Onate Flores 2003a - Revision history

Cinmemj at 08:45, 7 June 2019

2019-06-07T08:45:02Z

Cinmemj at 12:58, 6 June 2019

2019-06-06T12:58:08Z

Cinmemj at 12:57, 6 June 2019

2019-06-06T12:57:21Z

Cinmemj: Cinmemj moved page Draft Samper 226033773 to Onate Flores 2003a

2018-05-10T14:33:44Z

Cinmemj moved page Draft Samper 226033773 to Onate Flores 2003a

Cinmemj at 14:26, 10 May 2018

2018-05-10T14:26:28Z

Cinmemj at 14:24, 10 May 2018

2018-05-10T14:24:34Z

Cinmemj at 14:20, 10 May 2018

2018-05-10T14:20:43Z

Cinmemj at 14:17, 10 May 2018

2018-05-10T14:17:26Z

Cinmemj at 14:14, 10 May 2018

2018-05-10T14:14:41Z

Cinmemj at 14:13, 10 May 2018

2018-05-10T14:13:03Z

← Older revision		Revision as of 08:45, 7 June 2019
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−	~~Published in ''Computer Methods in Applied Mechanics and Engineering'', Vol. 194 (21-24), 2406-2443, 2005<br />~~
−	~~DOI: 10.1016/j.cma.2004.07.039~~
−

	== SUMMARY ==		== SUMMARY ==

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-Published in ''Computer Methods in Applied Mechanics and Engineering'', Vol. 194 (21-24), 2406-2443, 2005
+Published in ''Computer Methods in Applied Mechanics and Engineering'', Vol. 194 (21-24), 2406-2443, 2005<br />
-−
 DOI: 10.1016/j.cma.2004.07.039

← Older revision		Revision as of 12:57, 6 June 2019
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−	Published in ''Computer Methods in Applied Mechanics and Engineering, ~~vol~~. 194, 2406-2443, 2005''	+	Published in ''Computer Methods in Applied Mechanics and Engineering'', Vol. 194 (21-24), 2406-2443, 2005
		+
		+	DOI: 10.1016/j.cma.2004.07.039

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 where <math display="inline">\Gamma _{M}</math> is the boundary of the central triangle.
-Eq.([[#eq-4|4]]) defines the assumed constant curvature field within the central triangle in terms of the deflection gradient along the sides of the triangle. Equation (4) can be found to be equivalent to the standard conservation laws used in finite volume procedures as described in [28,29].
+Eq.([[#eq-4|4]]) defines the assumed constant curvature field within the central triangle in terms of the deflection gradient along the sides of the triangle. Eq.([[#eq-4|4]]) can be found to be equivalent to the standard conservation laws used in finite volume procedures as described in [28,29].
 The computation of the line integral in Eq.([[#eq-4|4]]) poses a difficulty as the deflection gradient is discontinuous along the element sides. A simple method to overcome this problem is to compute the deflection gradient at the element sides as the average values of the gradient contributed by the two triangles sharing the side <span id='citeF-29'></span>[[#cite-29|[21,29]]]. Following this idea the constant curvature field with the element is computed as
@@ Line 176: / Line 176: @@
 The resulting Basic Plate Triangle (BPT) has one degree of freedom per node and a wider bandwidth than the standard three node triangles as each triangular element is linked to its three neighbours through Eq.([[#eq-5|5]]).
-Examples of the good performance of the BPT element for analysis of thin plates can be found in [14,21]. The extension of the BPT element to the analysis of shells yields the Basic Shell Triangle (BST) <span id='citeF-29'></span>[[#cite-29|29]]. Different applications of the BST element to linear and non linear analysis of shells are reported in [14,18&#8211;21,24,26,27].
+Examples of the good performance of the BPT element for analysis of thin plates can be found in [14,21]. The extension of the BPT element to the analysis of shells yields the Basic Shell Triangle (BST) <span id='citeF-29'></span>[[#cite-29|[29]]]. Different applications of the BST element to linear and non linear analysis of shells are reported in [14,18&#8211;21,24,26,27].
 The ideas used to derive the BPT element will now be extended to derive two families of Basic Shell Triangles using a total lagrangian description.

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 {| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"
 |-
-|[[Image:draft_Samper_226033773-fig1.png|400px|Patch of three node triangular elements including the central triangle (M) and three adjacent triangles (1, 2 and 3)]]
+|[[Image:draft_Samper_226033773-fig1.png|200px|Patch of three node triangular elements including the central triangle (M) and three adjacent triangles (1, 2 and 3)]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" | '''Figure 1:''' Patch of three node triangular elements including the central triangle (M) and three adjacent triangles (1, 2 and 3)

← Older revision	Revision as of 14:33, 10 May 2018
(No difference)

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 <li>Update the shell geometry </li>
 <li>Check frictional contact conditions </li>
 </ol>
 Further details of the implementation of the standard BST element within an explicit solution scheme can be found in [26].

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 where the influence of variations in the length of vector <math display="inline">\boldsymbol \varphi  _{^{\prime }n}</math> has been neglected.
-For a simple supported (hinged) side, the problem is not completely defined. The simplest choice is to neglect the contribution to the side rotations from the adjacent element missing in the patch in the evaluation of the curvatures via eq.([[#eq-54|54]]) <span id='citeF-29'></span>[[#cite-29|29]]. This is equivalent to assume that the gradient at the side is equal to the gradient in the central element, i.e.
+For a simple supported (hinged) side, the problem is not completely defined. The simplest choice is to neglect the contribution to the side rotations from the adjacent element missing in the patch in the evaluation of the curvatures via eq.([[#eq-54|54]]) <span id='citeF-29'></span>[[#cite-29|[21,24]]]. This is equivalent to assume that the gradient at the side is equal to the gradient in the central element, i.e.
 {| class="formulaSCP" style="width: 100%; text-align: left;"

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 <br/><br/>
-==12 Membrane strain matrix and curvature matrix for the EBST element==
+==A.2 Membrane strain matrix and curvature matrix for the EBST element==
-===12.1 Membrane strain matrix===
+===A.2.1 Membrane strain matrix===
 {| class="formulaSCP" style="width: 100%; text-align: left;"
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 |}
-===12.2 Curvature matrix===
+===A.2.2 Curvature matrix===
 {| class="formulaSCP" style="width: 100%; text-align: left;"
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 |}
 In this last expression <math display="inline">L_{i,j} =L_{i,j}^{M}</math>