Qiao et al 2017a - Revision history

Rimni at 12:05, 18 December 2018

2018-12-18T12:05:56Z

Rimni at 10:21, 1 September 2017

2017-09-01T10:21:07Z

Rimni at 10:19, 1 September 2017

2017-09-01T10:19:46Z

Rimni at 10:17, 1 September 2017

2017-09-01T10:17:15Z

Rimni: Rimni moved page Draft Samper 831316476 to Qiao et al 2017a

2017-08-30T09:22:20Z

Rimni moved page Draft Samper 831316476 to Qiao et al 2017a

Rimni at 09:21, 30 August 2017

2017-08-30T09:21:48Z

Rimni at 10:52, 28 August 2017

2017-08-28T10:52:29Z

Rimni at 10:51, 28 August 2017

2017-08-28T10:51:51Z

Rimni at 10:51, 28 August 2017

2017-08-28T10:51:01Z

Rimni at 10:49, 28 August 2017

2017-08-28T10:49:21Z

@@ Line 39: / Line 39: @@
 | [[Image:draft_Aparicio Nogué_939719944-image2.png|534px]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" | '''Figura 1:''' Local displacement and rotation at the mid-plane of a laminated composite element.
+| colspan="1" | '''Figure 1:''' Local displacement and rotation at the mid-plane of a laminated composite element.
 |}
@@ Line 96: / Line 96: @@
 | [[Image:draft_Aparicio Nogué_939719944-image7.png|480px]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" | '''Figura 2:''' Laminated composite beam element.
+| colspan="1" | '''Figure 2:''' Laminated composite beam element.
 |}
@@ Line 389: / Line 389: @@
 | [[Image:draft_Aparicio Nogué_939719944-image49.png|342px]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" | '''Figura 3:''' Rotational vector.
+| colspan="1" | '''Figure 3:''' Rotational vector.
 |}
@@ Line 421: / Line 421: @@
 | [[Image:draft_Aparicio Nogué_939719944-image57.png|600px]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" | '''Figura 4:''' Element kinematics and coordinate systems.
+| colspan="1" | '''Figure 4:''' Element kinematics and coordinate systems.
 |}
@@ Line 839: / Line 839: @@
 | [[Image:draft_Aparicio Nogué_939719944-image137.png|318px]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" | '''Figura 5:''' Geometry proprieties of laminated spherical shell.
+| colspan="1" | '''Figure 5:''' Geometry proprieties of laminated spherical shell.
 |}
@@ Line 900: / Line 900: @@
 | style="padding:10px;"|[[Image:draft_Aparicio Nogué_939719944-image143.png|416px]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" | '''Figura 6:''' Load-deflection curve of laminated composite plate.
+| colspan="1" | '''Figure 6:''' Load-deflection curve of laminated composite plate.
 |}
@@ Line 912: / Line 912: @@
 | style="padding:10px;|[[Image:draft_Aparicio Nogué_939719944-image144.png|400px]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" | '''Figura 7:''' Pinched cantilever cylinder.
+| colspan="1" | '''Figure 7:''' Pinched cantilever cylinder.
 |}
@@ Line 944: / Line 944: @@
 | [[Image:draft_Aparicio Nogué_939719944-image157.png|400px]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" | '''Figura 9:''' Geometry proprieties of double-curved thin shell structure.
+| colspan="1" | '''Figure 9:''' Geometry proprieties of double-curved thin shell structure.
 |}
@@ Line 954: / Line 954: @@
 | [[Image:draft_Aparicio Nogué_939719944-image158.png|404px]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" | '''Figura 10:''' Load-displacement curve of double-curved thin shell structure.
+| colspan="1" | '''Figure 10:''' Load-displacement curve of double-curved thin shell structure.
 |}
@@ Line 972: / Line 972: @@
 | (c) using present element (16&#x00d7;10)
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" | '''Figura 11:''' Displacements of laminated thin cylinder by 1.2 KN.
+| colspan="1" | '''Figure 11:''' Displacements of laminated thin cylinder by 1.2 KN.
 |}

@@ Line 295: / Line 295: @@
 & \frac{\partial N_i^0}{\partial y} & 0 & 0 & 0\\
 \frac{\partial N_i^0}{\partial y} & \frac{\partial N_i^0}{\partial x} & 0 & 0 & 0
-\end{array}\right]\mbox{ }(i=1,2,3,4)\\
+\end{array}\right]\\
 \overline\mathit{\boldsymbol{a}}=\left[\begin{array}{cccc}
 \overline\mathit{\boldsymbol{a}}_1 & \overline\mathit{\boldsymbol{a}}_2 & \overline\mathit{\boldsymbol{a}}_3 & \overline\mathit{\boldsymbol{a}}_4
 \end{array}\right]
-\end{array}</math>
+\end{array}\qquad (i=1,2,3,4)</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (18)
@@ Line 325: / Line 325: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math>\mathit{\boldsymbol{\epsilon }}_p=\left\{\begin{array}{c}
+| <math>\mathit{\boldsymbol{\varepsilon }}_p=\left\{\begin{array}{c}
-\mathit{\boldsymbol{\epsilon }}^0\\
+\mathit{\boldsymbol{\varepsilon }}^0\\
-\overline\mathit{\boldsymbol{\kappa}}
+\mathit{\boldsymbol{\kappa}}
 \end{array}\right\}=\left\{\begin{array}{c}
 B_e\\

@@ Line 287: / Line 287: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math>\begin{array}{c}
+| <math>\begin{array}{l}
 B_e=[\begin{array}{cccc}
 B_{e1} & B_{e2} & B_{e3} & B_{e4}
@@ Line 296: / Line 296: @@
 \frac{\partial N_i^0}{\partial y} & \frac{\partial N_i^0}{\partial x} & 0 & 0 & 0
 \end{array}\right]\mbox{ }(i=1,2,3,4)\\
-\mathit{\boldsymbol{a}}=\left[\begin{array}{cccc}
+\overline\mathit{\boldsymbol{a}}=\left[\begin{array}{cccc}
-\mathit{\boldsymbol{a}}_1 & \mathit{\boldsymbol{a}}_2 & \mathit{\boldsymbol{a}}_3 & \mathit{\boldsymbol{a}}_4
+\overline\mathit{\boldsymbol{a}}_1 & \overline\mathit{\boldsymbol{a}}_2 & \overline\mathit{\boldsymbol{a}}_3 & \overline\mathit{\boldsymbol{a}}_4
 \end{array}\right]
 \end{array}</math>
@@ Line 325: / Line 325: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math>{\epsilon }_p=\left\{\begin{array}{c}
+| <math>\mathit{\boldsymbol{\epsilon }}_p=\left\{\begin{array}{c}
-{\epsilon }^0\\
+\mathit{\boldsymbol{\epsilon }}^0\\
-\kappa
+\overline\mathit{\boldsymbol{\kappa}}
 \end{array}\right\}=\left\{\begin{array}{c}
 B_e\\
 B_b
-\end{array}\right\}a^e=B_p\overline{a}</math>
+\end{array}\right\}\overline\mathit{\boldsymbol{a}}=B_p\overline\mathit{\boldsymbol{a}}</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (20)

@@ Line 296: / Line 296: @@
 \frac{\partial N_i^0}{\partial y} & \frac{\partial N_i^0}{\partial x} & 0 & 0 & 0
 \end{array}\right]\mbox{ }(i=1,2,3,4)\\
-a^e=\left[\begin{array}{cccc}
+\mathit{\boldsymbol{a}}=\left[\begin{array}{cccc}
-a_1^e & a_2^e & a_3^e & a_4^e
+\mathit{\boldsymbol{a}}_1 & \mathit{\boldsymbol{a}}_2 & \mathit{\boldsymbol{a}}_3 & \mathit{\boldsymbol{a}}_4
 \end{array}\right]
 \end{array}</math>

← Older revision		Revision as of 09:21, 30 August 2017
Line 1:		Line 1:
−	~~Subm: 03/03/2017~~

−	~~Accep.: 06/06/2017~~
	==Abstract==		==Abstract==

← Older revision	Revision as of 09:22, 30 August 2017
(No difference)

@@ Line 929: / Line 929: @@
 ====4.2.3 Double-curved thin shell structure====
-Double-curved thin shell structure can be seen everywhere in the actual project. The numerical example is to use present element to carry out the nonlinear analysis of the double-curved structure, which is always used in many engineering structures and shows significant different nonlinear. <math>16\times 10</math> meshes and lay-ups of  <math>[45/90/0/-45]_{S}</math> are used in this analysis. The length of <math>b=2000 mm</math> and width of <math>a=1250 mm</math> are shown in Figure 9, and the radius of the two sides in the direction of width are  <math>r_1 = 318mm</math>,  <math>r_2 = 504mm</math> and  <math>r'_1 = 1015mmmm</math>,  <math>r'_2 = 772mmmm</math>, respectively, the length of the section with radius as  <math>r_1</math> in the direction of width is  <math>c=645mm</math>, the length of the section with radius as  <math>r'_1</math> in the direction of width is  <math>d=860mm</math>, the total thickness of the laminates is  <math>h=3.2mm</math>. The material properties of T700/QY9511 are used as follows:
+Double-curved thin shell structure can be seen everywhere in the actual project. The numerical example is to use present element to carry out the nonlinear analysis of the double-curved structure, which is always used in many engineering structures and shows significant different nonlinear. <math>16\times 10</math> meshes and lay-ups of  <math>[45/90/0/-45]_{S}</math> are used in this analysis. The length of <math>b=2000 mm</math> and width of <math>a=1250 mm</math> are shown in Figure 9, and the radius of the two sides in the direction of width are  <math>r_1 = 318mm</math>,  <math>r_2 = 504mm</math> and  <math>r'_1 = 1015mm</math>,  <math>r'_2 = 772mm</math>, respectively, the length of the section with radius as  <math>r_1</math> in the direction of width is  <math>c=645mm</math>, the length of the section with radius as  <math>r'_1</math> in the direction of width is  <math>d=860mm</math>, the total thickness of the laminates is  <math>h=3.2mm</math>. The material properties of T700/QY9511 are used as follows:
 {| class="formulaSCP" style="width: 100%; text-align: left;"

@@ Line 994: / Line 994: @@
 ==References==
 [1] G.A. Wempner, Finite elements, finite rotation and small strains of flexible shells, International Journal of Solids and Structures, 5 (1969) 117-153.
@@ Line 1,042: / Line 1,043: @@
 [24] P. Norachan, S. Suthasupradit, K.D. Kim, A co-rotational 8-node degenerated thin-walled element with assumed natural strain and enhanced assumed strain, Finite Elements in Analysis and Design, 50 (2012) 70-85.