-sphere are proposed and the formulae for determining the computable nodes of the mesh are derived.Then a new optimization design method('Virtual Mesh Method'or V.M.M)is developed.Three examples are given,showing that the method proposed is especially suitable for the optimized design of complex structures,and that the global approximate optimal solution can be searched with remarkably reduced computational work.

Effects of fixed and dynamic mesh methods on simulation of stepped planing craft

In the present study,we investigate the effects of fixed and dynamic mesh methods on CFD simulation of stepped planing craft.To this accomplishment,three different body forms of without step,one step,and two step Cougar planing crafts are considered.Three-dimensional CFD analysis is conducted using finite volume method(FVM).Volume of fluid(VOF)model is used for free surface modeling.Overset mesh technique(dynamic mesh)and fixed mesh method are conducted by STAR CCM and ANSYS CFX CFD toolboxes,respectively.CFD results of total hydrodynamic resistance and dynamic trim angle are compared against our measured experimental data to assess the performance and accuracy of considered mesh methods.For more details,pressure distributions,wave patterns and streamlines around the hull models are also presented.Based on our CFD results,dynamic mesh method is more accurate and precise to simulate the stepped planing crafts compared to fixed mesh method.However,computational cost for dynamic mesh method is significantly greater than the fixed mesh method.We also found that the porpoising phenomenon is only detectable using dynamic mesh method in simulation of stepped Cougar planing craft.©2018 Shanghai Jiaotong University.Published by Elsevier B.V.

ON A MOVING MESH METHOD FOR SOLVING PARTIAL INTEGRO-DIFFERENTIAL EQUATIONS

This paper develops and analyzes a moving mesh finite difference method for solving partial integro-differential equations. First, the time-dependent mapping of the coordinate transformation is approximated by a a piecewise linear function in time. Then, piecewise quadratic polynomial in space and an efficient method to discretize the memory term of the equation is designed using the moving mesh approach. In each time slice, a simple piecewise constant approximation of the integrand is used, and thus a quadrature is constructed for the memory term. The central finite difference scheme for space and the backward Euler scheme for time are used. The paper proves that the accumulation of the quadrature error is uniformly bounded and that the convergence of the method is second order in space and first order in time. Numerical experiments are carried out to confirm the theoretical predictions.

AnAdaptive Moving Mesh Method for Two-Dimensional Relativistic Hydrodynamics

This paper extends the adaptive moving mesh method developed by Tang and Tang[36]to two-dimensional(2D)relativistic hydrodynamic(RHD)equations.The algorithm consists of two“independent”parts:the time evolution of the RHD equations and the(static)mesh iteration redistribution.In the first part,the RHD equations are discretized by using a high resolution finite volume scheme on the fixed but nonuniform meshes without the full characteristic decomposition of the governing equations.The second part is an iterative procedure.In each iteration,the mesh points are first redistributed,and then the cell averages of the conservative variables are remapped onto the new mesh in a conservative way.Several numerical examples are given to demonstrate the accuracy and effectiveness of the proposed method.

AnAdaptive Moving Mesh Method for Two-Dimensional Incompressible Viscous Flows

In this paper, we present an adaptive moving mesh technique for solvingthe incompressible viscous flows using the vorticity stream-function formulation. Themoving mesh strategy is based on the approach proposed by Li et al. [J. Comput. Phys.,170 (2001), pp. 562–588] to separate the mesh-moving and evolving PDE at each timestep. The Navier-Stokes equations are solved in the vorticity stream-function form bya finite-volume method in space, and the mesh-moving part is realized by solving theEuler-Lagrange equations to minimize a certain variation in conjunction with a moresophisticated monitor function. A conservative interpolation is used to redistributethe numerical solutions on the new meshes. This paper discusses the implementationof the periodic boundary conditions, where the physical domain is allowed to deformwith time while the computational domain remains fixed and regular throughout. Numericalresults demonstrate the accuracy and effectiveness of the proposed algorithm.

ANALYSIS OF MOVING MESH METHODS BASED ON GEOMETRICAL VARIABLES

Examines the moving mesh methods for solving one-dimensional time dependent partial differential equations. Introduction of the differential-algebraic formulations based on geometrical variables; Investigation of the well-posedness of the numerical approach; Discussion of some detailed numerical procedures.

A Numerical Study of Blowup in the Harmonic Map Heat Flow Using the MMPDE Moving Mesh Method

The numerical solution of the harmonic heat map flow problems with blowup in finite or infinite time is considered using an adaptive moving mesh method.A properly chosen monitor function is derived so that the moving mesh method can be used to simulate blowup and produce accurate blowup profiles which agree with formal asymptotic analysis.Moreover,the moving mesh method has finite time blowup when the underlying continuous problem does.In situations where the continuous problem has infinite time blowup,the moving mesh method exhibits finite time blowup with a blowup time tending to infinity as the number of mesh points increases.The inadequacy of a uniform mesh solution is clearly demonstrated.

Balanced Monitoring of Flow Phenomena in Moving Mesh Methods

Adaptive moving mesh research usually focuses either on analytical deriva-tions for prescribed solutions or on pragmatic solvers with challenging physical appli-cations. In the latter case, the monitor functions that steer mesh adaptation are oftendefined in an ad-hoc way. In this paper we generalize our previously used moni-tor function to a balanced sum of any number of monitor components. This avoidsthe trial-and-error parameter fine-tuning that is often used in monitor functions. Thekey reason for the new balancing method is that the ratio between the maximum andaverage value of a monitor component should ideally be equal for all components.Vorticity as a monitor component is a good motivating example for this. Entropy alsoturns out to be a very informative monitor component. We incorporate the monitorfunction in an adaptive moving mesh higher-order finite volume solver with HLLCfluxes, which is suitable for nonlinear hyperbolic systems of conservation laws. Whenapplied to compressible gas flow it produces very sharp results for shocks and otherdiscontinuities. Moreover, it captures small instabilities (Richtmyer-Meshkov, Kelvin-Helmholtz). Thus showing the rich nature of the example problems and the effective-ness of the new monitor balancing.

An Adaptive Moving Mesh Method for the Five-Equation Model

The five-equation model of multi-component flows has been attracting much attention among researchers during the past twenty years for its potential in the study of the multi-component flows.In this paper,we employ a second order finite volume method with minmod limiter in spatial discretization,which preserves local extrema of certain physical quantities and is thus capable of simulating challenging test problems without introducing non-physical oscillations.Moreover,to improve the numerical resolution of the solutions,the adaptive moving mesh strategy proposed in[Huazhong Tang,Tao Tang,Adaptive mesh methods for one-and two-dimensional hyperbolic conservation laws,SINUM,41:487-515,2003]is applied.Furthermore,the proposed method can be proved to be capable of preserving the velocity and pressure when they are initially constant,which is essential in material interface capturing.Finally,several classical numerical examples demonstrate the effectiveness and robustness of the proposed method.

A Moving Mesh Method for Kinetic/Hydrodynamic Coupling

This paper deals with the application of a moving mesh method for kinetic/hydrodynamic coupling model in two dimensions.With some criteria,the domain is dynamically decomposed into three parts:kinetic regions where fluids are far from equilibrium,hydrodynamic regions where fluids are near thermodynamical equilibrium and buffer regions which are used as a smooth transition.The Boltzmann-BGK equation is solved in kinetic regions,while Euler equations in hydrodynamic regions and both equations in buffer regions.By a well defined monitor function,our moving mesh method smoothly concentrate the mesh grids to the regions containing rapid variation of the solutions.In each moving mesh step,the solutions are conservatively updated to the new mesh and the cut-off function is rebuilt first to consist with the region decomposition after the mesh motion.In such a framework,the evolution of the hybrid model and the moving mesh procedure can be implemented independently,therefore keep the advantages of both approaches.Numerical examples are presented to demonstrate the efficiency of the method.

Moving Mesh Method with Conservative Interpolation Based on L2-Projection

We develop an efficient one-dimensional moving mesh algorithm for solving partial differential equations.The main contribution of this paper is to design an effective interpolation scheme based on L2-projection for the moving mesh method.The proposed method preserves not only the mass-conservation but also the first order momentum of the underlying numerical solution at each mesh redistribution step.Numerical examples are presented to demonstrate the effectiveness of the new interpolation technique.

一种基于Mesh网络的混合AOA/RSSI协作定位算法

传统到达角度(Angle-Of-Arrival,AOA)/接受信号强度指示(Received Signal Strength Indicator,RSSI)混合定位往往需要多个锚节点布设阵列天线以实现高精度定位,为解决在锚节点资源受限下精度较低的问题,提出了一种基于Mesh网络的混合AOA/RSSI协作定位方法。仅有中心主锚节点提供AOA角度的情况下,采取最小二乘法对联合真实和虚拟锚节点所对应角度和距离信息进行初步定位;利用未知节点之间的协作通信和测距信息,位置估计问题被转换为无约束非线性优化问题,给予短距离链路更高权重,通过迭代求解最终实现协作定位。仿真结果表明,所提算法在锚节点资源受限情况下有效地提升了定位精度。

METHOD FOR ADAPTIVE MESH GENERATION BASED ON GEOMETRICAL FEATURES OF 3D SOLID

In order to provide a guidance to specify the element size dynamically during adaptive finite element mesh generation, adaptive criteria are firstly defined according to the relationships between the geometrical features and the elements of 3D solid. Various modes based on different datum geometrical elements, such as vertex, curve, surface, and so on, are then designed for generating local refined mesh. With the guidance of the defmed criteria, different modes are automatically selected to apply on the appropriate datum objects to program the element size in the local special areas. As a result, the control information of element size is successfully programmed covering the entire domain based on the geometrical features of 3D solid. A new algorithm based on Delatmay triangulation is then developed for generating 3D adaptive finite element mesh, in which the element size is dynamically specified to catch the geometrical features and suitable tetrahedron facets are selected to locate interior nodes continuously. As a result, adaptive mesh with good-quality elements is generated. Examples show that the proposed method can be successfully applied to adaptive finite element mesh automatic generation based on the geometrical features of 3D solid.

Meshfree Method Numerical Simulation of Sheet Metal Forming Process

Metal forming plays an important role in manufacturing industry and is widely applied in industries.The tradi- tional finite element method(FEM)numerical simulation is commonly used to predict metal forming process.Conventional finite element analysis of metal forming processes often breaks down due to severe mesh distortion,therefore time-consuming remeshing is necessary.Meshfree methods have been developed since 1977 and can avoid this problem.This new generation of computational methods reduces time-consuming model generation and refinement effort,and its shape function has higher order connectivity than FEM’s.In this paper the velocity shape functions are developed from a reproducing kernel approximation that satisfies consistency conditions and is used to analyze metal tension rigid viscoplastic deforming and Magnesium Alloy(MB 15)sheet superplastic ten- sion forming.A meshfree method metal forming modeling program is set up,the partition of unity method is used to compute the integrations in weak form equations and penalty method is used to impose the essential boundary condition exactly.Metal forming examples,such as sheet metal superplastic tension forming and metal rigid viscoplastic tension forming,are analyzed to demon- strate the performance of mesh free method.

Spherical harmonics method for neutron transport equation based on unstructured-meshes

Based on a new second-order neutron transport equation, self-adjoint angular flux (SAAF) equation, the spherical harmonics (PN) method for neutron transport equation on unstructured-meshes is derived. The spherical harmonics function is used to expand the angular flux. A set of differential equations about the spatial variable, which are coupled with each other, can be obtained. They are solved iteratively by using the finite element method on un- structured-meshes. A two-dimension transport calculation program is coded according to the model. The numerical results of some benchmark problems demonstrate that this method can give high precision results and avoid the ray effect very well.

Study on boundary search method for DFM mesh generation

The boundary mesh of the casting model was determined by direct calculation on the triangular facets extracted from the STL file of the 3D model. Then the inner and outer grids of the model were identified by the algorithm in which we named Inner Seed Grid Method. Finally, a program to automatically generate a 3D FDM mesh was compiled. In the paper, a method named Triangle Contraction Search Method (TCSM) was put forward to ensure not losing the boundary grids; while an algorithm to search inner seed grids to identify inner/outer grids of the casting model was also brought forward. Our algorithm was simple, clear and easy to construct program. Three examples for the casting mesh generation testified the validity of the program.

Nodeless variable finite element method for heat transfer analysis by means of flux-based formulation and mesh adaptation

Based on flux-based formulation, a nodeless variable element method is developed to analyze two-dimensional steady-state and transient heat transfer problems. The nodeless variable element employs quadratic interpolation functions to provide higher solution accuracy without necessity to actually generate additional nodes. The flux-based formulation is applied to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method, The solution accuracy is further improved by implementing an adaptive meshing technique to generaie finite element mesh that can adapt and move along corresponding to the solution behavior. The technique generates small elements in the regions of steep solution gradients to provide accurate solution, and meanwhile it generates larger elements in the other regions where the solution gradients are slight to reduce the computational time and the computer memory. The effectiveness of the combined procedure is demonstrated by heat transfer problems that have exact solutions. These problems tire： （a） a steady-state heat conduction analysis in a square plate subjected to a highly localized surface heating, and （b） a transient heat conduction analysis in a long plate subjected to moving heat source.

A simple and robust method for essential boundary condition treatments in mesh-less methods

To improve the treatment efficiency of essential boundary condition in mesh-less methods,a simple and robust method is proposed in this paper.Rising weight of nodes in the construction of trail function,specified for essential boundary condition,can make the trail function pass through these nodes.And then,the trail function can satisfy the essential boundary condition previously by setting diagonal element to 1 or multiplying diagonal element by a big number in FEM.The MLS method is adopted to validate this method,and it is proved that this method is costless and robust in most of mesh-less methods.

Analysis of the equal width wave equation with the mesh-free reproducing kernel particle Ritz method

In this paper,we analyse the equal width（EW） wave equation by using the mesh-free reproducing kernel particle Ritz（kp-Ritz） method.The mesh-free kernel particle estimate is employed to approximate the displacement field.A system of discrete equations is obtained through the application of the Ritz minimization procedure to the energy expressions.The effectiveness of the kp-Ritz method for the EW wave equation is investigated by numerical examples in this paper.