Implicit-Explicit Finite Elements in Transient Analysis: Implementation and Numerical Examples

1978 ◽  
Vol 45 (2) ◽  
pp. 375-378 ◽  
Author(s):  
T. J. R. Hughes ◽  
W. K. Liu
Keyword(s):  
Finite Element ◽  
Transient Analysis ◽  
Numerical Evaluation ◽  
Slight Modification ◽  
Companion Paper ◽  
Explicit Finite Element ◽  
Numerical Tests ◽  
New Methods ◽  
New Family ◽  
Stability And Accuracy

Computer implementation aspects and numerical evaluation of a new family of implicit-explicit finite element, transient algorithms are presented. It is shown that the new methods are easily coded, and may be introduced into many existing implicit, finite-element codes with only slight modification. Numerical tests confirm the theoretical stability and accuracy characteristics of the methods presented in a companion paper.

Implicit-Explicit Finite Elements in Transient Analysis: Stability Theory

1978 ◽  
Vol 45 (2) ◽  
pp. 371-374 ◽  
Author(s):  
T. J. R. Hughes ◽  
W. K. Liu
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Transient Analysis ◽  
Critical Time ◽  
Unconditional Stability ◽  
Time Step ◽  
Explicit Finite Element ◽  
New Family ◽  
Critical Time Step ◽  
Analysis Stability

A stability analysis is carried out for a new family of implicit-explicit finite-element algorithms. The analysis shows that unconditional stability may be achieved for the implicit finite elements and that the critical time step of the explicit elements governs for the system.

scholarly journals A New Jarratt-Type Fourth-Order Method for Solving System of Nonlinear Equations and Applications

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Moin-ud-Din Junjua ◽  
Saima Akram ◽  
Nusrat Yasmin ◽  
Fiza Zafar
Keyword(s):  
Nonlinear Equations ◽  
Fourth Order ◽  
Basins Of Attraction ◽  
Systems Of Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
Numerical Tests ◽  
New Methods ◽  
New Family ◽  
Engineering Problems ◽  
Fourth Order Method

Solving systems of nonlinear equations plays a major role in engineering problems. We present a new family of optimal fourth-order Jarratt-type methods for solving nonlinear equations and extend these methods to solve system of nonlinear equations. Convergence analysis is given for both cases to show that the order of the new methods is four. Cost of computations, numerical tests, and basins of attraction are presented which illustrate the new methods as better alternates to previous methods. We also give an application of the proposed methods to well-known Burger's equation.

Prediction of Tread Pattern Wear by an Explicit Finite Element Model3

2007 ◽  
Vol 35 (4) ◽  
pp. 276-299 ◽  
Author(s):  
J. C. Cho ◽  
B. C. Jung
Keyword(s):  
Finite Element ◽  
Wear Rate ◽  
Tangential Stress ◽  
Rate Equation ◽  
Constitutive Equations ◽  
Slip Velocity ◽  
Test Results ◽  
Explicit Finite Element ◽  
Driving Condition ◽  
Driving Conditions

Abstract Tread pattern wear is predicted by using an explicit finite element model (FEM) and compared with the indoor drum test results under a set of actual driving conditions. One pattern is used to determine the wear rate equation, which is composed of slip velocity and tangential stress under a single driving condition. Two other patterns with the same size (225/45ZR17) and profile are used to be simulated and compared with the indoor wear test results under the actual driving conditions. As a study on the rubber wear rate equation, trial wear rates are assumed by several constitutive equations and each trial wear rate is integrated along time to yield the total accumulated wear under a selected single cornering condition. The trial constitutive equations are defined by independently varying each exponent of slip velocity and tangential stress. The integrated results are compared with the indoor test results, and the best matching constitutive equation for wear is selected for the following wear simulation of two other patterns under actual driving conditions. Tens of thousands of driving conditions of a tire are categorized into a small number of simplified conditions by a suggested simplification procedure which considers the driving condition frequency and weighting function. Both of these simplified conditions and the original actual conditions are tested on the indoor drum test machines. The two results can be regarded to be in good agreement if the deviation that exists in the data is mainly due to the difference in the test velocity. Therefore, the simplification procedure is justified. By applying the selected wear rate equation and the simplified driving conditions to the explicit FEM simulation, the simulated wear results for the two patterns show good match with the actual indoor wear results.

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 Some transpose-free CG-like solvers for nonsymmetric ill-posed problems

2020 ◽  
Vol 28 (1) ◽  
pp. 15-32
Author(s):  
Silvia Gazzola ◽  
Paolo Novati
Keyword(s):  
Krylov Subspace ◽  
Main Idea ◽  
System Matrix ◽  
Numerical Tests ◽  
New Methods ◽  
Arnoldi Algorithm ◽  
Ill Posed ◽  
Efficient Alternative ◽  
Original Class ◽  
Theoretical Insight

AbstractThis paper introduces and analyzes an original class of Krylov subspace methods that provide an efficient alternative to many well-known conjugate-gradient-like (CG-like) Krylov solvers for square nonsymmetric linear systems arising from discretizations of inverse ill-posed problems. The main idea underlying the new methods is to consider some rank-deficient approximations of the transpose of the system matrix, obtained by running the (transpose-free) Arnoldi algorithm, and then apply some Krylov solvers to a formally right-preconditioned system of equations. Theoretical insight is given, and many numerical tests show that the new solvers outperform classical Arnoldi-based or CG-like methods in a variety of situations.

The Study on Crashworthiness Performance of Thin-Walled Structures and the Effect of Welding Performance on it

2011 ◽  
Vol 63-64 ◽  
pp. 655-658
Author(s):  
Qi Hao ◽  
Sheng Jun Wu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Welded Joints ◽  
Impact Force ◽  
Deformation Energy ◽  
Optimal Shape ◽  
Explicit Finite Element Method ◽  
Explicit Finite Element ◽  
Thin Walled Structures ◽  
Thin Walled

Explicit finite element method is adopted to simulate the crashworthiness performance of four types of typical thin—walled structures used in vehicle by software LS-DYNA. The structures with the same material、area and length are crash by a rigid body with 40km/h in10ms, The crash processes and crashworthiness characters are analyzed by a series crash parameters: deformation energy with unit displacement, impact force and deceleration to look for the optimal shape with crashworthiness. With comparing, the double caps section has ascendant performance than the others. The simulating methods of welded-joints are discussed to analysis their effects on crashworthiness simulation.

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