From: Subject: Tutorial Femap & NX Nastran sobre materiales compuestos laminares: NAFEMS Benchmark Composite Test R0031/3 Date: Wed, 17 Feb 2010 20:56:36 -0300 MIME-Version: 1.0 Content-Type: multipart/related; type="text/html"; boundary="----=_NextPart_000_00CE_01CAB013.B1C5ADF0" X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.5579 This is a multi-part message in MIME format. ------=_NextPart_000_00CE_01CAB013.B1C5ADF0 Content-Type: text/html; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable Content-Location: http://www.iberisa.com/soporte/femap/composites/nafems_benchmark_composite_test_r0031_3.htm Tutorial Femap & NX Nastran sobre materiales = compuestos laminares: NAFEMS Benchmark Composite Test R0031/3

Propiedad

Valor

Mass = density

1E-4 = lbf-sec²/in⁴

Young=92s modulus X=20 (E1)

1E7 = psi

Young=92s modulus Y = (E2)

4E6 = psi

Poisson=92s ratio X=20 (nu12)

0.3

Shear modulus X = (G12)

1.875E6 = psi

Shear modulus Y = (G13)

1.875E6 = psi

Shear modulus Z = (G23)

1.875E6=20 = psi

FEMAP & NX Nastran = Tutorial
NAFEMS=20 Benchmark Composite Test R0031/3
(Septiembre, = 2009)

1. Introducci=F3n a los Materiales = Compuestos=20 Laminares (Composites)
El t=E9rmino = "Composite" se=20 refiere a un material de ingenier=EDa que est=E1 formado por m=E1s = de un=20 compuesto o material. Para la Teor=EDa Cl=E1sica de L=E1minas el = t=E9rmino=20 Composite se aplica a un material que est=E1 compuesto de montones = de capas=20 plegadas o l=E1minas, en donde cada l=E1mina tiene sus respectivas = propiedades=20 ortotr=F3picas. Un laminado es un apilado de l=E1minas = individuales en donde=20 cada l=E1mina est=E1 orientada de forma diferente a la direcciones = del=20 material principal. El laminado est=E1 todo unido mediante una = fina capa de=20 material adhesivo que se considera que tiene espesor = cero.

L=E1minas ordenadas=20 formando un Composite

Cada capa o l=E1mina = puede considerarse=20 como un grupo de fibras unidireccionales. La posibilidad de = orientar las=20 fibras en una direcci=F3n particular permite ajustar a medida las=20 propiedades mec=E1nicas un material compuesto laminar para = soportar las=20 cargas del entorno. Los ejes principales del material de la = l=E1mina son=20 paralelos y perpendiculares a la direcci=F3n de las fibras. Las = direcciones=20 principales se denominan = como:

	=93Longitudinal=94 o = direcci=F3n-1 de=20 la = fibra
	=93Transversal=94 o = direcci=F3n- 2 de=20 la fibra para la direcci=F3n perpendicular (direcci=F3n de = la=20 = matriz)

La siguiente figura = muestra una vista=20 explosionada de tres placas laminadas con capas cruzadas = ("cross-ply"). La=20 l=E1mina-n (n =3D 1,2,3,4) de cada una de las tres configuraciones = son=20 normales al eje-Z del sistema de coordenadas indicado y los ejes 1 = y 2=20 unidos a cada l=E1mina individual denotan las direcciones de los = ejes=20 principales del material. Las direcciones de los ejes principales = del=20 material de cada l=E1mina se alternan tal como indica la palabra = "cross-ply"=20 para describir la configuraci=F3n. El plano X-Y del sistema de = coordenadas=20 est=E1 definido en el plano medio geom=E9trico del = laminado.

Vista=20 explosionada de tres placas laminadas con capas en cruz=20 ("cross-ply")

Las capas est=E1n hechas en general de fibras pegadas sobre una = matriz.=20 Si la capa es una cinta, todas las fibras est=E1n orientadas en la = misma=20 direcci=F3n. Las capas de tejido tienen fibras en dos direcciones. = Se pueden=20 utilizar numerosos materiales tanto para fibras como matrices. = Como=20 ejemplos de fibras m=E1s comunes tenemos las fibras de carbono, = vidrio,=20 boro, carburo de silicio y tungsteno. Como ejemplos de matrices = tenemos la=20 resina ep=F3xica y el aluminio.

Los materiales compuestos = estructurales est=E1n=20 formados tanto por composites como por materiales sencillos y sus=20 propiedades dependen fundamentalmente de la geometr=EDa y de su = dise=F1o. Los=20 m=E1s abundantes son los laminares y los llamados paneles=20 sandwich:

Los laminares=20 est=E1n formadas por paneles unidos entre si por alg=FAn = tipo de=20 adhesivo u otra uni=F3n. Lo m=E1s usual es que cada l=E1mina = est=E9=20 reforzada con fibras y tenga una direcci=F3n preferente, = m=E1s=20 resistente a los esfuerzos. De esta manera obtenemos un = material=20 is=F3tropo, uniendo varias capas marcadamente anis=F3tropas. = Es el caso,=20 por ejemplo, de la madera contrachapada, en la que las = direcciones=20 de m=E1xima resistencia forman entre s=ED =E1ngulos = rectos.

Los paneles=20 sandwich consisten en dos l=E1minas exteriores de elevada = dureza y=20 resistencia (normalmente pl=E1sticos reforzados, aluminio o = incluso=20 titanio) separadas por un material menos denso y menos = resistente=20 (pol=EDmeros espumosos, cauchos sint=E9ticos, madera balsa o = cementos=20 inorg=E1nicos). Estos materiales se utilizan con frecuencia = en=20 construcci=F3n, en la industria aeron=E1utica y en la = fabricaci=F3n de=20 condensadores el=E9ctricos = multicapas.

Composite tipo=20 Sandwich

2. Descripci=F3n del = Problema
Se = trata de=20 estudiar el comportamiento estructural de un composite tipo = sandwich con=20 n=FAcleo tipo panal de abeja (Honeycomb Panel) de dimensiones 10 x = 10=20 pulgadas sometido a una presi=F3n normal uniforme de 100 psi. El = Composite=20 est=E1 simplemente apoyado en las cuatro aristas. Por existir = simetr=EDa de=20 cargas y de geometr=EDa se estudiar=E1 1/4 del problema. El = espesor de las=20 l=E1minas exteriores (Face Sheet) es de 0.028 pulgas y el espesor = del n=FAcleo=20 central (Core) es de 0.750 pulgadas.

Se pide = obtener los=20 siguientes = resultados:

	Tensiones=20 SIGMA-XX y SIGMA-YY as=ED como el desplazamiento m=E1ximo en = el punto=20 medio "C" de la placa = (X=3D5,Y=3D5).
	Tensi=F3n de=20 cortadura TAU-XY en el punto "E" situado en el centro del = primer=20 cuadrante = (X=3D2.5,Y=3D2.5).

El modelo de Elementos Finitos se = crear=E1 en=20 FEMAP V10.1 y los resultados de desplazamientos y tensiones se = calcular=E1n=20 con el solver NX NASTRAN 6.1.

3. = Definici=F3n de la=20 Geometr=EDa en FEMAP
Directamente desde=20 "Geometry > Surface > Corner" definir una superficie = por=20 cuatro puntos (0,0,0), (5,0,0), (5,5,0) y (0,5,0) que es = justamente 1/4 de=20 modelo:

1/4 de placa de 5x5 pulgadas = creada en=20 FEMAP

Para tener el Punto "E" lo m=E1s sencillo es = dividir la=20 superficie en cuatro partes iguales con la orden "Geometry > = Solid=20 > Split", seleccionamos el m=E9todo "Global Plane", = partimos=20 por el plano YZ por el punto (2.5,0,0) y repetimos la orden = cortando las=20 dos superficies por el plano ZX por el punto (0,2.5,0), resultando = en 4=20 nuevas superficies:

1/4 de placa dividida en = cuatro=20 partes

4. Definici=F3n de las Propiedades = Ortotr=F3picas=20 del Material
Desde "Model = >=20 Material" definimos las propiedades de material para las = l=E1minas=20 exteriores y el n=FAcleo. Haz click en el bot=F3n TYPE y = selecciona el tipo de=20 material "ORTHOTROPIC (2D)", escribe un nombre para el = material=20 (por ejemplo "Face Sheet") y mete las siguientes = propiedades:

Propiedad

Valor

Mass = density

1E-4 = lbf-sec²/in⁴

Young=92s modulus X=20 (E1)

10 = psi

Young=92s modulus Y = (E2)

10 = psi

Poisson=92s ratio X=20 (nu12)

Shear modulus X = (G12)

10 = psi

Shear modulus Y = (G13)

3E4 = psi

Shear modulus Z = (G23)

1.2E4=20 = psi

Material Ortotr=F3pico n=BA = 2 correspondiente=20 al n=FAcleo

La secci=F3n "Limit = Stress/Strain" se=20 usa para calcular los =EDndices de fallo. Hay varios =EDndices que = Nastran=20 calcula:

<= /TR>

	Hill
	Hoffman
	Tsai-Wu,=20 y
	Maximum=20 = Strain

Tsai-Wu require meter un valor experimental = funci=F3n del=20 material, y es en la definici=F3n del material donde se debe = especificar=20 este valor. En este caso no se nos facilitan los valores l=EDmite = de tensi=F3n=20 a tracci=F3n, compresi=F3n y cortadura as=ED que no calcularemos = ning=FAn =EDndice=20 de fallo.

5. Definici=F3n del Layout del=20 Composite
Tras definir las = propiedades=20 ortotr=F3picas de los diferentes materiales que forman el = composite, pasamos=20 a definir en FEMAP c=F3mo se sit=FAan las capas laminadas mediante = el Layout=20 Editor desde "Model > Layout". Aqu=ED tenemos la = cl=E1sica=20 configuraci=F3n llamada "honeycom panel" en la que las = capas superior=20 e inferior son de un material muy r=EDgido mientras que el = n=FAcleo est=E1=20 formado por un material de bajo peso. En el campo "Material" = seleccionar=20 el material 1 correspondiente a una de las l=E1minas exteriores, = asignar un=20 espesor de 0.028 pulgadas y un =E1ngulo de 0 grados: esto = significa que la=20 direcci=F3n del material 1 de la l=E1mina exterior est=E1 alineado = con el eje-X=20 del sistema de coordenadas absoluto. Haz click sobre "New=20 Ply":

Definici=F3n de la capa =

Seguidamente definimos la capa n=BA2 = correspondiente al=20 n=FAcleo del composite: en el campo "Material" seleccionar = el=20 material 2 correspondiente al n=FAcleo, asignar un espesor de 0.75 = pulgadas=20 y un =E1ngulo de 0 grados: esto significa que la direcci=F3n de la = cinta del=20 n=FAcleo est=E1 alineado con el eje-X del sistema de coordenadas = absoluto. Haz=20 click sobre "New Ply":

Definici=F3n de la capa =

Para definir la capa n=BA3 correspondiente a = la l=E1mina=20 exterior por ejemplo selecciona la capa n=BA 1 y haz click en el = bot=F3n=20 "Copy" y seguidamente en "Paste", y tendremos creado = el=20 Layout final del Sandwich de espesor total =3D 0.806 = pulgadas:

Definici=F3n de la capa =

A la derecha del bot=F3n = "New Play"=20 tienes un icono que permite pre-visualizar el Layout, obteniendo = la=20 siguiente imagen:

Previsualizaci=F3n del = Layout del=20 Composite

El Layout de FEMAP ofrece una gran opci=F3n = para obtener=20 las propiedades isotr=F3picas equivalentes del composite. Pulsando = sobre el=20 bot=F3n "Compute" FEMAP calcula las propiedades completas = del=20 composite y las muestra en la ventana de mensajes, as=ED como en = la ventana=20 "Entity Info":

Laminate Equivalent = Properties
3=20 Plies - Total Thickness =3D 0.806=20

In-Plane = Properties
Ex =3D=20 694799.2 Ey =3D 277925.1 Gxy =3D 130282.3
NUxy =3D = 0.29999 NUyx =3D=20 0.119998
Alphax =3D 0. Alphay =3D 0. Alphaxy =3D = 0.

Bending/Flexural=20 Properties
Exb =3D 1942910. Eyb =3D 777168.8 Gxyb =3D = 364302.1
NUxyb=20 =3D 0.12 NUyxb =3D 0.299997
Alphaxb =3D 0. Alphayb =3D 0. = Alphaxyb =3D=20 0.

A = Matrix
5.80920E+5=20 6.97095E+4 0.00000E+0
6.97095E+4 2.32373E+5=20 0.00000E+0
0.00000E+0 0.00000E+0 = 1.05008E+5

B = Matrix
0.00000E+0=20 0.00000E+0 0.00000E+0
0.00000E+0 0.00000E+0=20 0.00000E+0
0.00000E+0 0.00000E+0 = 0.00000E+0

D = Matrix
8.79426E+4=20 1.05531E+4 0.00000E+0
1.05531E+4 3.51773E+4=20 0.00000E+0
0.00000E+0 0.00000E+0 = 1.58959E+4

A-Inv = Matrix
1.78569E-6=20 -5.3569E-7 0.00000E+0
-5.3569E-7 4.46413E-6=20 0.00000E+0
0.00000E+0 0.00000E+0 = 9.52313E-6

B-Inv = Matrix
0.00000E+0=20 0.00000E+0 0.00000E+0
0.00000E+0 0.00000E+0=20 0.00000E+0
0.00000E+0 0.00000E+0 = 0.00000E+0

D-Inv = Matrix
1.17957E-5=20 -3.5387E-6 0.00000E+0
-3.5387E-6 2.94890E-5=20 0.00000E+0
0.00000E+0 0.00000E+0 = 6.29092E-5

<= !--mstheme-->

6. Definici=F3n de las Propiedades=20 Laminate
Dentro de las = propiedades del=20 tipo de elemento Laminate podemos definir el par=E1metro = "BondShr=20 Allow" que permite calcular el factor de seguridad de la = uni=F3n (este=20 valor se obtiene dividiendo la tensi=F3n cortante entre capas por = el=20 par=E1metro "BondShr Allow"). Tambi=E9n aqu=ED se=20 especifica la Teor=EDa de Fallo deseada (Hill, Hoffman, Tsai-Wu o = Max=20 Strain). Estas teor=EDas de fallo producen =EDndices de fallo. = As=ED, un =EDndice=20 mayor de 1 denota fallo. Cada capa del laminado tendr=E1 un = =EDndice de fallo=20 asociado.

=20

7. Definici=F3n de la Densidad de=20 Malla
Seguidamente asignamos = la=20 densidad de malla a todas las superficies mediante "Mesh > = Mesh=20 Control > Size on Surface". Mallaremos con un tama=F1o de = elemento de=20 0.625 que corresponde a una malla de 8x8 elementos, es decir, = Tama=F1o de=20 Elemento =3D Long. Curva / N=BA de Elementos =3D 5/8 =3D = 0.625.

Definici=F3n=20 del Tama=F1o del Elemento

En FEMAP podemos pre-visualizar el n=BA de = divisiones en cada=20 curva antes de mallar mediante "F6 > Labels, Entities, = ..> Curve=20 - Mesh Size > 3..Symbols & Count > Draw Entity=20 ON". Nota: asegurarse que las curvas est=E1n visibles = mediante=20 "Ctrl-Q"

Previsualizaci=F3n del=20 n=BA de divisiones en las curvas del modelo

8. Asignaci=F3n de Atributos a las=20 Superficies
Antes de mallar = las=20 superficies asignamos la propiedad de tipo de elemento y material=20 directamente a la geometr=EDa mediante "Mesh > Mesh Control = >=20 Attributes on Surfaces". En la opci=F3n "Connect Edge = Nodes"=20 aseg=FArate de meter un valor de tolerancia razonable, por = ejemplo, 0.5, de=20 esta forma se garantiza que FEMAP mergee nodos comunes entre = superficies=20 con lados coincidentes:

9. Mallado de=20 Superficies
Mallamos todas = las=20 superficies mediante "Mesh > Geometry > Surface". = FEMAP=20 autom=E1ticamente mergea nodos coincidentes entre curvas de = superficies. Con=20 "Ctrl-Q" puedes ver los nodos y elementos del modelo con sus = etiquetas=20 respectivas:

Aprovechando la visualizaci=F3n de etiquetas de nodos = y elementos=20 vemos que el nodo#1 corresponde al Punto-E y el nodo#9 al Punto-C, = el=20 nodo#9 pertene al Elemento#16, y el nodo#1 est=E1 rodeado por los=20 elementos#1,20,36 y 64

10. Especificar el Angulo del=20 Material
Tras mallar el = composite es=20 necesario asignar a todos los elementos un =E1ngulo espec=EDfico=20 correspondiente a la direcci=F3n principal del Layout mediante = "Modify=20 > Update Elements > Material Angle". En este caso = seleccionar el=20 eje-X del sistema de coordenadas global cartesiano. Es importante=20 asegurarse que todos los elementos laminares tienen asignado un = =E1ngulo.=20 Nastran no ejecuta el an=E1lisis si los elementos no tienen = asignado un=20 =E1ngulo. Para visualizar el =E1ngulo del material ir a = "F6 >=20 Labels, Entities, ..> Element - Orientation/Shape > Show = Orientation=20 ON". Tambi=E9n es importante verificar las normales de los = elementos=20 mediante "F6 > Labels, Entities, ..> Element - Directions = >=20 Show Direction ON":

11. Aplicaci=F3n de Condiciones de=20 Contorno
La placa est=E1 simplemente apoyada en = los=20 cuatro bordes, y adem=E1s debido a la = existencia de=20 simetr=EDa de cargas y geometr=EDa estudiaremos 1/4 de modelo, = as=ED que las=20 condiciones de contorno a aplicar est=E1n resumidas en la = siguiente=20 imagen:

Condiciones=20 de Contorno

Las siguientes im=E1genes explican de forma = secuencial el=20 proceso a seguir para aplicar la condici=F3n de contorno en el = borde=20 izquierdo de la placa llamado "Apoyo Simple = (TY=3DTZ=3DRX=3D0)"=20 desde "Model > Constraint > Curve":

Definimos=20 el set de restricci=F3n n=BA1

Selecionamos las curvas a aplicar la = restricci=F3n

Definimos=20 restricciones en el sistema de coordenadas global=20 cartesiano

Repitiendo el proceso de forma ordenada para el = resto de=20 curvas del modelo tendremos el siguiente resultado final:

Resultado=20 final con todas las condiciones de contorno = aplicadas

=20 12. Aplicaci=F3n de Cargas
Desde = "Model >=20 Load > On Surface" aplicamos una presi=F3n normal uniforme = de valor=20 100 psi a todas las superficies del modelo:

Presi=F3n=20 normal y uniforme en todas las superficies

Resultado=20 de la distribuci=F3n de las cargas de presi=F3n

=20 13. Definici=F3n del Tipo de = An=E1lisis
Desde=20 "Model > Analysis" haz click en "New..." para = definir los=20 par=E1metros del an=E1lisis est=E1tico lineal SOL101 con el solver = NX Nastran.=20 Aceptamos todas las opciones por defecto y ejecutamos el = an=E1lisis haciendo=20 click sobre el bot=F3n "Analyze":

Defici=F3n=20 del An=E1lisis Est=E1tico Lineal SOL101 con NX = Nastran

../..

En la=20 =FAltima pantalla seleccionado "Results Dstination: 3..Print & = Postprocesses"
tendremos un listado completo de = resultados en el=20 fichero *.F06

q = 13.1. = Modelado de Composites en NX=20 Nastran
NX Nastran usa elementos CQUAD4, = CQUAD8,=20 CTRIA3, y CTRIA6 para modelar composites y materiales no = uniformes. NX=20 Nastran se basa en la teor=EDa cl=E1sica de l=E1minas para la = formulaci=F3n del=20 comportamiento de los elementos Shell con propiedades de = materiales=20 compuestos laminares y no uniformes.

NX Nastran permite modelar un Composite con = m=FAltiples=20 capas con un =FAnico elemento Shell con la opci=F3n PCOMP ya que = las=20 propiedades de material del compuesto laminar quedan reflejadas = por=20 completo en las matrices del m=F3dulo de elasticidad del elemento. = El=20 programa calcula autom=E1ticamente dichas matrices a partir de la = definici=F3n=20 del espesor, propiedades de material y orientaci=F3n relativa de = cada=20 l=E1mina. Una vez que el software calcule las matrices del = m=F3dulo de=20 elasticidad, se procede a ejecutar el an=E1lisis.

Debido a que las propiedades del material = del=20 compuesto laminar est=E1n completamente contenidas en las matrices = del=20 m=F3dulo de elasticidad, se puede usar un m=E9todo estandard de = obtenci=F3n de=20 resultados para calcular las tensiones en las l=E1minas = individuales as=ED=20 como las fuerzas que soporta cada l=E1mina. Por tanto NX Nastran=20 permite:

	Evaluar tensiones y deformaciones = unitarias y=20 aproximar =EDndices de fallo en capas de forma = individual.
	Calcular tensiones y deformaciones = cortantes=20 interlaminares as=ED como =EDndices de=20 = fallo.

Si la carga en la estructura excede el = l=EDmite el=E1stico=20 del material, entonces es necesario utilizar m=E9todos no lineales = para=20 predecir la naturaleza del estado de deformaci=F3n pl=E1stica = (permanente).=20 Tambi=E9n es necesario realizar un an=E1lisis no lineal si el = material=20 presenta comportamiento no lineal en su rango el=E1stico (modelo = de material=20 el=E1stico no lineal).

En an=E1lisis 2-D de composites existen dos = m=E9todos para=20 definir un laminado:

	M=E9todo PSHELL: permite introducir = directamente de=20 forma expl=EDcita las relaciones constitutivas de rigidez de = membrana,=20 flexi=F3n, acoplamiento membrana-flexi=F3n y=20 cortante.
	M=E9todo PCOMP: el composite se define = de forma=20 expl=EDcita, capa-a-capa. Cuanto se utiliza PCOMP, NX = Nastran calcula=20 las correspondientes entradas PSHELL y=20 = MAT2.

En el an=E1lisis de composites 3D, el propio = usuario=20 debe introducir la matriz de material anisotr=F3pica. = T=EDpicamente, se usa=20 MAT9 para definir la matriz del material

q = 13.2. = M=E9todo PCOMP
El m=E9todo = PCOMP es una=20 forma eficiente de introducir propiedades de materiales en = composites a=20 base de capas con fibras unidireccionales. Las entradas de PCOMP = consiste=20 en la definici=F3n del material capa-a-capa. Se puede usar PCOMP = para=20 definir el espesor, orientaci=F3n, y el n=BA de identificaci=F3n = del material de=20 cada l=E1mina individual.

Cuando se ejecuta el c=E1lculo, NX Nastran = calcula las=20 propiedades del material del composite (membrana, flexi=F3n, = cortante y=20 acoplamiento flexi=F3n-membrana) como un todo a partir de los = datos=20 especificados en la entrada PCOMP. El programa saca las = propiedades=20 calculadas en la forma de una entrada PSHELL equivalente y cuatro = entradas=20 MAT2 equivalentes, tal como muestra la siguiente figura. Si se = especifica=20 ECHO =3D PUNCH en la secci=F3n "Case Control", el programa escribe = las=20 entradas PSHELL y MAT2 en un fichero PUNCH.

Generaci=F3n=20 de entradas PSHELL y MAT2 equivalentes

INIT MASTER(S)
NASTRAN SYSTEM(442)=3D-1, SYSTEM(319)=3D1
ID Model2,Femap
SOL SESTATIC
TIME 10000
CEND
  TITLE =3D Sandwich Shell (NAFEMS Benchmark R0031/3)
  ECHO =3D NONE
  DISPLACEMENT(PRINT) =3D ALL
  SPCFORCE(PRINT) =3D ALL
  OLOAD(PRINT) =3D ALL
  GPFORCE(PRINT) =3D ALL
  FORCE(PRINT,CORNER) =3D ALL
  STRESS(PRINT,CORNER) =3D ALL
  SPC =3D 1
  LOAD =3D 1
BEGIN BULK
$ =
*************************************************************************=
**
$   Written by : Femap with NX Nastran
$   Version    : 10.10
$   Translator : NX Nastran
$   Date       : Mon Sep 14 12:42:26 2009
$ =
*********************************************************************=

../..

$ Femap with NX Nastran Property 1 : Sandwich Panel
PCOMP          1              0.            =
                            +      =20
+              1    .028      0.     YES       2     .75      0.     =
YES+      =20
+              1    .028      0.     YES
$ Femap with NX Nastran Material 1 : Face Sheet (psi)
MAT8           1    1.+74000000.      =
.31875000.1875000.1875000.    1.-4+MT    1
+MT    1      0.      0.      0.                                        =
+MA    1
+MA    1                       =20
$ Femap with NX Nastran Material 2 : Core (psi)
MAT8           2     10.     10.      0.    =
 10.  30000.  12000.      0.+MT    2
+MT    2      0.      0.      0.                                        =
+MA    2
+MA    2                       =20
../..

=20 14. Postprocesado de Resultados
La = siguiente=20 imagen muestra el aspecto que presenta el programa FEMAP with NX = Nastran=20 una vez finalizado el c=E1lculo. El m=E1ximo desplazamiento = corresponde al=20 punto-C (nodo#9) y tiene un valor de 0.123 pulgadas que = corresponde=20 exactamente con el valor objetivo de NAFEMS.

Resultados=20 de Desplazamiento M=E1ximo en el Punto-"C"

Lo primero que me gusta comprobar siempre que = realizo=20 cualquier an=E1lisis es que las reacciones resultantes est=E1n en = equilibrio=20 con las cargas aplicadas. En efecto, la fuerza aplicada es 100=20 lb/in2x5inx5in=3D2500 lb, en perfecto acuerdo con la reacci=F3n = obtenida=20 RFZ=3D2.5e3 Lb.

                * * * * * * * * * * * * * * * * * * * *
                * * * * * * * * * * * * * * * * * * * *
                * *                                 * *
                * *                                 * *
                * *                                 * *
                * *                                 * *
                * *       N X   N a s t r a n       * *
                * *                                 * *
                * *         VERSION -   6.1         * *
                * *                                 * *
                * *          JAN 19, 2009           * *
                * *                                 * *
                * *                                 * *
                * *Intel64 Family 6 Model 23 Steppi * *
                * *                                 * *
                * *Intel(R) Core(TM)2 Quad CPU Q955 * *
                * *                                 * *
                * *          Windows Vista          * *
                * *                                 * *
                * *       Compiled for X86-64       * *
                * *                                 * *
                * * * * * * * * * * * * * * * * * * * *
                * * * * * * * * * * * * * * * * * * * *
0                                                                        =
                               =20
0 RESULTANTS ABOUT ORIGIN OF SUPERELEMENT BASIC COORDINATE SYSTEM IN =
SUPERELEMENT BASIC SYSTEM COORDINATES
0                                                  SPCFORCE RESULTANT    =
  =20
  SUBCASE/    LOAD
  DAREA ID    TYPE       T1            T2            T3            R1    =
        R2            R3
0        1     FX    0.000000E+00     ----          ----          ----   =
    0.000000E+00  0.000000E+00
               FY       ----       0.000000E+00     ----       =
0.000000E+00     ----       0.000000E+00
               FZ       ----          ----       2.500000E+03  =
4.519660E+03 -2.914388E+03     ---- =20
               MX       ----          ----          ----       =
1.730340E+03     ----          ---- =20
               MY       ----          ----          ----          ----   =
   -3.335612E+03     ----  =20
               MZ       ----          ----          ----          ----   =
       ----       0.000000E+00
             TOTALS  0.000000E+00  0.000000E+00  2.500000E+03  6.250000E+03 -6.250000E+03  =
0.000000E+00

<= FONT=20 face=3D"Arial, Arial, Helvetica">

Pulsar "F5 > Deform > Contour > = Deformed &=20 Contour Data > Lam Ply1 X Normal Stress" para representar = las=20 tensiones SIGMA-XX en la capa n=BA 1. Vemos que la m=E1xima = tensi=F3n se produce=20 en el punto "C" (nodo#9, elemento#16) con un valor m=E1ximo de = 34030=20 psi:

Resultados de Tensiones = SIGMA-XX en el=20 Punto-"C"

Repetimos "F5 > Deform > Contour > = Deformed=20 & Contour Data > Lam Ply1 Y Normal Stress" para = representar las=20 tensiones SIGMA-YY en la capa n=BA 1. Vemos que la m=E1xima = tensi=F3n se produce=20 en el punto "C" (nodo#9, elemento#16) con un valor de 13294 = psi:

Resultados de Tensiones = SIGMA-YY en el=20 Punto-"C"

Con elementos Laminares Composite NX Nastran = calcula las=20 tensiones s=F3lo en el centro del elemento:

                          F O R C E S   I N   Q U A D R I L A T =
E R A L   E L E M E N T S   ( Q U A D 4 )        OPTION =3D BILIN  =20
    ELEMENT                    - MEMBRANE  FORCES -                      =
- BENDING   MOMENTS -            - TRANSVERSE SHEAR FORCES -
      ID       GRID-ID     FX            FY            FXY           MX  =
          MY            MXY           QX            QY
0        16    CEN/4  0.0           0.0           0.0           =
7.416273E+02  2.897313E+02 -1.912638E+00 -2.195387E+01 -9.208935E+00
                  25  0.0           0.0           0.0           =
7.362260E+02  2.878116E+02 -1.912638E+00 -2.195387E+01 -9.208935E+00
                   8  0.0           0.0           0.0           =
7.362260E+02  2.916510E+02 -1.912638E+00 -2.195387E+01 -9.208935E+00
                   9  0.0           0.0           0.0           =
7.470287E+02  2.916510E+02 -1.912638E+00 -2.195387E+01 -9.208935E+00
                  10  0.0           0.0           0.0           =
7.470286E+02  2.878116E+02 -1.912638E+00 -2.195387E+01 =
-9.208935E+00

 *** USER WARNING MESSAGE 6417 (SQD41)
     THE (BILIN) OPTION FOR STRESSES IS NOT AVAILABLE FOR NONLINEAR =
MATERIAL OR COMPOSITE ELEMENTS.
     USER INFORMATION: STRESS (CENTER) WILL BE APPLIED TO THOSE =
ELEMENTS.
     User information:
     CUBIC refers to corner output for element STRESS, STRAIN, and =
FORCE.
     Corner output is not available for nonlinear analysis, so only =
center stresses are computed for nonlinear CQUAD4 =
elements.

                   S T R E S S E S   I N   L A Y E R E D   C O M =
P O S I T E   E L E M E N T S   ( Q U A D 4 )
   ELEMENT  PLY  STRESSES IN FIBRE AND MATRIX DIRECTIONS    =
INTER-LAMINAR  STRESSES  PRINCIPAL STRESSES (ZERO SHEAR)      MAX
     ID      ID    NORMAL-1     NORMAL-2     SHEAR-12     SHEAR XZ-MAT  =
SHEAR YZ-MAT  ANGLE    MAJOR        MINOR        SHEAR
0       16    1   3.40298E+04  =
1.32944E+04 -8.77603E+01   -2.82061E+01 =
-1.18315E+01   -0.24  3.40301E+04  1.32940E+04  1.03681E+04
0       16    2  -2.87695E-10 -2.20519E-10  4.48237E-12   -2.82061E+01 =
-1.18315E+01   86.20 -2.20222E-10 -2.87992E-10  3.38853E-11
0       16    3  -3.40298E+04 -1.32944E+04  8.77603E+01    0.0          =
0.0           89.76 -1.32940E+04 -3.40301E+04  =
1.03681E+04

<= FONT=20 face=3D"Arial, Arial, Helvetica">

Repetimos "F5 > Deform > Contour > = Deformed=20 & Contour Data > Lam Ply1 XY Shear Stress" para = representar las=20 tensiones cortantes TAU-XY en la capa n=BA 1. En la barra de = herramientas=20 SELECT se recomienda activar el selector de entidad a Nodo y en el = Modo de=20 Selecci=F3n activar "Show Tooltips", de esta forma al = colocar el=20 cursor encima del nodo#1 nos aparece en pantalla un cuadro con = todos los=20 resultados de desplazamientos y tensiones disponibles en ese nodo. = Vemos=20 que la tensi=F3n a cortadura TAU-XY en el punto "E" (nodo#1, = elementos#1,=20 20, 36 y 64) tiene un valor de -5040 psi:

Resultados de Tensiones = TAU-XY en el=20 Punto-"E"

=20 15. Comparaci=F3n de Resultados
La = siguiente tabla=20 muestra los resultados de NX NASTRAN comparados con los valores = objetivo=20 del NAFEMS Benchmark Test No. R0031/3 (Date Issue = 17/12/98):

Tabla Comparativa de = Resultados NX Nastran=20 vs. NAFEMS"

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FEMAP & NX Nastran = TutorialNAFEMS=20 Benchmark Composite Test R0031/3(Septiembre, = 2009)

FEMAP & NX Nastran = Tutorial
NAFEMS=20 Benchmark Composite Test R0031/3
(Septiembre, = 2009)