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finite difference method

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Series: ASM Handbook
Volume: 4C
Publisher: ASM International
Published: 09 June 2014
DOI: 10.31399/asm.hb.v04c.a0005876
EISBN: 978-1-62708-167-2
...-element method, finite difference method, boundary-element method or volume-integral method, and direct-solution method. The article also discusses the typical structure of commercial codes (preprocessor, solver, and postprocessor) to solve field problems mainly in finite-element method. computer...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005431
EISBN: 978-1-62708-196-2
... Abstract Several methods are developed for the numerical solution of partial differential equations, namely, meshed-solution methods such as the finite-element method (FEM), finite-difference method, and boundary-element method; and numerical algorithms consisting of so-called meshed-solution...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005426
EISBN: 978-1-62708-196-2
... techniques. It introduces some common techniques for discretizing the fluid-flow equations and methods for solving the discrete equations. These include finite-difference methods, finite-element methods, spectral methods, and computational particle methods. The article describes the approaches for grid...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005533
EISBN: 978-1-62708-197-9
.... The article explains the finite-difference method, finite-element method, mutual impedance method, and boundary-element method for the numerical computation of the induction heat treating processes. It also discusses the direct and indirect coupling approaches for coupling the electromagnetic and heat...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005506
EISBN: 978-1-62708-197-9
... and trivial loading and boundary conditions. The article discusses approximate and advanced solution techniques that can be employed in practice for simulation of residual stress relief: finite-difference method and finite-element method. It also describes advanced techniques applicable to transient creep...
Series: ASM Handbook
Volume: 4C
Publisher: ASM International
Published: 09 June 2014
DOI: 10.31399/asm.hb.v04c.a0005897
EISBN: 978-1-62708-167-2
... Abstract Estimation of process parameters for selective heating and heat treating of simple- and complex-shaped workpieces in induction hardening can be accurately carried out using numerical simulation techniques such as the finite-element analysis and the finite-different method. Along...
Image
Published: 01 October 2014
Fig. 17 Probabilistic approach, which captures process variations during the carburizing operation and predicts quality variations in terms of case-depth variations. FDM, finite-difference method. Source: Ref 42 More
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005233
EISBN: 978-1-62708-187-0
... to solve the CFD equations are discussed. The article also demonstrates the application of CFD to a few casting problems. casting applications computational fluid dynamics discretization finite-difference method finite-element method finite-volume method numerical methods thermal-fluids...
Series: ASM Desk Editions
Publisher: ASM International
Published: 01 December 1998
DOI: 10.31399/asm.hb.mhde2.a0003176
EISBN: 978-1-62708-199-3
..., and the molding method used. Designers can predict the effect of the design on the structure of the final part using solidification simulation models, namely finite element and finite difference models, and rapid prototyping. The article concludes with a short note on how the quality is assured in the foundry...
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002444
EISBN: 978-1-62708-194-8
... to the CFD techniques for their solution. It introduces discretization techniques that are used by finite-difference, finite-volume, finite-element, spectral, and some particle methods. Associated concepts of numerical stability and accuracy are also reviewed. The article describes two approaches for grid...
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002446
EISBN: 978-1-62708-194-8
... that contains Δ b i . Significant disadvantages of the finite difference method exist when it is used with CAE analysis tools, namely, computational expense and lack of accuracy. Performance measures and thus the system response must be evaluated N + 1 times to compute the design sensitivity...
Series: ASM Handbook
Volume: 4A
Publisher: ASM International
Published: 01 August 2013
DOI: 10.31399/asm.hb.v04a.a0005789
EISBN: 978-1-62708-165-8
... or Dirichlet's boundary condition for the heat-conduction equation ( Eq 10 ) on [0, r n ]. Solve this problem, for example, by using the implicit finite-difference method ( Ref 19 , 20 ). In each time step, simple iterations can be used to adjust all thermal properties to new temperatures. Extend...
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002443
EISBN: 978-1-62708-194-8
... ) and: (Eq 11) B = ( 2 P L 3 ) / ( 27 π 4 E I ) Comparing this new solution to the analytical solution, deflections are everywhere within a ±1% band of the analytical solution, and peak stress differs from the accepted solution by 8%. The finite element method...
Series: ASM Handbook
Volume: 13A
Publisher: ASM International
Published: 01 January 2003
DOI: 10.31399/asm.hb.v13a.a0003596
EISBN: 978-1-62708-182-5
... methods such as finite-element methods, finite-difference methods, or boundary-element methods are applied to analyze the ECM process. A single equation has been derived ( Ref 6 ) for numerical methods analysis. It is applicable simultaneously to both the cases, that is, for f = 0 and f ≠ 0. Equation...
Image
Published: 01 August 2018
Fig. 9 Finite-element method model for Rayleigh wave incident on (a) a normal crack and (b) an inclined crack, showing the different interaction behavior More
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005540
EISBN: 978-1-62708-197-9
... include ABAQUS Explicit and LS-DYNA. The essence of the FEM, as opposed to other discrete treatments such as the finite-difference method, lies in an equivalent work principle. Continuous displacements within an element are represented by a small number of nodal displacements (and possibly other...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005503
EISBN: 978-1-62708-197-9
... a finite-difference method is used in the z -direction (thickness), making use of the same finite elements in the x - y plane for solving Eq 3 . The finite-difference method (FDM) is a relatively efficient and simple numerical method for solving differential equations. In this method, the physical...
Series: ASM Handbook
Volume: 6A
Publisher: ASM International
Published: 31 October 2011
DOI: 10.31399/asm.hb.v06a.a0005587
EISBN: 978-1-62708-174-0
... analysis of welds. Solving the Energy Equation The energy equation defined previously can now be solved for a specific welding situation. Finite-element methods (FEMs) have been the method of choice for stress analysis. Finite-difference methods (FDMs) have been the method of choice for fluid flow...
Series: ASM Handbook
Volume: 6
Publisher: ASM International
Published: 01 January 1993
DOI: 10.31399/asm.hb.v06.a0001480
EISBN: 978-1-62708-173-3
... the method of choice for stress analysis. Finite-difference methods (FDM) have been the method of choice for fluid flow. Whether the FDM or FEM method is best is an old argument. In rough terms, FEM has been used more frequently for complex geometries and for stress analysis, whereas FDM has been used more...
Series: ASM Handbook
Volume: 21
Publisher: ASM International
Published: 01 January 2001
DOI: 10.31399/asm.hb.v21.a0003387
EISBN: 978-1-62708-195-5
... problem, and a wide variety of models have been developed. This work was pioneered by Pipes and Pagano ( Ref 1 ), who used finite difference solutions to calculate free-edge stress distributions. More recent models, such as that presented by Flanagan in Ref 2 , use series solutions based on stress...