Hamiltonian Nodal Position Finite Element Method for Cable Dynamics

2017 ◽  
Vol 09 (08) ◽  
pp. 1750109 ◽  
Author(s):  
Huaiping Ding ◽  
Zheng H. Zhu ◽  
Xiaochun Yin ◽  
Lin Zhang ◽  
Gangqiang Li ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Rigid Body ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Frequency Mode ◽  
Integration Scheme ◽  
Long Period ◽  
Nodal Position ◽  
Element Method

This paper developed a new Hamiltonian nodal position finite element method (FEM) to treat the nonlinear dynamics of cable system in which the large rigid-body motion is coupled with small elastic cable elongation. The FEM is derived from the Hamiltonian theory using canonical coordinates. The resulting Hamiltonian finite element model of cable contains low frequency mode of rigid-body motion and high frequency mode of axial elastic deformation, which is prone to numerical instability due to error accumulation over a very long period. A second-order explicit Symplectic integration scheme is used naturally to enforce the conservation of energy and momentum of the Hamiltonian finite element system. Numerical analyses are conducted and compared with theoretical and experimental results as well as the commercial software LS-DYNA. The comparisons demonstrate that the new Hamiltonian nodal position FEM is numerically efficient, stable and robust for simulation of long-period motion of cable systems.

Viscoplastic Analysis of Mixed Polygonal Granular Material

2012 ◽  
Vol 446-449 ◽  
pp. 3578-3581
Author(s):  
Hui Liang Chen ◽  
Yu Ching Wu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Model ◽  
Granular Material ◽  
Rigid Body ◽  
Incompressible Material ◽  
Body Motion ◽  
Governing Equations ◽  
Deformable Bodies ◽  
Element Method

In this paper, a series of mixed visco-plastic analyses for assembles of three types of asphalt are made using finite element method. Governing equations are derived for motion and deformation for particles, including coupling of rigid body motion and deformation for deformable bodies. Nonlinear viscous analysis is made for the assemblies using an implicit discrete element method. Among particles, three different contact types, cohering, rubbing and sliding, are taken into account. The numerical model is applied to simulate the compaction of aggregates consisting of mixed particles of different nonlinear viscous incompressible material. After minor modification, the application of the proposed numerical model to industry is possible.

Transonic Flow Computations in Cascades Using Finite Element Method

1981 ◽  
Vol 103 (4) ◽  
pp. 657-664 ◽  
Author(s):  
H. U. Akay ◽  
A. Ecer
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Transonic Flow ◽  
Method Development ◽  
Time Integration ◽  
Integration Scheme ◽  
Complex Flow ◽  
Time Integration Scheme ◽  
Naca 0012 ◽  
Element Method

Analysis of transonic flow through a cascade of airfoils is investigated using the finite element method. Development of a computational grid suitable for complex flow structures and different types of boundary conditions is presented. An efficient pseudo-time integration scheme is developed for the solution of equations. Modeling of the shock and the convergence characteristics of the developed scheme are discussed. Numerical results include a 45 deg staggered cascade of NACA 0012 airfoils with inlet flow Mach number of 0.8 and angles of attack 1, 0, and −1 deg.

THE NUMERICAL MANIFOLD METHOD: A REVIEW

2010 ◽  
Vol 07 (01) ◽  
pp. 1-32 ◽  
Author(s):  
GUOWEI MA ◽  
XINMEI AN ◽  
LEI HE
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Distinct Element ◽  
Discontinuous Deformation Analysis ◽  
Deformation Analysis ◽  
Integration Scheme ◽  
Numerical Manifold Method ◽  
Strong Discontinuities ◽  
Numerical Manifold ◽  
Element Method

This paper presents a review on the numerical manifold method (NMM), which covers the basic theories of the NMM, such as NMM components, NMM displacement approximation, formulations of the discrete system of equations, integration scheme, imposition of the boundary conditions, treatment of contact problems involved in the NMM, and also the recent developments and applications of the NMM. Modeling the strong discontinuities within the framework of the NMM is specially emphasized. Several examples demonstrating the capability of the NMM in modeling discrete block system, strong discontinuities, as well as weak discontinuities are given. The similarities and distinctions of the NMM with various other numerical methods such as the finite element method (FEM), the extended finite element method (XFEM), the generalized finite element method (GFEM), the discontinuous deformation analysis (DDA), and the distinct element method (DEM) are investigated. Further developments on the NMM are suggested.

SINGULAR ENRICHMENT FINITE ELEMENT METHOD FOR ELASTODYNAMIC CRACK PROPAGATION

2004 ◽  
Vol 01 (01) ◽  
pp. 1-15 ◽  
Author(s):  
TED BELYTSCHKO ◽  
HAO CHEN
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Crack Propagation ◽  
Degrees Of Freedom ◽  
Time Integration ◽  
Integration Scheme ◽  
Dynamic Crack ◽  
Discrete Equations ◽  
Enrichment Technique ◽  
Element Method

An enrichment technique for accurately modeling two dimensional crack propagation within the framework of the finite element method is presented. The technique uses an enriched basis that spans the asymptotic dynamic crack-tip solution. The enrichment functions and their spatial derivatives are able to exactly reproduce the asymptotic displacement field and strain field for a moving crack. The stress intensity factors for Mode I and Mode II are taken as additional degrees of freedom. An explicit time integration scheme is used to solve the resulting discrete equations. Numerical simulations of linear elastodynamic problems are reported to demonstrate the accuracy and potential of the technique.

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