scholarly journals A PETSc-Based Parallel Implementation of Finite Element Method for Elasticity Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Jianfei Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Parallel Implementation ◽  
Good Choice ◽  
Finite Element Code ◽  
Finite Element Discretization ◽  
Element Analysis ◽  
Element Discretization ◽  
Elasticity Problems ◽  
Parallel Code

Starting a parallel code from scratch is not a good choice for parallel programming finite element analysis of elasticity problems because we cannot make full use of our existing serial code and the programming work is painful for developers. PETSc provides libraries for various numerical methods that can give us more flexibility in migrating our serial application code to a parallel implementation. We present the approach to parallelize the existing finite element code within the PETSc framework. Our approach permits users to easily implement the formation and solution of linear system arising from finite element discretization of elasticity problem. The main PETSc subroutines are given for the main parallelization step and the corresponding code fragments are listed. Cantilever examples are used to validate the code and test the performance.

A Finite Element Analysis of Curing Bladder Shaping

1988 ◽  
Vol 16 (3) ◽  
pp. 128-145 ◽  
Author(s):  
T. C. Warholic ◽  
R. G. Pelle
Keyword(s):  
Finite Element Method ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Finite Element Code ◽  
The Finite Element Method ◽  
Primary Interest ◽  
Molding Process ◽  
Element Analysis ◽  
Equal Importance ◽  
Significant Step

Abstract The molding process is a critical step in the manufacture of pneumatic tires. It affects the design and consequently the performance of the tire. The present paper covers work aimed at analyzing the molding process using the finite element method. Specifically, the finite element code MARC is used to analyze the inflation of a curing bladder inside a rigid tire profile. Incompressible elements are used to model the bladder and GAP elements are used to simulate the contact between the two surfaces. Of primary interest is the bladder-profile interface, namely how contact occurs at the interface and the magnitude and uniformity of the interfacial pressures. Two different bladder shapes and two different inside tire profiles are studied. Of equal importance is the ability to model this type of contact problem as it is a significant step toward analyzing the tire molding process.

Hierarchical bases and the finite element method

Acta Numerica ◽  
1996 ◽  
Vol 5 ◽  
pp. 1-43 ◽  
Author(s):  
Randolph E. Bank
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Error Estimation ◽  
Linear Equations ◽  
A Posteriori ◽  
The Finite Element Method ◽  
Finite Element Discretization ◽  
Element Discretization ◽  
Hierarchical Bases ◽  
Finite Element Calculations

In this work we present a brief introduction to hierarchical bases, and the important part they play in contemporary finite element calculations. In particular, we examine their role in a posteriori error estimation, and in the formulation of iterative methods for solving the large sparse sets of linear equations arising from finite element discretization.

Finite Element Discretization of Piezothermoelastic Equations Using the Generalized Equation of Heat Conduction

2005 ◽  
Author(s):  
Zsolt Vi´zva´ry
Keyword(s):  
Finite Element ◽  
Heat Conduction ◽  
Generalized Equation ◽  
Finite Element Code ◽  
Spatial Discretization ◽  
Finite Element Discretization ◽  
Fourier’S Law ◽  
Galerkin’S Method ◽  
Element Discretization ◽  
Equation Of Heat Conduction

In this paper, the derivation of the finite element equations of piezothermoelasticity is presented using the classical and generalized Fourier’s law. Galerkin’s method is used to the spatial discretization of the equations. Based upon these equations, a finite element code is under development.

scholarly journals One-dimensional finite element discretization of crack propagation through parallel computation

1970 ◽  
Vol 5 (1) ◽  
pp. 19-28 ◽  
Author(s):  
Md Rajibul Islam ◽  
Norma Alias
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Crack Propagation ◽  
Parallel Computer ◽  
Finite Element Discretization ◽  
Element Discretization ◽  
One Dimensional ◽  
Parallel Virtual Machine ◽  
Dimensional Finite Element ◽  
Element Method

In this study, a new approach of the application of finite element method is presented, to solve the initial stages of crack propagation problems which mean the deformation due to the stress and strain of a material. In early applications of the finite element method for the analysis of crack propagation, the crack-tip motion was modelled by discontinuous jumps. We have implemented one dimensional finite element discretization to solve crack propagation problem. The parallel algorithm with parallel computer system has been used in order to perform the computational analysis of finite element for this study. Parallel Virtual Machine (PVM) has been used as a message passing software with Parallel Computer System. The result of this study will be useful in the mathematics and engineering fields. In mathematics, the research will widen the application of finite elements in solving the engineering science problems. Keywords: Finite Element Method (FEM), Crack Propagation, Parallel computation, Parallel Virtual Machine (PVM). DOI: 10.3329/diujst.v5i1.4378 Daffodil International University Journal of Science and Technology Vol.5(1) 2010 pp.19-28

GPU Based Boundary Element Analysis for 3D Elastostatics with GMRES-DC Algorithm Solving System Equations

2011 ◽  
Vol 308-310 ◽  
pp. 2345-2348 ◽  
Author(s):  
Gang Wang ◽  
Qi Fu Wang ◽  
Ying Jun Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element ◽  
Geometric Modeling ◽  
Parallel Implementation ◽  
Generation Process ◽  
Element Analysis ◽  
Dc Algorithm ◽  
System Equations ◽  
Element Method

During the modern product design, CAD softwares are widely used for geometric modeling and finite element method is used for structural performance analysis. Plenty of designers’ working time is spending in the pre-processing work of finite element analysis. Boundary Element Method(BEM) has been studied in recent years to analyze 3D elastostatics instead of Finite Element Method(FEM) because of the decrease of unknowns and easier mesh generation process. But the calculation amount of BEM is large, especially for the coefficient integrals and system equations solution. In this paper, we present a Boundary Element parallel computation technique for 3D elastostatics using Computing Unified Device Architecture (CUDA) that runs on GPU. Furthermore, we propose GMRES-DC (GMRES with Dual Compensation) algorithm based on the classic GMRES algorithm to gain a higher solving efficiency. The examples show that the GPU parallel implementation in this paper can accelerate BEM computation greatly, and the GMRES-DC algorithm can solve the BEM system equations efficiently.

Towards Predicting Relative Belt Edge Endurance With the Finite Element Method

1990 ◽  
Vol 18 (4) ◽  
pp. 216-235 ◽  
Author(s):  
J. De Eskinazi ◽  
K. Ishihara ◽  
H. Volk ◽  
T. C. Warholic
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Shear Deformations ◽  
Element Analysis ◽  
Vertical Loading ◽  
Predicted Values ◽  
Element Method

Abstract The paper describes the intention of the authors to determine whether it is possible to predict relative belt edge endurance for radial passenger car tires using the finite element method. Three groups of tires with different belt edge configurations were tested on a fleet test in an attempt to validate predictions from the finite element results. A two-dimensional, axisymmetric finite element analysis was first used to determine if the results from such an analysis, with emphasis on the shear deformations between the belts, could be used to predict a relative ranking for belt edge endurance. It is shown that such an analysis can lead to erroneous conclusions. A three-dimensional analysis in which tires are modeled under free rotation and static vertical loading was performed next. This approach resulted in an improvement in the quality of the correlations. The differences in the predicted values of various stress analysis parameters for the three belt edge configurations are studied and their implication on predicting belt edge endurance is discussed.

Tire Cornering Simulation Using an Explicit Finite Element Analysis Code

1998 ◽  
Vol 26 (2) ◽  
pp. 109-119 ◽  
Author(s):  
M. Koishi ◽  
K. Kabe ◽  
M. Shiratori
Keyword(s):  
Finite Element Method ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Test System ◽  
Experimental Results ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Explicit Finite Element ◽  
Explicit Finite Element Analysis ◽  
Element Method

Abstract The finite element method has been used widely in tire engineering. Most tire simulations using the finite element method are static analyses, because tires are very complex nonlinear structures. Recently, transient phenomena have been studied with explicit finite element analysis codes. In this paper, the authors demonstrate the feasibility of tire cornering simulation using an explicit finite element code, PAM-SHOCK. First, we propose the cornering simulation using the explicit finite element analysis code. To demonstrate the efficiency of the proposed simulation, computed cornering forces for a 175SR14 tire are compared with experimental results from an MTS Flat-Trac Tire Test System. The computed cornering forces agree well with experimental results. After that, parametric studies are conducted by using the proposed simulation.

scholarly journals Shape Sensing of a Complex Aeronautical Structure with Inverse Finite Element Method

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1388
Author(s):  
Daniele Oboe ◽  
Luca Colombo ◽  
Claudio Sbarufatti ◽  
Marco Giglio
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Strain Field ◽  
Element Analysis ◽  
Inverse Finite Element Method ◽  
Shape Sensing ◽  
Definition Of ◽  
High Level ◽  
Element Method

The inverse Finite Element Method (iFEM) is receiving more attention for shape sensing due to its independence from the material properties and the external load. However, a proper definition of the model geometry with its boundary conditions is required, together with the acquisition of the structure’s strain field with optimized sensor networks. The iFEM model definition is not trivial in the case of complex structures, in particular, if sensors are not applied on the whole structure allowing just a partial definition of the input strain field. To overcome this issue, this research proposes a simplified iFEM model in which the geometrical complexity is reduced and boundary conditions are tuned with the superimposition of the effects to behave as the real structure. The procedure is assessed for a complex aeronautical structure, where the reference displacement field is first computed in a numerical framework with input strains coming from a direct finite element analysis, confirming the effectiveness of the iFEM based on a simplified geometry. Finally, the model is fed with experimentally acquired strain measurements and the performance of the method is assessed in presence of a high level of uncertainty.

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