Huertas Esteban 2024a - Revision history

Marherna: Marherna moved page Review 901310686673 to Huertas Esteban 2024a

2024-01-27T11:49:44Z

Marherna moved page Review 901310686673 to Huertas Esteban 2024a

Marherna at 11:47, 27 January 2024

2024-01-27T11:47:15Z

MiguelHuertas at 10:44, 29 August 2023

2023-08-29T10:44:08Z

MiguelHuertas at 10:41, 29 August 2023

2023-08-29T10:41:29Z

MiguelHuertas at 10:35, 29 August 2023

2023-08-29T10:35:42Z

MiguelHuertas at 10:32, 29 August 2023

2023-08-29T10:32:32Z

Show changes

MiguelHuertas at 10:30, 29 August 2023

2023-08-29T10:30:17Z

MiguelHuertas at 10:24, 29 August 2023

2023-08-29T10:24:27Z

MiguelHuertas at 10:22, 29 August 2023

2023-08-29T10:22:47Z

MiguelHuertas at 10:08, 29 August 2023

2023-08-29T10:08:40Z

Show changes

@@ Line 11: / Line 11: @@
 [mailto:miguel.huertas-collado@airbus.com miguel.huertas-collado@airbus.com], [mailto:jose.b.martin@airbus.com jose.b.martin@airbus.com]</div>
 -->
 ==1. Introduction==

@@ Line 120: / Line 120: @@
 As it was explained in the introduction, the energy methods are typically limited to basic geometries due to the difficulty of finding a shape function that defines the panel deflection along the integration domain while fulfilling the boundary conditions. To solve this constraint, it is necessary to carry out a transformation of the domain of integration, switching from <math display="inline">(x,y)</math> to <math display="inline">(\xi ,\eta )</math> , using a variable change and a panel division that will allow to convert the holed panel into an assembly of 4 basic rectangular panels, which constitutes one of the innovations of this work.
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
 Figure 1: Panel division into sub-panels</div>
-The panel will be divided in four sub-panels so that the holed edge is split in four edges, each one belonging to one of the sub-panels. The division is made joining the center of the hole with the four corners of the panel, as shown in previous figure (1).
+Each of these sub-panels is transformed into an iso-parametric square with sides of length 2, with the new axes <math display="inline">(\xi ,\eta )</math> passing through the midpoint of each edge:[[Image:Review_901310686673-image2.png|center|480px]]<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-−
-−
-[[Image:Review_901310686673-image2.png|center|480px]]
 Each of these sub-panels is transformed into an iso-parametric square with sides of length 2, with the new axes <math display="inline">(\xi ,\eta )</math> passing through the midpoint of each edge:
-−
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
 Figure 2: Transformed element</div>
@@ Line 644: / Line 640: @@
 In order to account for all real scenarios, the number of different shapes of holes should be increased. Accessibility, associated structure and structural requirements are some of the variables when deciding the shape of the hole to be applied on the panel. The methodology to include these shapes will be the same, applying a different change of variable for each case.
 In some cases, the panel needs to be reinforced to increase its stiffness, leading to the addition of longitudinal or transverse stiffeners, as it is shown in the next figure (3):
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
 Figure 3: Thickness reinforcement around the web of the hole.</div>

@@ Line 120: / Line 120: @@
 As it was explained in the introduction, the energy methods are typically limited to basic geometries due to the difficulty of finding a shape function that defines the panel deflection along the integration domain while fulfilling the boundary conditions. To solve this constraint, it is necessary to carry out a transformation of the domain of integration, switching from <math display="inline">(x,y)</math> to <math display="inline">(\xi ,\eta )</math> , using a variable change and a panel division that will allow to convert the holed panel into an assembly of 4 basic rectangular panels, which constitutes one of the innovations of this work.
-<br/>The panel will be divided in four sub-panels so that the holed edge is split in four edges, each one belonging to one of the sub-panels. The division is made joining the center of the hole with the four corners of the panel, as shown in previous figure (1).[[Image:Review_901310686673-picture-x0000_t202.svg|center]]
+<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-Each of these sub-panels is transformed into an iso-parametric square with sides of length 2, with the new axes <math display="inline">(\xi ,\eta )</math> passing through the midpoint of each edge:[[Image:Review_901310686673-picture-Zone de texte 2.svg|center|600px]]
+Figure 1: Panel division into sub-panels</div>
 ===3.2. Strain Energy and work of the external loads===
@@ Line 445: / Line 456: @@
 |-
 |  style="text-align: center;"|BUHO
-|  style="text-align: center;width: 23%;"|[[Image:Review_901310686673-image11.png|132px]]
+|  style="text-align: center;width: 22%;"|[[Image:Review_901310686673-image11.png|132px]]
-|  style="text-align: center;width: 23%;"|[[Image:Review_901310686673-image12.png|132px]]
+|  style="text-align: center;width: 22%;"|[[Image:Review_901310686673-image12.png|132px]]
-|  style="text-align: center;width: 23%;"|[[Image:Review_901310686673-image13.png|132px]]
+|  style="text-align: center;width: 22%;"|[[Image:Review_901310686673-image13.png|132px]]
-|  style="text-align: center;width: 23%;"|[[Image:Review_901310686673-image14.png|132px]]
+|  style="text-align: center;width: 22%;"|[[Image:Review_901310686673-image14.png|132px]]
 |-
 |  style="text-align: center;"|NASTRAN
-|  style="text-align: center;width: 23%;"|[[Image:Review_901310686673-image15.png|132px]]
+|  style="text-align: center;width: 22%;"|[[Image:Review_901310686673-image15.png|132px]]
-|  style="text-align: center;width: 23%;"|[[Image:Review_901310686673-image16.png|132px]]
+|  style="text-align: center;width: 22%;"|[[Image:Review_901310686673-image16.png|132px]]
-|  style="text-align: center;width: 23%;"|[[Image:Review_901310686673-image17.png|138px]]
+|  style="text-align: center;width: 22%;"|[[Image:Review_901310686673-image17.png|138px]]
-|  style="text-align: center;width: 23%;"|[[Image:Review_901310686673-image18.png|132px]]
+|  style="text-align: center;width: 22%;"|[[Image:Review_901310686673-image18.png|132px]]
 |-
 |  style="border-bottom: 2pt solid black;text-align: center;"|Error
 |  style="border-bottom: 2pt solid black;text-align: center;"|1.2%
 |  style="border-bottom: 2pt solid black;text-align: center;"|0.8%
 |  style="border-bottom: 2pt solid black;text-align: center;"|1.4%
 |  style="border-bottom: 2pt solid black;text-align: center;"|0.8%
@@ Line 464: / Line 477: @@
-{| style="width: 100%;border-collapse: collapse;"
+<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-|-
+Table 2: Comparison for a 400x200 rectangular panel with Nx</div>
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|Table 2: Comparison for a 400x200 rectangular panel with Nx
-|-
-|  style="border: 1pt solid black;vertical-align: top;"|
-|}
-−
 ===4.2. Trapezoidal panels===
@@ Line 540: / Line 548: @@
-{| style="width: 100%;border-collapse: collapse;"
+<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-|-
+Table 3: Comparison for a trapezoidal panel with Nx, Ny Nxy</div>
-|  style="border: 1pt solid black;vertical-align: top;"|Table 3: Comparison for a trapezoidal panel with Nx, Ny Nxy
-|-
-|  style="border: 1pt solid black;vertical-align: top;"|
-|}
-−
 ===4.3. Free Edge===
@@ Line 620: / Line 623: @@
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
 Table 4: Comparison for a free-edge panel with Nx</div>
 ==5. Conclusions and future developments==
@@ Line 658: / Line 645: @@
-[[Image:Review_901310686673-picture-Zone de texte 5.svg|center|600px]]
+[[Image:Review_901310686673-image39-c.png|center|600px]]
-In some cases, the panel needs to be reinforced to increase its stiffness, leading to the addition of longitudinal or transverse stiffeners, as it is shown in the next picture (6):
+In some cases, the panel needs to be reinforced to increase its stiffness, leading to the addition of longitudinal or transverse stiffeners, as it is shown in the next figure (3):
 This scenario would be approached by placing the stiffener in one of the edges, so when the panel division is performed, the stringer is not deformed. In addition, the strain energy and the external forces work for each stiffener should be added to the overall solution.

@@ Line 120: / Line 120: @@
 As it was explained in the introduction, the energy methods are typically limited to basic geometries due to the difficulty of finding a shape function that defines the panel deflection along the integration domain while fulfilling the boundary conditions. To solve this constraint, it is necessary to carry out a transformation of the domain of integration, switching from <math display="inline">(x,y)</math> to <math display="inline">(\xi ,\eta )</math> , using a variable change and a panel division that will allow to convert the holed panel into an assembly of 4 basic rectangular panels, which constitutes one of the innovations of this work.
-<br/>The panel will be divided in four sub-panels so that the holed edge is split in four edges, each one belonging to one of the sub-panels. The division is made joining the center of the hole with the four corners of the panel, as shown in previous figure (1).
+<br/>The panel will be divided in four sub-panels so that the holed edge is split in four edges, each one belonging to one of the sub-panels. The division is made joining the center of the hole with the four corners of the panel, as shown in previous figure (1).[[Image:Review_901310686673-picture-x0000_t202.svg|center]]
+Each of these sub-panels is transformed into an iso-parametric square with sides of length 2, with the new axes <math display="inline">(\xi ,\eta )</math> passing through the midpoint of each edge:[[Image:Review_901310686673-picture-Zone de texte 2.svg|center|600px]]
-−
-[[Image:Review_901310686673-picture-Zone de texte 2.svg|center|600px]]
 Each of these sub-panels is transformed into an iso-parametric square with sides of length 2, with the new axes <math display="inline">(\xi ,\eta )</math> passing through the midpoint of each edge:
-−
 ===3.2. Strain Energy and work of the external loads===

@@ Line 120: / Line 120: @@
-[[Image:Review_901310686673-image1.png|center|600px]]
+[[Image:Review_901310686673-image1.png|center|600px]]Figure 1: Panel division into sub-panels[[Image:Review_901310686673-picture-Zone de texte 1.svg|center|Figure 1: Panel divisioooon]]As it was explained in the introduction, the energy methods are typically limited to basic geometries due to the difficulty of finding a shape function that defines the panel deflection along the integration domain while fulfilling the boundary conditions. To solve this constraint, it is necessary to carry out a transformation of the domain of integration, switching from <math display="inline">(x,y)</math> to <math display="inline">(\xi ,\eta )</math> , using a variable change and a panel division that will allow to convert the holed panel into an assembly of 4 basic rectangular panels, which constitutes one of the innovations of this work.
-[[Image:Review_901310686673-picture-Zone de texte 1.svg|center|600px]]As it was explained in the introduction, the energy methods are typically limited to basic geometries due to the difficulty of finding a shape function that defines the panel deflection along the integration domain while fulfilling the boundary conditions. To solve this constraint, it is necessary to carry out a transformation of the domain of integration, switching from <math display="inline">(x,y)</math> to <math display="inline">(\xi ,\eta )</math> , using a variable change and a panel division that will allow to convert the holed panel into an assembly of 4 basic rectangular panels, which constitutes one of the innovations of this work.
 <br/>
@@ Line 128: / Line 127: @@
-[[Image:Review_901310686673-picture-Zone de texte 2.svg|center|600px]]
+Each of these sub-panels is transformed into an iso-parametric square with sides of length 2, with the new axes <math display="inline">(\xi ,\eta )</math> passing through the midpoint of each edge:[[Image:Review_901310686673-picture-Zone de texte 2.svg|center|600px]]
 Each of these sub-panels is transformed into an iso-parametric square with sides of length 2, with the new axes <math display="inline">(\xi ,\eta )</math> passing through the midpoint of each edge:
-−
 ===3.2. Strain Energy and work of the external loads===

← Older revision	Revision as of 11:49, 27 January 2024
(No difference)

@@ Line 10: / Line 10: @@
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
 [mailto:miguel.huertas-collado@airbus.com miguel.huertas-collado@airbus.com], [mailto:jose.b.martin@airbus.com jose.b.martin@airbus.com]</div>
 '''RESUMEN:''' El análisis de estabilidad de paneles de material compuesto se calcula siguiendo básicamente dos procedimientos: modelos de elementos finitos y modelos analíticos utilizando el método de la energía. La ventaja de los modelos de elementos finitos reside en su amplia aplicación sin importar geometría, configuración o combinación de cargas. Sin embargo, tienen como inconveniente los tiempos de preparación y cálculo, así como el análisis de los resultados. Por el contrario, la ventaja de los modelos analíticos reside en la rapidez de la obtención de los resultados, pero están limitados a geometrías sencillas, tales como paneles rectangulares sin agujeros.
@@ Line 16: / Line 17: @@
 '''Palabras clave: '''método analítico, Rayleigh-Ritz, pandeo, agujeros, modelo de elementos finitos (FEM).
 '''ABSTRACT:''' The stability of composite material plates is being developed following basically two procedures: finite element analysis (FEA) and mathematical approaches using the energy method. The advantage of the finite element models is that they can be used with any geometry, configuration and load combination. However, it requires a significant pre-processing, computation and post-processing time of the results. On the other hand, analytical methods require much less time to obtain the results compared to them, but are limited to just basic geometries, such as rectangular panels without lightening holes.