Insausti et al 2017a - Revision history

Materiales.Compuestos at 16:24, 19 September 2022

2022-09-19T16:24:18Z

Materiales.Compuestos at 16:18, 19 September 2022

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Materiales.Compuestos at 16:16, 19 September 2022

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Scipediacontent at 13:26, 29 April 2022

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Scipediacontent: Scipediacontent moved page Draft Content 746867093 to Insausti et al 2017a

2022-03-31T12:57:06Z

Scipediacontent moved page Draft Content 746867093 to Insausti et al 2017a

Scipediacontent: Created page with "== Abstract == In the formulation of the Stiffness-Force method (SFM) are taken into account the equilibrium equations and the compatibility conditions. These are obtained fr..."

2022-03-31T12:57:04Z

Created page with "== Abstract == In the formulation of the Stiffness-Force method (SFM) are taken into account the equilibrium equations and the compatibility conditions. These are obtained fr..."

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== Abstract ==

In the formulation of the Stiffness-Force method (SFM) are taken into account the equilibrium equations and the compatibility conditions. These are obtained from the principles of virtual work and complementary virtual work. The structure of the governing equation of this method is similar to that of stiffness-method (SM) as the principal unknows are the displacements. This method is equivalent to IFMD formulated by Patnaik and to the hybrid methods formulated by Pian.For the Stiffness-Force method finite element analysis, a user subroutine UEL for a four node quadrilateral element has been developed. This subroutine has been implemented in the commercial program Abaqus. The procedure followed for the analysis of the model has been:1. Analysis of the model using the program Abaqus that employs the SM in its formulation.2. Analysis of the same model using the user subroutine UEL employing the SFM.3. Comparison of the results of both analysis, using varying degrees of discretization, to those obtained by an analytical approach.This procedure has been used in the analysis of the open-hole tensile strength test of a unidirectional composite.

== Full document ==
<pdf>Media:Draft_Content_746867093native-articles-51.pdf</pdf>

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 |-
-| <span id='ZEqnNum154337'></span> <math>\left({{\int }_V\left[B\right]}^T\left[Y\right]dV\right)\left\{F^j\right\}=</math><math>\left\{P^i\right\}</math>
+| <span id='ZEqnNum154337'></span> <math>\left({{\int }_V\left[B\right]}^T\left[Y\right]dV\right)\left\{F^j\right\}=\left\{P^i\right\}</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (7)
@@ Line 133: / Line 133: @@
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 |-
-| <span id='ZEqnNum538662'></span> <math>\left({{\int }_V\left[Y\right]}^T\left[S\right]\left[Y\right]dV\right)\left\{F\right\}=</math><math>{\left[E^e\right]}^T\left\{a^i\right\}</math>
+| <span id='ZEqnNum538662'></span> <math>\left({{\int }_V\left[Y\right]}^T\left[S\right]\left[Y\right]dV\right)\left\{F\right\}={\left[E^e\right]}^T\left\{a^i\right\}</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (10)
@@ Line 230: / Line 230: @@
 En esta sección se describe la formulación del método SFM correspondiente al elemento cuadrilateral isoparamétrico bidimensional de 4 nodos que se muestra en la figura 1.
+[[File:Insausti_et_al_2017a-image23.png|centre|600x600px]]
-[[Image:Insausti_et_al_2017a-image23.png|600px]]
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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 La distribución de tensiones horizontales ''&#x03c3;<sub>x</sub>'' y verticales ''&#x03c3;<sub>y</sub>'' se indican en las figuras 4 y 5, respectivamente<span style="text-align: center; font-size: 75%;">.</span>
+[[File:Insausti_et_al_2017a-image32.png|centre|600x600px]]
-[[Image:Insausti_et_al_2017a-image32.png|600px]]
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
 <span style="text-align: center; font-size: 75%;">'''Figura 4.''' Distribución de tensiones horizontales</span> <span style="text-align: center; font-size: 75%;">''&#x03c3;<sub>x</sub>''.</span></div>
+[[File:Insausti_et_al_2017a-image33.png|centre|600x600px]]
-[[Image:Insausti_et_al_2017a-image33.png|600px]]
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">

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-| <span id='ZEqnNum658249'></span> <math>\left\{\epsilon \right\}=\left[L\right]\left[N\right]\left\{a^i\right\}=</math><math>\left[B\right]\left\{a^i\right\}</math>
+| <span id='ZEqnNum658249'></span> <math>\left\{\epsilon \right\}=\left[L\right]\left[N\right]\left\{a^i\right\}=\left[B\right]\left\{a^i\right\}</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (4)

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 ==1 Introducción==
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 |-
-| <span id='ZEqnNum153541'></span><span id='ZEqnNum560606'></span> <math display="inline">\int_V^{~}{\left\{\delta \epsilon \right\}}^T\left\{\sigma \right\}dV=</math><math>{\left\{\delta a^i\right\}}^T\left\{P^i\right\}</math>  <math></math>
+| <span id='ZEqnNum153541'></span><span id='ZEqnNum560606'></span> <math display="inline">\int_V^{~}{\left\{\delta \epsilon \right\}}^T\left\{\sigma \right\}dV={\left\{\delta a^i\right\}}^T\left\{P^i\right\}</math>  <math></math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (1)
@@ Line 105: / Line 28: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <span id='ZEqnNum209681'></span> <math display="inline">\int_V^{~}{\left\{\delta \sigma \right\}}^T\left\{\epsilon \right\}dV=</math><math>{\left\{\delta P^i\right\}}^T\left\{a^i\right\}</math>
+| <span id='ZEqnNum209681'></span> <math display="inline">\int_V^{~}{\left\{\delta \sigma \right\}}^T\left\{\epsilon \right\}dV={\left\{\delta P^i\right\}}^T\left\{a^i\right\}
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (2)

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