Flores Onate 2005b - Revision history

Cinmemj at 09:39, 14 June 2019

2019-06-14T09:39:24Z

Cinmemj: Cinmemj moved page Draft Samper 933320449 to Flores Onate 2005b

2019-05-02T11:42:35Z

Cinmemj moved page Draft Samper 933320449 to Flores Onate 2005b

Cinmemj at 11:41, 2 May 2019

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Cinmemj at 11:41, 2 May 2019

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Cinmemj at 11:40, 2 May 2019

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Cinmemj at 11:39, 2 May 2019

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Cinmemj at 11:39, 2 May 2019

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Cinmemj at 11:38, 2 May 2019

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-Published in ''Recent Advances in Textile Membranes and Inflatable Structures'' Springer Verlag, pp. 69 - 88, 2005<br />
+Published in ''Recent Advances in Textile Membranes and Inflatable Structures'', Springer Verlag, pp. 69 - 88, 2005<br />
 DOI: 10.1007/1-4020-3317-6_5
 ==Abstract==

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 ==5 Concluding Remarks ==
-We have presented in the paper the formulation of a rotation-free enhanced basic shell triangle (EBST) using an assumed strain approach. The element is based on an assumed constant curvature field expressed in terms of the nodal deflections of a patch of four elements and an assumed linear membrane strain field for the in-plane behaviour. A simple and economic version of the element using a single integration point has been presented. The EBST1 element has proven to be an excellent candidate for solving practical engineering shell and membrane problems involving complex geometry, dynamics, material non linearity and frictional contact conditions. In the simulation of membranes, bending have been included to avoid massive wrinkling in the compressed zones. The inclusion of bending energy (two integration points through the thickness instead of one) represents an increase of 40% of CPU time.
+We have presented in the paper the formulation of a rotation-free enhanced basic shell triangle (EBST) using an assumed strain approach. The element is based on an assumed constant curvature field expressed in terms of the nodal deflections of a patch of four elements and an assumed linear membrane strain field for the in-plane behaviour. A simple and economic version of the element using a single integration point has been presented. The EBST1 element has proven to be an excellent candidate for solving practical engineering shell and membrane problems involving complex geometry, dynamics, material non linearity and frictional contact conditions. In the simulation of membranes, bending have been included to avoid massive wrinkling in the compressed zones. The inclusion of bending energy (two integration points through the thickness instead of one) represents an increase of <math>40%</math> of CPU time.
 ==Acknowledgments==

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 {| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"
 |-
-|[[Image:Draft_Samper_933320449-tubo3.png|600px|Inflation of a tubular arch. (a) Deflated tube. (b),(c) Deformed configuration during the inflation process. (d) Final inflated configuration]]
+|[[Image:Draft_Samper_933320449-tubo3.png|500px|Inflation of a tubular arch. (a) Deflated tube. (b),(c) Deformed configuration during the inflation process. (d) Final inflated configuration]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" | '''Figure 11:''' Inflation of a tubular arch. (a) Deflated tube. (b),(c) Deformed configuration during the inflation process. (d) Final inflated configuration

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 {| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"
 |-
-|[[Image:Draft_Samper_933320449-fig10.png|461px|Inflation and deflation of a closed tube. L=6, D=2, h=5×10⁻⁴. Left figure: results obtained with the full bending formulation. Right figure: results obtained with a pure membrane solution]]
+|[[Image:Draft_Samper_933320449-fig10.png|400px|Inflation and deflation of a closed tube. L=6, D=2, h=5×10⁻⁴. Left figure: results obtained with the full bending formulation. Right figure: results obtained with a pure membrane solution]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" | '''Figure 10:''' Inflation and deflation of a closed tube. <math>L=6</math>, <math>D=2</math>, <math>h=5\times  10^{-4}</math>. Left figure: results obtained with the full bending formulation. Right figure: results obtained with a pure membrane solution

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 {| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"
 |-
-|[[Image:Draft_Samper_933320449-fig9.png|461px|Inflation of a square airbag against an spherical object. Deformed configurations for different times. Left figure: results obtained with the full bending formulation. Right figure: results obtained with a pure membrane solution]]
+|[[Image:Draft_Samper_933320449-fig9.png|400px|Inflation of a square airbag against an spherical object. Deformed configurations for different times. Left figure: results obtained with the full bending formulation. Right figure: results obtained with a pure membrane solution]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" | '''Figure 9:''' Inflation of a square airbag against an spherical object. Deformed configurations for different times. Left figure: results obtained with the full bending formulation. Right figure: results obtained with a pure membrane solution

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 {| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"
 |-
-|[[Image:Draft_Samper_933320449-fig7.png|500px|Deflation of a circular air-bag. Left figure: results obtained with the full bending formulation. Right figure: results obtained with a pure membrane solution]]
+|[[Image:Draft_Samper_933320449-fig7.png|450px|Deflation of a circular air-bag. Left figure: results obtained with the full bending formulation. Right figure: results obtained with a pure membrane solution]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" | '''Figure 7:''' Deflation of a circular air-bag. Left figure: results obtained with the full bending formulation. Right figure: results obtained with a pure membrane solution

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 {| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"
 |-
-|[[Image:Draft_Samper_933320449-fig6.png|500px|Inflation of a circular airbag. Deformed configurations for final pressure. (a) bending effects included (b) membrane solution only]]
+|[[Image:Draft_Samper_933320449-fig6.png|450px|Inflation of a circular airbag. Deformed configurations for final pressure. (a) bending effects included (b) membrane solution only]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" | '''Figure 6:''' Inflation of a circular airbag. Deformed configurations for final pressure. (a) bending effects included (b) membrane solution only

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 {| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"
 |-
-|[[Image:Draft_Samper_933320449-fig5.png|500px|Inflation of sphere of Mooney-Rivlin material. (a)-(c) EBST1 meshes used in the analysis (d)Radius as a function of the internal pressure]]
+|[[Image:Draft_Samper_933320449-fig5.png|450px|Inflation of sphere of Mooney-Rivlin material. (a)-(c) EBST1 meshes used in the analysis (d)Radius as a function of the internal pressure]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" | '''Figure 5:''' Inflation of sphere of Mooney-Rivlin material. (a)-(c) EBST1 meshes used in the analysis (d)Radius as a function of the internal pressure

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 ===3.2 Cylindrical Roof===
-In this example an effective membrane interpolation is of primary importance. Hence this is good test to assess the rotation-free element. The geometry is a cylindrical roof supported by a rigid diaphragm at both ends and it is loaded by a uniform dead weight (see Fig.&nbsp;[[#img-4|4]].a). Only one quarter of the structure is meshed due to symmetry conditions. Unstructured and structured meshes are considered. In the latter case two orientations are possible (Fig.&nbsp;[[#img-4|4]].a shows orientation B).
+In this example an effective membrane interpolation is of primary importance. Hence this is good test to assess the rotation-free element. The geometry is a cylindrical roof supported by a rigid diaphragm at both ends and it is loaded by a uniform dead weight (see Fig.&nbsp;[[#img-4|4.a]]). Only one quarter of the structure is meshed due to symmetry conditions. Unstructured and structured meshes are considered. In the latter case two orientations are possible (Fig.&nbsp;[[#img-4|4.a]] shows orientation B).
 <div id='img-4'></div>
 {| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"
 |-
-|[[Image:Draft_Samper_933320449-fig4.png|600px|Cylindrical roof under dead weight. E=3×10⁶, ν=0.0, Thickness =3.0, shell weight =0.625 per unit area. (a)Geometry. (b)Normalized displacement of point “C” for different meshes]]
+|[[Image:Draft_Samper_933320449-fig4.png|550px|Cylindrical roof under dead weight. E=3×10⁶, ν=0.0, Thickness =3.0, shell weight =0.625 per unit area. (a)Geometry. (b)Normalized displacement of point “C” for different meshes]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" | '''Figure 4:''' Cylindrical roof under dead weight. <math>E=3\times{10}^{6}</math>, <math>\nu=0.0</math>, Thickness =3.0, shell weight =0.625 per unit area. (a)Geometry. (b)Normalized displacement of point “C” for different meshes
 |}
-Figure&nbsp;[[#img-4|4]].b shows the normalized vertical displacement of the midpoint of the free side (point-C) over both (<math display="inline">A</math> and <math display="inline">B</math>) structured and (<math display="inline">U</math>) unstructured meshes as a function of the number of free degrees of freedom. Value used for normalization is <math display="inline">u_{C}=-3.610</math> as quoted in <span id='citeF-15'></span>[[#cite-15|[15]]].
+Figure&nbsp;[[#img-4|4.b]] shows the normalized vertical displacement of the midpoint of the free side (point-C) over both (<math display="inline">A</math> and <math display="inline">B</math>) structured and (<math display="inline">U</math>) unstructured meshes as a function of the number of free degrees of freedom. Value used for normalization is <math display="inline">u_{C}=-3.610</math> as quoted in <span id='citeF-15'></span>[[#cite-15|[15]]].
 An excellent convergence of the EBST element can be seen.  The version with only one integration point (EBST1) presents a behaviour a little more flexible and converges from above.  For non-structured meshes the result converges to the reference value but a bit more slowly.