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explicit numerical solution

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Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005234
EISBN: 978-1-62708-187-0
... be readily applied to modeling casting processes. The article also summarizes the key features of the conservation equations in these tools. casting modeling transport phenomena conservation equations electromagnetics explicit numerical solution thermal energy conservation solute conservation...
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
.... Advances in the technology also have moved beyond discussions on the validity of forming simulation methods, such as the debate about implicit versus explicit solution schemes and comparison or validation of results. The current focus has been on the drive to simulate the entire forming process...
Series: ASM Handbook
Volume: 14B
Publisher: ASM International
Published: 01 January 2006
DOI: 10.31399/asm.hb.v14b.a0005131
EISBN: 978-1-62708-186-3
.... The results in Fig. 6 correspond to the analytic solution as follows, where C 1 and C 2 are numerical constants: (Eq 29) ( z t ) = C 1 cosh ( y α w ) cos ( y α w )                           + C 2 sinh ( y α w...
Series: ASM Handbook
Volume: 14B
Publisher: ASM International
Published: 01 January 2006
DOI: 10.31399/asm.hb.v14b.a0005151
EISBN: 978-1-62708-186-3
.... It is true that the inertia force may be exaggerated, mostly due to user error. In that case, the quality of the solution will deteriorate. If a user chooses a proper setting so that the inertia is no more than 5%, the solution quality should be good. Static explicit codes were presented as taking...
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
... to consult the cited and Selected References at the end of the article for more information. Other approaches to engineering design that also seek the best design solution can be found elsewhere (see, for example, Taguchi methods in the article “Robust Design” in this Volume). Numerical Optimization...
Series: ASM Desk Editions
Publisher: ASM International
Published: 01 December 1998
DOI: 10.31399/asm.hb.mhde2.a0003122
EISBN: 978-1-62708-199-3
... is the registrar under ANSI H35.1 with respect to the designation and composition of aluminum alloys and tempers registered in the United States. Wrought Aluminum and Aluminum Alloy Designation System A four-digit numerical designation system is used to identify wrought aluminum and aluminum alloys...
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
... and process design Background and History Computational fluid dynamics has as its objective the numerical solution of fluid-flow equations. The calculus problem of solving a coupled system of nonlinear partial differential equations (PDEs) for the variables of interest (e.g., velocity, pressure...
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: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005528
EISBN: 978-1-62708-197-9
... validated finite-element models for analyzing the classes of shearing processes. The article also discusses the use of microstructural characterization with stereology to render three-dimensional volumetric parameters. It concludes with information on the numerical simulation of an edge-shearing process...
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
... on the solution of Maxwell's equations (MEs) and provides some basic information regarding the heat transfer and fluid equations, because these physical phenomena usually are strongly coupled to magnetic and electric fields. The solutions are usually obtained by using specific numerical methods such as finite...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005415
EISBN: 978-1-62708-196-2
... energy. In the phase-field method, nucleation has been implemented mainly in two ways: (1) numerically solving the stochastic phase-field equations with additional Langevin force terms ( Ref 52 , Ref 53 , Ref 54 , Ref 55 , Ref 56 , Ref 57 , Ref 58 ), and (2) an explicit nucleation algorithm...
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
... the concrete workpiece. In this case, a more precise hardness prediction can be expected. Numerical Solution of the Inverse Heat-Conduction Problem This section includes discussion of the simplified 1-D temperature-distribution model, the calculation of the HTC, and the finite-volume method for the heat...
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: 7
Publisher: ASM International
Published: 30 September 2015
DOI: 10.31399/asm.hb.v07.a0006033
EISBN: 978-1-62708-175-7
... of the simulation tools have selected explicit and implicit algorithms for time advancement, numerical contact algorithms for problems such as surface separation, and remeshing algorithms as required for large deformations such as seen in some sintered materials, where up to 25% dimensional contraction is possible...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005502
EISBN: 978-1-62708-197-9
... for the press and sinter simulations, developers of the simulation tools have selected explicit and implicit algorithms for time advancement, numerical contact algorithms for problems such as surface separation, and remeshing algorithms as required for large deformations such as seen in some sintered materials...
Series: ASM Handbook
Volume: 14B
Publisher: ASM International
Published: 01 January 2006
DOI: 10.31399/asm.hb.v14b.a0005168
EISBN: 978-1-62708-186-3
... Abstract This article discusses the numerical simulation of the forming of aluminum alloy sheet metals. The macroscopic and microscopic aspects of the plastic behavior of aluminum alloys are reviewed. The article presents constitutive equations suitable for the description of aluminum alloy...
Series: ASM Handbook
Volume: 13A
Publisher: ASM International
Published: 01 January 2003
DOI: 10.31399/asm.hb.v13a.a0003642
EISBN: 978-1-62708-182-5
... ). The mathematical solution is found at the intersection points, or nodes, of the mesh. The solution is numerical, because an approximate form of Laplace's equation governs variations of the solution between adjacent nodes. However, creating a finite-element mesh can be an extremely tedious and time-consuming...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005525
EISBN: 978-1-62708-197-9
.... The examples demonstrate the utility of scaling analysis to explain the fundamental physics in a process and to demonstrate the limitations of simplifying assumptions. The article concludes with information on the solidification behavior of alloys as predicted by full numerical solutions of the transport...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005238
EISBN: 978-1-62708-187-0
... into the mushy zone, and primary shrinkage depressions that affect casting shape. In addition, incompressibility of the metal in the liquid state is accounted for by increasing Poisson's ratio to close to 0.5 which sometimes makes the solution prone to numerical instability ( Ref 31 , 32 ). A third strategy...
Series: ASM Handbook
Volume: 21
Publisher: ASM International
Published: 01 January 2001
DOI: 10.31399/asm.hb.v21.a0003389
EISBN: 978-1-62708-195-5
... and Wilson ( Ref 2 ) describe numerous ways to classify the finite element (FE) formulations, even when restricting oneself to the solution of structural mechanics problems based on variational principles. A FE formulation can be displacement- based, stress-based, mixed, or hybrid. The displacement-based FE...