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.

scholarly journals Application of the Generalized Finite Element Method to the acoustic wave simulation in exploration seismology

Geophysics ◽  
2020 ◽  
pp. 1-70
Author(s):  
Edith Sotelo Gamboa ◽  
Marco Favino ◽  
Richard L. Gibson, Jr.
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Acoustic Wave ◽  
Time Integration ◽  
Integration Scheme ◽  
Generalized Finite Element Method ◽  
Time Step ◽  
Time Integration Scheme ◽  
Exploration Seismology ◽  
Element Method

The Generalized Finite Element Method (GFEM) has been applied frequently to solve harmonic wave equations, but its use in the simulation of transient wave propagation is still limited. We apply GFEM to the simulation of the acoustic wave equation in models relevant to exploration seismology. We also perform an assessment of its accuracy and efficiency. The main advantage of GFEM is that it provides an enhanced solution accuracy in comparison to the Standard Finite Element Method (FEM). This is attained by adding user-defined enrichment functions to standard FEM approximations. For the acoustic wave equation,we consider plane waves oriented in different directions as the enrichments, whose argument include the largest wavenumber of the wavefield. We combine GFEM with an unconditionally stable time integration scheme with constant time step. To assess the accuracy and efficiency of GFEM, we present a comparison of GFEM simulation results against those obtained with the Spectral Element Method (SEM). We use SEM because it is the method of choice for wave propagation simulation due to its proven accuracy and efficiency. In the numerical examples, we perform first a convergence study in space and time,evaluating the accuracy of both methods against a semi-analytical solution. Then, we consider two simulations of relevant models in exploration seismology that include low-velocity features, an inclusion with a complex geometrical boundary and topography. Results using these models show that the GFEM presents a comparable accuracy and efficiency to the ones based on SEM. For the given examples, GFEM efficiency stems from the combined effect of local mesh refinement, non-conforming or unstructured, and the unconditionally stable time integration scheme with constant time step. Moreover, these features providegreat flexibility to the GFEM implementations, proving to be advantageous when using, for example, unstructured grids that impose severe time step size restrictions in SEM.

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.

scholarly journals FINITE ELEMENT METHOD FOR NUMERICAL MODELING OF ELASTIC-PLASTIC DEFORMATION OF WOOD UNDER SHOCK LOADING

2020 ◽  
Vol 82 (4) ◽  
pp. 428-441
Author(s):  
M.V. Bezhentseva ◽  
L.I. Vutsin ◽  
A.I. Kibets ◽  
L. Kruszka
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Shock Loading ◽  
Complex Dynamics ◽  
Time Integration ◽  
Three Dimensional ◽  
Integration Scheme ◽  
System Of Equations ◽  
Computational Domain ◽  
Element Method

The 3D problem of wood deformation under shock loading is considered. The governing system of equations is formulated in Lagrange variables. A defining system of equations in a three-dimensional formulation is presented. The equation of motion is derived from the balance of the virtual powers of work. Wood is modeled as a unidirectionally reinforced material with a description of the descending branch of the deformation diagram. Deformations and stresses are determined in a local basis, the position of which in space is related to the direction of the wood grain. Wood material is represented as a combination of reinforcing fibers and a matrix, the elastoplastic deformation of which is described by the relations of the theory of flow with combined kinematic and isotropic strengthening. The deformation characteristics of the matrix and fibers are determined on the basis of a computational and experimental study of the mechanical properties of wood along and across the fibers. In numerical simulation, the moment scheme of the finite element method and an explicit time integration scheme of the “cross” type are used. Discretization of the computational domain is based on an eight-node isoparametric finite element adapted to the specifics of the problem under consideration. Software realization of the developed mathematical model and numerical methodology is implemented within the computing complex “Dynamics-3”. Computer simulation of compression of an experimental specimen of spruce along and across the fibers has been performed. The reliability of the calculation results is confirmed by good agreement with the experimental data.

Fracture simulations using edge-based smoothed finite element method for isotropic damage model via Delaunay/Voronoi dual tessellations

2021 ◽  
pp. 105678952110405
Author(s):  
Young Kwang Hwang ◽  
Suyeong Jin ◽  
Jung-Wuk Hong
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Voronoi Tessellation ◽  
Damage Model ◽  
Time Integration ◽  
Voronoi Cell ◽  
Smoothed Finite Element Method ◽  
Isotropic Damage ◽  
Edge Based ◽  
Element Method

In this study, an effective numerical framework for fracture simulations is proposed using the edge-based smoothed finite element method (ES-FEM) and isotropic damage model. The duality between the Delaunay triangulation and Voronoi tessellation is utilized for the mesh construction and the compatible use of the finite element solution with the Voronoi-cell lattice geometry. The mesh irregularity is introduced to avoid calculating the biased crack path by adding random variation in the nodal coordinates, and the ES-FEM elements are defined along the Delaunay edges. With the Voronoi tessellation, each nodal mass is calculated and the fractured surfaces are visualized along the Voronoi edges. The rotational degrees of freedom are implemented for each node by introducing the elemental formulation of the Voronoi-cell lattice model, and the accurate visualizations of the rotational motions in the Voronoi diagram are achieved. An isotropic damage model is newly incorporated into the ES-FEM formulation, and the equivalent elemental length is introduced with an additional geometric factor to simulate the consistent softening behaviors with reducing the mesh sensitivity. The full matrix form of the smoothed strain-displacement matrix is constructed for optimal use in the element-wise computations during explicit time integration, and parallel computing is implemented for the enhancement of the computational efficiency. The simulated results are compared with the theoretical solutions or experimental results, which demonstrates the effectiveness of the proposed methodology in the simulations of the quasi-brittle fractures.

Time Integration of Impact Phenomena in Solid Mechanics: A One-Dimensional Model Problem

1996 ◽  
Author(s):  
V. Chawla ◽  
T. A. Laursen
Keyword(s):  
Finite Element ◽  
Solid Mechanics ◽  
Exact Analytical Solution ◽  
Time Integration ◽  
Dynamic Contact ◽  
Momentum Conservation ◽  
Integration Scheme ◽  
Mass System ◽  
Element Discretization ◽  
Time Integration Scheme

Abstract 1D impact between two identical bars is modeled as a simple spring-mass system as would be generated by a finite element discretization. Some commonly used time integrators are applied to the system to demonstrate defects in the numerical solution as compared to the exact analytical solution. Using energy conservation as the criterion for stability, a new time integration scheme is proposed that imposes a persistency condition for dynamic contact. Finite element simulation with Lagrange multipliers for enforcing the contact constraints shows exact energy and momentum conservation.

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.

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.

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