Lafontaine et al 2013b - Revision history

Scipediacontent at 11:55, 20 March 2018

2018-03-20T11:55:30Z

Scipediacontent at 10:46, 20 March 2018

2018-03-20T10:46:44Z

Cinmemj: Cinmemj moved page Draft Samper 836349612 to Lafontaine et al 2013b

2018-03-06T10:28:56Z

Cinmemj moved page Draft Samper 836349612 to Lafontaine et al 2013b

Cinmemj at 13:51, 1 March 2018

2018-03-01T13:51:00Z

Cinmemj: Created page with "==On the Arc Length Method: Combining Ideas and Implementations Aspects== '''N. M. Lafontaine $^1$ , X. R. Wang $^2$ , K.F. Huang $^2$ , M. W. Yua..."

2018-03-01T11:47:34Z

Created page with "==On the Arc Length Method: Combining Ideas and Implementations Aspects== '''N. M. Lafontaine<math>^1</math>, X. R. Wang<math>^2</math>, K.F. Huang<math>^2</math>, M. W. Yua..."

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 <span style="text-align: center; font-size: 75%;">([[#fnc-1|<sup>1</sup>]]) By author's experiences, it necessary to take care about computer precision, due to sometimes the value of the quantities in quadratic equations are really small and can be lost significant digits.</span>
-===4.2 Method 2. Elimination of <math>\boldsymbol {r}^{\perp }</math>===
+===4.2 Method 2. Elimination of r<sup>⊥</sup>===
 Generally the quadratic equation [[#eq-25|25]] solved for <math display="inline">\eta _i</math> gives real roots. Since it is not possible to find a real roots to give the chosen arc length,  Lam and Morley (1992) suggested that the main problem is that the orthogonal  error <math display="inline">\boldsymbol {r}^{\perp }</math> is too large. In case that Eqn [[#eq-25|25]] leads to complex values,  the follow procedure proposed by Lam and Morley (1992) is adopted <span id='citeF-4'></span>[[#cite-4|[4]]].

← Older revision		Revision as of 10:46, 20 March 2018
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	A basic arc length algorithm implemented in NOLM program is summarized in the following box depicted in [[#6.1 Summary Arc Length Algorithm Procedure\|6.1]]. This algorithm correspond to the spherical arc-length method, however, with small change in the code, a cylindrical arc-length procedure can also be used .		A basic arc length algorithm implemented in NOLM program is summarized in the following box depicted in [[#6.1 Summary Arc Length Algorithm Procedure\|6.1]]. This algorithm correspond to the spherical arc-length method, however, with small change in the code, a cylindrical arc-length procedure can also be used .
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−	~~boxed BOXHbox BOXBox~~

	<span style="text-align: center; font-size: 75%;"> Arc length scheme.		<span style="text-align: center; font-size: 75%;"> Arc length scheme.

← Older revision		Revision as of 13:51, 1 March 2018
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−	~~==On the Arc Length Method: Combining Ideas and Implementations Aspects==~~
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−	~~'''N. M. Lafontaine<math>^1</math>, X. R. Wang<math>^2</math>, K.F. Huang<math>^2</math>, M. W. Yuan <math>^2</math> and E. Oñate<math>^{1,3}</math>'''~~
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−	~~<math>^1</math>~~
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−	~~Universidad Politècnica de Catalunya (UPC)~~
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−	~~Campus Norte UPC, 08034 Barcelona, Spain~~
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−	~~<math>^2</math>~~
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−	~~Pekin University~~
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−	~~100871 Beijing, China~~
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−	~~Web page: http://english.pku.edu.cn~~
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−	~~<math>^3</math>~~
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−	~~Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE)~~
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−	~~Universidad Politècnica de Catalunya (UPC)~~
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−	~~Campus Norte UPC, 08034 Barcelona, Spain~~
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−	~~Web page: http://www.cimne.upc.edu~~
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−	~~e-mail: maireni@cimne.upc.edu, inglafontaine@gmail.com~~

	==1 Introduction==		==1 Introduction==