AN ADVANCED ADAPTIVE FINITE ELEMENT CODE APPLIED FOR COATING-SUBSTRATE SIMULATION

2011 ◽  
Vol 03 (01n02) ◽  
pp. 91-107 ◽  
Author(s):  
JÜRGEN LEOPOLD ◽  
KATRIN HELLER ◽  
ARNDT MEYER ◽  
REINER WOHLGEMUTH
Keyword(s):  
Finite Element ◽  
Fe Simulation ◽  
Scale Up ◽  
Computational Time ◽  
Adaptive Finite Element ◽  
Workpiece Surface ◽  
Coated Tools ◽  
Geometrical Simulation ◽  
The Stability ◽  
And Storage

The stability of coating-substrate systems influences the chip formation and the surface integrity of the new generated workpiece surface, too. Using finite element (FE) simulation, deformations, strains and stresses in coated tools, caused by external and internal loads, can be computed on a microscopic scale. Since both, the whole macroscopic tool (in mm-scale) and the microscopic coating layers (in μm-scale up to nm-scale) must be included in the same geometrical simulation model, graded high-resolution FE meshes must be used. Nevertheless, the number of nodes in the 3D computational FE grid reaches some millions, leading to large computational time and storage requirements. For this reason, an advanced adaptive finite element (AAFEM) software has been developed and used for the simulation.

Coating-Substrate-Simulation with an Advanced Adaptive Finite Element Code

2011 ◽  
Vol 223 ◽  
pp. 191-202
Author(s):  
Katrin Heller ◽  
Reiner Wohlgemuth ◽  
Arnd Meyer ◽  
Juergen Leopold
Keyword(s):  
Finite Element ◽  
Fe Simulation ◽  
Scale Up ◽  
Computational Time ◽  
Adaptive Finite Element ◽  
Workpiece Surface ◽  
Coated Tools ◽  
Geometrical Simulation ◽  
The Stability ◽  
And Storage

The stability of coating-substrate-systems in uences the chip formation and the surface integrity of the new generated workpiece surface, too. Using FE simulation, deformations, strains and stresses in coated tools, caused by external and internal loads, can be computed on a microscopic scale. Since both, the whole macroscopic tool (in mm-scale) and the microscopic coating layers (in m-scale up to nm-scale) must be included in the same geometrical simulation model, graded high-resolution FE meshes must be used. Nevertheless, the number of nodes in the 3-D computational FE grid reaches some millions, leading to large computational time and storage requirements. For this reason, an Advanced Adaptive Finite Element (AAFEM) software has been developed and used for the simulation.

An H-Adaptive Finite Element Model for Constructing 3-D Wind Fields

2004 ◽  
Author(s):  
Xiuling Wang ◽  
Darrell W. Pepper ◽  
Yitung Chen ◽  
Hsuan-Tsung Hsieh
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Wind Field ◽  
Compressible Flows ◽  
Element Model ◽  
Computational Time ◽  
Individual Element ◽  
Adaptive Finite Element ◽  
Wind Fields ◽  
Irregular Terrain

Calculating wind velocities accurately and efficiently is the key to successfully assessing wind fields over irregular terrain. In the finite element method, decreasing individual element size (increasing the mesh density) and increasing shape function interpolation order are known to improve accuracy. However, computational speed is typically impaired, along with tremendous increases in computational storage. This problem becomes acutely obvious when dealing with atmospheric flows. An h-adaptation scheme, which allows one to start with a coarse mesh that ultimately refines in high gradients regions, can obtain high accuracy at reduced computational time and storage. H-adaptation schemes have been shown to be very effective in compressible flows for capturing shocks [1], but have found limited use in atmospheric wind field simulations [2]. In this paper, an h-adaptive finite element model has been developed that refines and unrefines element regions based upon velocity gradients. An objective analysis technique is applied to generate a mass consistent 3-D flow field utilizing sparse meteorological data. Results obtained from the PSU/NCAR MM5 atmospheric model are used to establish the initial velocity field in lieu of available meteorological tower data. Wind field estimations for the northwest area of Nevada are currently being examined as potential locations for wind turbines.

Error Analysis and Adaptive Methods of Least Squares Nonconforming Finite Element for the Transport Equations

2016 ◽  
Vol 8 (5) ◽  
pp. 871-886
Author(s):  
Huipo Liu ◽  
Shuanghu Wang ◽  
Hongbin Han
Keyword(s):  
Finite Element ◽  
Least Squares ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
Adaptive Methods ◽  
Transport Equations ◽  
Adaptive Finite Element Method ◽  
Nonconforming Finite Element ◽  
Adaptive Finite Element ◽  
The Stability

AbstractIn this paper, we consider a least squares nonconforming finite element of low order for solving the transport equations. We give a detailed overview on the stability and the convergence properties of our considered methods in the stability norm. Moreover, we derive residual type a posteriori error estimates for the least squares nonconforming finite element methods underH–1-norm, which can be used as the error indicators to guide the mesh refinement procedure in the adaptive finite element method. The theoretical results are supported by a series of numerical experiments.

A decoupled finite element method with diferent time steps for the nonstationary Darcy–Brinkman problem

2020 ◽  
Vol 28 (1) ◽  
pp. 33-62 ◽  
Author(s):  
Cheng Liao ◽  
Pengzhan Huang ◽  
Yinnian He
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stability Analysis ◽  
Error Estimates ◽  
Computational Time ◽  
Coupled Method ◽  
Numerical Tests ◽  
The Stability ◽  
Element Method

AbstractA decoupled finite element method with different time steps for the nonstationary Darcy--Brinkman problem is considered in this paper. Moreover, for the presented method, the stability analysis and error estimates are deduced. Finally, numerical tests are provided that demonstrate the efficiency of the method. It is found the presented method can save lots of computational time compared with standard coupled method.

ADAPTIVE FINITE ELEMENT METHODS FOR REACTIVE COMPRESSIBLE FLOW

1999 ◽  
Vol 09 (02) ◽  
pp. 211-241 ◽  
Author(s):  
ROBERT SANDBOGE
Keyword(s):  
Finite Element ◽  
Compressible Flow ◽  
Error Control ◽  
Posteriori Error ◽  
Posteriori Error Estimate ◽  
Stability Factor ◽  
Adaptive Finite Element ◽  
Adaptive Finite Element Methods ◽  
Adaptive Error Control ◽  
The Stability

We extend the adaptive streamline diffusion finite element method for compressible flow in conservation variables using P1× P0 space–time elements to include chemical reactions. The adaptive error control is based on an a posteriori error estimate involving a stability factor, which is estimated numerically. We prove for a model problem that the stability factor is bounded by a moderate constant.

A Finite Element Approach by Contact Transformation for the Prediction of Structural Wear

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
James Shih-Shyn Wu ◽  
Yi-Tsung Lin ◽  
Yuan-Lung Lai ◽  
P.-Y. Ben Jar
Keyword(s):  
Finite Element ◽  
Strain Energy ◽  
Fe Simulation ◽  
Current Method ◽  
Solution Procedure ◽  
Computational Time ◽  
Contact Transformation ◽  
Qualitative Comparison ◽  
Finite Element Approach ◽  
Element Approach

Understanding of the wear behaviors between mechanical components is a significant task in engineering design. Finite element (FE) simulation may offer valuable wear information. However, longer computational time, poor data precision, and possible divergence of results are unavoidable in repetitive procedures, especially for large FE structures. To address these issues, the current method proposes a hypothesis that the strain energy is completely transferred through the contact regions of components; further that only variables on the contact surface are involved in the solution procedure. Our qualitative comparison demonstrates that the formulations in the current study are valid, offering significant implications for further application.

Finite Element Stress Analysis with Consideration of Equivalent Stress in ANSYS – Case Study of Namchien Dam under Static and Dynamic Conditions

2012 ◽  
Vol 188 ◽  
pp. 270-276
Author(s):  
Hoang Hung Vu ◽  
Tong Chun Li ◽  
Quang Hung Nguyen
Keyword(s):  
Finite Element ◽  
Stress Analysis ◽  
Equivalent Stress ◽  
Arch Dam ◽  
Physical Models ◽  
Adaptive Finite Element Method ◽  
Adaptive Finite Element ◽  
Contraction Joints ◽  
The Stability

A research on numerical modeling of arch dam with contraction joints under static and seismic conditions is performed in this study. Discussions on the use of the adaptive finite element method with consideration of the “equivalent stress” and simulating technique for the contact between dam segments are presented. A case study of stress analysis for the Namchien hydropower arch dam in Vietnam is given. The results showed that the numerical model established in this paper is effective to simulate complex physical models. The stability analysis is easily performed by using the self-adapting technique with consideration of equivalent stress, and the contraction joints between dam segments can be successfully simulated by assigning zero-thickness contact elements to control complex contact behaviors, such as slip, opening or closing of the contact surfaces. The results of this study will be a useful reference for the assessment of the dam safety in the future.

scholarly journals Finite Element Implementation of Nonlinear Heat Equation in Enthalpy Formulation using ALBERT(A)

2018 ◽  
Author(s):  
Agah D. Garnadi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Approximate Solution ◽  
Heat Equation ◽  
Adaptive Finite Element Method ◽  
Nonlinear Heat Equation ◽  
Adaptive Finite Element ◽  
Finite Element Implementation ◽  
Enthalpy Formulation ◽  
The Stability

In this paper we describe an implementation of approximate solution to the enthalpy formulation of the Stefan problem. We allow the thermal properties to have a space and temperature dependence. The algorithm is not explicit in the timevariable and hence the stability condition on the time steps is not too severe.The main aim of this note is program documentation of solving non-linear heat equation implementedin ALBERT(A) an adaptive finite element method package.

scholarly journals Energy Contraction and Optimal Convergence of Adaptive Iterative Linearized Finite Element Methods

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Pascal Heid ◽  
Dirk Praetorius ◽  
Thomas P. Wihler
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Degrees Of Freedom ◽  
Linear Convergence ◽  
Nonlinear Problems ◽  
Iterative Solution ◽  
Computational Time ◽  
Galerkin Methods ◽  
Adaptive Finite Element ◽  
Adaptive Finite Element Methods

Abstract We revisit a unified methodology for the iterative solution of nonlinear equations in Hilbert spaces. Our key observation is that the general approach from [P. Heid and T. P. Wihler, Adaptive iterative linearization Galerkin methods for nonlinear problems, Math. Comp. 89 2020, 326, 2707–2734; P. Heid and T. P. Wihler, On the convergence of adaptive iterative linearized Galerkin methods, Calcolo 57 2020, Paper No. 24] satisfies an energy contraction property in the context of (abstract) strongly monotone problems. This property, in turn, is the crucial ingredient in the recent convergence analysis in [G. Gantner, A. Haberl, D. Praetorius and S. Schimanko, Rate optimality of adaptive finite element methods with respect to the overall computational costs, preprint 2020]. In particular, we deduce that adaptive iterative linearized finite element methods (AILFEMs) lead to full linear convergence with optimal algebraic rates with respect to the degrees of freedom as well as the total computational time.

Symmetric Multistep Methods Revisited: II. Numerical Experiments

1999 ◽  
Vol 173 ◽  
pp. 309-314 ◽  
Author(s):  
T. Fukushima
Keyword(s):  
Multistep Methods ◽  
Computational Time ◽  
Integration Time ◽  
Implicit Methods ◽  
Symmetric Methods ◽  
Celestial Bodies ◽  
The Stability ◽  
Predictor Corrector ◽  
Symmetric Multistep Methods ◽  
Integration Errors

AbstractBy using the stability condition and general formulas developed by Fukushima (1998 = Paper I) we discovered that, just as in the case of the explicit symmetric multistep methods (Quinlan and Tremaine, 1990), when integrating orbital motions of celestial bodies, the implicit symmetric multistep methods used in the predictor-corrector manner lead to integration errors in position which grow linearly with the integration time if the stepsizes adopted are sufficiently small and if the number of corrections is sufficiently large, say two or three. We confirmed also that the symmetric methods (explicit or implicit) would produce the stepsize-dependent instabilities/resonances, which was discovered by A. Toomre in 1991 and confirmed by G.D. Quinlan for some high order explicit methods. Although the implicit methods require twice or more computational time for the same stepsize than the explicit symmetric ones do, they seem to be preferable since they reduce these undesirable features significantly.

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