Tutorial for ANSYS Espanol

®

Tutorial for ANSYS Release 6.1 Finite Element Analysis Software

For Unix Based Workstations

Truss, Frame, and Plate Examples

By Andrew R. Mondi Using examples and revisions from: Cosmos-GeoStar Tutorial  January 2000 by Keith M. Mueller  Department of General Engineering at the University of Illinois at Urbana-Champaign May 2003 Corrections: May 18 2004 ii ,

,

,

ACKNOWLEDGMENTS

This tutorial is based upon Cosmos-Geostar Tutorial written by Dr. Keith M. Mueller in January 2000. The example problems solved in that tutorial are also solved here. I tried to incorporate the strengths of  Cosmos-GeoStar Tutorial into this ANSYS tutorial even though the structure and content of each are quite different. I thank Professor David E. Goldberg for his guidance while writing this booklet. He is a skilled manager and leader. I thank Mr. Raja R. Katta for his assistance. His concise and timely explanations of difficult material in ANSYS were essential for swiftly completing this project. Also I thank Professor Thomas F. Conry for his advice and suggestions for refining and improving this tutorial. iii ,

,

TABLE OF CONTENTS

1. INTRODUCTION What is ANSYS? 1-1 Helpful Web Links 1-1 Purpose of this Tutorial 1-1 Using this Tutorial Effectively 1-1 Starting up in a Unix System 1-2 Default View in ANSYS 1-3 Familiarizing Yourself with ANSYS 1-3 2. TRUSS EXAMPLE 2-1 Preprocessing 2-1 Introduction 2-1 Modeling 2-2 Element Type 2-7 Real Constants 2-8 Material Properties 2-10 Meshing 2-12 Solution Phase 2-16 Analysis Type 2-16 Apply Constraints 2-16 Apply Loads 2-17 Apply Solution 2-19 Post-processing 2-20 Reaction Forces 2-20 Member Forces and Axial Stresses 2-20 Displacements 2-23 3. FRAME EXAMPLE 3-1 Preprocessing 3-1 Introduction 3-1 Modeling 3-1 Element Type 3-2 Real Constants 3-2 Material Properties 3-4 Define Sections 3-4 Meshing 3-5 Solution Phase 3-7 Introduction 3-7 Analysis Type 3-7 Define Frame Constraints 3-7 Define Frame Loads 3-7 Apply Solution 3-9 iv

3. FRAME EXAMPLE (continued) Post-processing 3-9 Introduction 3-9 Reaction Forces 3-10 Member Forces and Stresses 3-10 Member Displacements and Rotations 3-10 4. PLATE EXAMPLE 4-1 Preprocessing 4-1 Introduction 4-1 Modeling 4-2 Element Type 4-4 Real Constants 4-5 Material Properties 4-6 Meshing (and refining a mesh) 4-6 Solution Phase 4-8 Introduction 4-8 Analysis Type 4-8 Apply Constraints 4-8 Apply Loads 4-9 Apply Solution 4-10 Post-processing 4-10 5. APPENDIX 5-1 Working with ANSYS in Unix 5-1 Saving an ANSYS file 5-1 Opening a previously saved ANSYS file 5-1 Printing result tables 5-2 Printing graphical output 5-2 Managing your EWS Account 5-2 How to Access EWS files 5-2 Deleting EWS files in Unix 5-2 Creating Axisymmetric Models 5-3 General Notes on Understanding ANSYS 5-5 v

1. INTRODUCTION ¿Qué es ANSYS?

ANSYS es un análisis del elemento finito (FEA) el paquete del software. Usa un artefacto de software de preprocesador para crear la geometría. Entonces usa una rutina de la solución para aplicar las cargas a la geometría mallada. Finalmente los rendimientos deseados los resultan post-procesados. El análisis del elemento finito se desarrolló primero por la industria del avión para predecir  la conducta de metales cuando formó para las alas. Ahora FEA se usa a lo largo de casi todos plan de la ingeniería incluso los sistemas mecánicos y las estructuras de la ingeniería civiles. ANSYS se usa a lo largo de la industria en muchas disciplinas de la ingeniería. Este paquete del software incluso se usó por los ingenieros que investigaron el derrumbamiento de Centro de Comercio Mundial en 2001. Más información sobre el ANSYS FEA empaqueta y otros productos de ANSYS pueden encontrarse a . Los Eslabones de Tejido útiles

Otra guía didáctica de ANSYS producida por la Universidad de Alberta Canadá puede accederse a . los Eslabones y puntas del  plan pueden accederse a . Algún comentario en el matemática detrás del software de FEA por el Instituto Nacional de  Normas y Tecnología puede accederse a . ,

El propósito de esta Guía didáctica

El propósito de esta guía didáctica es guiar a los estudiantes en la Sección de Ingeniería General en la Universidad de Illinois a Urbana-Champaign a través de sus cursos de las estructuras (GE 221 y GE 232). se diseña para familiarizarse al usuario con las funciones  básicas de ANSYS el software de FEA. Los ejemplos de un braguero simple un marco (usando a los miembros de la viga) y un plato bidimensional se explora. ,

,

Usando esta Guía didáctica Eficazmente

Esta guía didáctica se diseña para que el lector complete cada ejemplo en el orden que se  presenta. Las últimas guías didáctica (el marco y plato) se asume que el usuario entiende ciertas funciones del programa cubiertas en los ejemplos más tempranos. Primero un  braguero se analiza. Esto es que los más simples de los tres modelos investigaron en esta guía didáctica. Éste también es el más largo de las tres guías didáctica porque es el de mayor detalle de los tres ejemplos y no asume cualquier conocimiento anterior del usuario. Luego un marco se explora. Aquí el usuario define secciones y rendimientos los momentos del miembro interiores y rotaciones del miembro. Completando esta guía didáctica una vez el usuario debe poder aplicar sus principios a todos los tipos de problemas de la viga dimensionales. Finalmente un plato dimensional se analiza. Este ejemplo es útil para esos usuarios que investigan concentraciones de tensión y otras propiedades de las mecánicas sólidas. 1-1

,

Poniendo en marcha en un Sistema de Unix

Después de anotar hacia el puesto de trabajo usted verá una ventana del x-térm (Figura 1-1) en la cima del escritorio: ,

Figure 1-1  x-termwindow Sugerencia en esta ventana tipo de ansys que crea una nueva ventana (Figura 1-2) en la cima del escritorio "Tansys" con los iconos cuadrados. Pulse el botón de la cima ANSYS  NOW. La nota: el icono del pregunta-marca accede la Ayuda. ,

,

,

Figure 1-2 Tansyswindow Primero una pantalla de archivo de sesión (Figura 1-3) aparece automáticamente. Usted no debe realizar ningún funcionamiento en esta ventana. Usted puede necesitar esperar por unos segundos hasta que el componente de la gráficointerface del programa lanza y usted ve la interface gráfica (Figura 1-4 en la próxima  página): 1-2 ,

Figure 1-3 Session file window

Figure 1-4 ANSYS with graphical interface La vista predefinida en ANSYS está bien preparada para los planes bidimensionales con el x-eje que apunta horizontalmente al derecho y-eje que apunta verticalmente a los pupilos y el z-eje que señala de la pantalla. El zumbido y repinta (o se refresca la pantalla) las órdenes son muy similares a aquéllos usados en most CAD o  procesador de texto software. La Vista predefinida en ANSYS

,

,

Familiarizándose con ANSYS

La manera más rápida más fácil y más lógica de usar ANSYS ha terminado el Menú Principal localizado en el lado de la izquierdo-mano lejano de la pantalla (Figura 1-5 a la izquierda). puede mirar intimidando al principio sin embargo la mirada piensa sobre la información que usted necesita resolver para todos los componentes en una estructura. Usted necesita saber la posición longitud y material de los miembros ,

,

,

estructurales la posición magnitud y dirección de todo las cargas en la estructura y los constreñimiento en la estructura. ¡Para conseguir que ANSYS trabaje apropiamente usted necesita decir esta información al programa simplemente y hará el resto para usted! ,

,

,

,

Figure 1-5 MainMenu

1-3

El Menú Principal se diseña que para que usted complete los pasos requeridos para construir su modelo empezando a la cima del menú y trabajando asihasta abajo. Para los  propósitos de esta guía didáctica usted necesitará estar familiarizado con tres de las órdenes en el Menú Principal: El Pre-procesador  Solución y Poste-procesador (nombrado como Postproc General en el ANSYS del menú principal) - como usted puede ver en Fig. 1-5 éstos son los primeros tres órdenes en el Menú Principal. La construcción se encamina para ser lograda en cada orden de la lista debajo: Preprocessor Solution ,

,

,

,

Post-processor

1. El miembro longitud 2. el miembro posición 3. el miembro material

1. la posición de Carga Consiga al miembro del desplazamiento 2. la magnitud de Carga fuerce los datos en ambos gráficos 3. la dirección de Carga y rendimiento del texto.

Usted usará este Menú Principal sólo como Explorador de Windows o cualquier otra función que es organizada en un "modo del árbol." Usted debe completar estos tres pasos del comandante: (1) Pre-procesando la fase (2) la Solución y (3) Post-procesando la fase EN EL ORDEN DADO. Si usted no lo hace ANSYS no sabrá cómo resolver su estructura propiamente y dara resultados malos. ,

,

,

El resto de esta guía didáctica lo traerá a través de tres ejemplos útiles que lo familiarizarán con ANSYS. También la información acerca de la impresión manejando su EWS consideran y otros puntos de Unix útiles están en el Apéndice al final de esta guía didáctica. ,

1-4

2.

EJEMPLO del BRAGUERO Dado el braguero cargado siguiente, encuentre las fuerzas interiores en todos los miembros y desplazamientos de todas las junturas.

Figure 2-1 Giventruss Se asumirá que los cuatro miembros diagonales son aluminio y tienen un área de 30 in2  para los propósitos ilustrativos y se asumirá que los tres miembros horizontales son acero y tienen un área de 10 in2. Mientras esto crea un braguero algo poco realista permitirá la demostración de modelar un braguero que contiene materiales diferentes y tamaños del miembro. ,

,

Recuerde: Piense sobre el proceso modelado como tener 3 pasos maximo: Preprocesando, la Solución, y Poste-procesando.

ANSYS se construye en un formato del contorno. En cada uno de estos pasos mayores hay subalterno-pasos pequeños. Esta guía didáctica se construye para imitar esta estructura del contorno. Siempre está pensando sobre dónde usted está en el proceso modelado y cómo los pasos que usted está completando son significantes y pueden usarse en otros  problemas que usted resolverá en sus clases. ,

1. Pre-procesando A. - la Introducción - se completarán varios pasos en la fase del Pre-proceso: 1. planeando (defina puntos Importantes y líneas y usando la parcela controla) 2. el Tipo del elemento (2D braguero boxea) 3. las Constantes reales (defina áreas cruz-particulares de braguero boxea) 4. enredando (una división por elemento)

2-1

El B. Planeando 1. los puntos importantes - El primer paso diseñando cualquier estructura en ANSYS es definir los puntos Importantes de la estructura. Estos puntos simulan las junturas de los miembros estructurales y también sirven como los puntos del extremo de los miembros. a. En el Menú Principal clic izquierdo señal mas al lado del Pre-procesador. Un subalterno-menú gota-bajará la inscripción todos los órdenes que usted puede usar en la fase del Pre-proceso. ,

 b. pulse el botón Izquierdo la señal mas pequeña al lado de Planear. Otro subalterno-menú de órdenes todo modelados se lista aquí. c. pulse el botón Izquierdo la señal mas pequeña al lado de Cree. Este menú lista todos los objetos que usted puede crear en ANSYS. Usted estará creando puntos y líneas. d. pulsa el botón Izquierdo la señal mas pequeña al lado de los puntos de la Llave. Pulse el  botón el icono pequeño al lado de CS Activo. La ventana automática lo incitará para un número del punto importante y un juego de coordenadas para ese punto de la llave.

Figure 2-2 MainMenu

nota: Esta sucesión de pasos que usa la a notación siguiente se resumirá: Preprocessor>Modeling>Create>Keypoints>Active CS

la ventana de Keypoints aparecerá:

Figure 2-3 Create Keypoints window

2-2

e. En esta coyuntura usted debe escoger cómo definir todos los Keypoints en su estructura. Recuerde que Keypoints representan junturas de la geometría de su estructura para que enumere TODAS las junturas en su  plan. Es a menudo mejor numerar las junturas de una manera lógica que usted puede recordar fácilmente. Para esteejemplolasjunturas se handefinidodebajo:

Figure 2-4 Given truss with numbered keypoints (joints) f. la ventana de thecreateKeypoints (Figura 2-3) le dice a ANSYS dónde su keypoints (o  junturas) se localiza. En la caja de número de punto Importante entre en un 1. En el X Y y Z coordinan el lugar de las cajas un 0. ,

,

g. Seleccione Aplique. A veces las entradas en la caja aclararán otros de ellos no se disiparán y usted debe borrarlos. ANSYS está ahora listo aceptar las coordenadas para otro  punto. ,

nota: ANSYS no trabaja en cualquiera pre-definió del sistema de u nidades - es su respon sabilidad para ser con sistente con sus unidades (es decir no entre en sus lon gitudes en los pies y cargas e n los Newton!). Para este ejemplo, nosotros usaremos las pulgadas  para la lon gitud y libras para la carga. Esta manera nosotros estaremos seguros que nuestras ten siones estarán en las unidades de psi.

h. Defina punto 2 así como usted hizo para punto 1: entre en 2 en el keypoint numere la caja a la cima y 200 en el x embale 200 en los y y 0 en la caja de z. ,

La Indirecta útil: Si usted no entra en un valor del punto ANSYS asignará un cero para ese componente de la coordenada. Así para los modelos bidimensionales usted puede dejar  siempre el espacio en blanco de caja de z-coordenada. ,

,

,

i. Defina puntos 3 y 4 como anteriormente. Una vez usted ha entrado en toda la información  para el último keypoint (punto 5) pulse el botón el "OK" el botón. Esto creará el punto y cerrará la caja del diálogo. ,

nota: Si usted selecciona "Aplique" en el último punto usted necesita entrar  no SELECCIONE "OK". En cambio escoge "Cancelación". Como mencionado antes ANSYS toma las coordenadas predefinidas como cero ,

,

2-3

 si usted aprieta "OK", ANSYS defi nirá un nuevo punto a (0,0,0 )!  La nota: Si usted  necesita quitar keypoi nts que usted ya ha creado, va a  Preprocessor>Modelin g>Delete. Usted encontrará que hay Anule órdenes que correspo nden a todos Crean los órdenes.  Ahora se han definido todos los pu ntos para nuestro braguero.

Figure 2-5 Allkeypointsdefined 2. las líneas (Definiendo a los Miembros) - En ANSYS las líneas representan a los miembros estructurales. Usted define las líneas conectando el keypoints creado  previamente. ,

a. Empieza numerando a los miembros de su estructura en su copia del papel para sus  propios archivos. Esto se haceparausteddebajo:

2-4

Figure 2-6 Given truss with numbered members  b. Vaya a Preprocessor>Modeling>Create>Lines>Lines> la Línea Recta en el Menú Principal. la ventana de crear la Línea Recta aparecerá (al derecho). c. Esté seguro que las opciones Escogen Singularice y la Lista de Artículos se seleccionen. Mueva su cursor del ratón a un Keypoint que servirá como la salida del primer miembro usted desea definir; nosotros empezaremos con miembro 1. Su cursor del ratón parecerá ser una flecha vertical pequeña que apunta el upwards. El clic salido una vez en punto 1 (0 0). UNA caja amarilla resaltará este punto. d. - el Movimiento el derecho del cursor para apuntar 2 (200 200). Izquierdo  pulse el botón una vez cerca o en punto 2. Esto define al miembro 1. ANSYS proporcionará un boceto de la vista previa de miembro 1. ,

,

,

,

Figure 2-7 Create Straight Line window

Figure 2-8 Line (member) 1 defined La nota: El proceso es el mismo por definir a todos los otros miembros: clicizquierdo una vez en el punto de salida mueva una vez al punto del extremo y de clic izquierdo. ,

2-5

e. Defina a los otros seis miembros del braguero en el orden que fueron asignados. Una vez todas las líneas (los miembros) se han definido su modelo debe parecerse al del debajo. ,

Figure 2-9 All members defined  La nota: Las lí neas (los miembros ) se denotan por L1, L2 etc . Su keypoints (las junturas )  simplemente se denotan por los números. Recuerde, puede haber u na diferencia numerando entre KEYPOINTS y NODOS (esto se discutirá después e n el detalle mayor  ). 3. usando la Parcela Co ntroles - ahora que usted ha termi nado de trazar las li neas, usted  debe familiarizarse co n helpfulviewin goption s útiles en ANSYS . a. Va al menú de la Parcela e n la barra del menú a la cima de su pa ntalla.

Figure 2-10 Plot command on the menu bar   b. Seleccione el primer orden adelante el drop-down menú Replot. Vea que las líneas y quizás sus keypoints han desaparecido. Para ver a su modelo usted debe cambiar los mandos de plotcontrols. c. En plotdrop-down menú seleccione lines. Ahora usted debe poder ver a su modelo. d. Vaya al menú de PlotCtrls (al derecho del plotmenú ) y seleccionenumbering. la ventana theplotnumberingcontrols se abriráautomáticamente ,

,

2-6

Figure 2-11  Numbering window e. Encienda el Keypoint y la Línea numera opciones y OK selecto. Ahorausted debe  poderversubragueronumeradocompletamente. La nota: A lo largo de esta guía didáctica usted puede necesitar a Replot sus varios ejemplares para conseguir una representación visual buena de su modelo. Sepa que usted puede encender y apagar los componentes visuales de su ejemplar usando las opciones abajo de Plot y PlotCtrls comandos en la barra de menú de arriba C. Tipo de elemento 1. vaya a Preprocessor>ElementType>Add/Edit/Delete en el Menú Principal. La ventana de Tipo de Elemento se abreautomáticamente.

Figure 2-12 Element Type window 2. Seleccione ³Add...´ la ventana ElementType Library se abre automáticamente.

2-7

Figure 213 Element Type Library window 3. En esta ventana ponga lo siguiente : a. Seleccione "link" en el cuadro de la parte izquierda. Esto significa que este elemento será un eslabón del braguero.  b. Seleccione "2D spar" en el cuadrado de la derecha. Esto les obligará a sus miembros del braguero a que sean cambiados de sitio en 2 dimensiones. c. Salga el predefinido 1 para el elemento referencia tipo número. d. Selecccione OK  esto cerrará la ventana de la Biblioteca. e. Usted volverá la ventana tipo de elemento (Figura 2-12). Pulse el botóncerrar. ,

D. Real Constants - next you must define the cross-sectional areas for the members of  your truss. 1. Go to Preprocessor>Real Constants>Add/Edit/Delete in the Main Menu. The Real Constants window will pop-up.

Figure 2-14 Real Constants window 2. Seleccione Agregue... para que el Tipo del Elemento de las Constantes Real la ventana se abre automáticamente. 2-8

Figure 2-15 Element Type for Real Constants window 3. Note que "Tipo 1 - LINK1" ya se resalta.seleccione OK. La ventana de las Constantes Fijas sale automáticamente.note que usted está en la Real Constante Número 1.

Figure 2-16 Set Constants window 4. Entre en la siguiente ventana de las Constantes Fijas: a. Entre en el área cross-sectional para Al (30) [en las unidades de in2].  b. la Tensión Inicial es 0. c. Pulse en el botón Aplique. Esto guardará la información para aluminio. ANSYS se  prepara recibir el juego de constantes reales para acero ahora (tipo 2). d. note que la Constante Real Puso a No.2 e. Entre en el área cross-sectional para acero (10) [en las unidades de in2]. f. la tensión Inicial a 0

2-9

window with those for steel

Figure 2-17 Set Constants

g. Pulse el botón OK. el cuadro se cerrará y usted devolverá a la ventana de las Constantes Reales. h. Pulse el botón cerrar en la ventana de las Constantes Real. Hay dos juegos de constantes reales ahora para área cross-sectionalr definida (uno para cada material). E. las Propiedades Materiales - ahora usted debe definir los materiales que constituyen a sus miembros del braguero. Recuerde que los miembros diagonales son aluminios y los miembros horizontales son acero. 1. vaya a Preprocessor>Material Props>Material Models. La ventana de Conducta Material aparecerá. Esta ventana esta dividido en dos regiones: Los Modelos materiales Definieron en la izquierda y Modelos del Material Disponible en el derecho. Note que "Material 1" ya se ha creado - ANSYS está esperando para que usted pueda definirlo.

Figure 2-18 Material Model Behavior window 2. en esta ventana clic izquierdo en Material 1 para que se resalte (esto ya puede hacerse). 3. en el lado de la derecha de clic doble en Structural>Linear>Elastic>Isotropic. Esto lanzará una nueva ventana automática las Propiedades Materiales para el Material Número ,

12-10

Figure 2-19 Material Properties for Material Number 1 4. El cuadro de EX es para el Módulo Elástico del material. PRXY es para la Proporción de Poisson. Para todos los modelos bidimensionales (cuadros) la proporción de Poisson no se usa para que no tiene que ser entrado pero es una idea buena para estar en el hábito de entrar en él. Para este ejemplo  permítanos hacer Material 1 compórtese como aluminio con un Módulo Elástico de 10 000 000 psi (10 000 ksi). a. ingrese en 10000000 en la caja de EX  b. ingrese 0.3 en el cuadro de PRXY c. Seleccione OK. Usted volverá a la ventana de Defina Conducta Material. d. Seleccione el Material en el menú drop-down en la esquina de la izquierda superior de la ventana y selecciona al Nuevo Modelo. Una ventana automática que le pide un ID para el Material pulse el botón OK (el número predefinido es suficiente).

,

,

,

,

,

,

,

,

Figure 2-20 Material Menu location in Define Material Behavior window

Figure 2-21 Material ID window 5. En la ventana de Material ModelBehavior (Figura 2-18) pulsa el botón en Material 2 en el cuadro de la izquierda para que se resalte. La nota: nosotros seguiremos los mismos pasos para definir Material 2 (acero) como nosotros hicimos para Material 1 (aluminio).

2-11

6. En el cuadro de la derecha de clic doble en Structural>Linear>Elastic>Isotropic (esto ya  puede hacerse). La ventana de propiedades para las Propiedades Materiales para el Número del Material 2 sale automáticamente (Figura 2-19). 7. defina el módulo elástico (EX) para ser eso de acero para este ejemplo (30000000 psi) y la proporción de Poisson (PRXY) para ser 0.3. 8. OK seleccione y termina fuera de esta ventana pulsando el botón en la caja íntima o la Salida seleccionando en el Menú Material. F. Meshing - la función de la Malla es el corazón de ANSYS! Enredar es como la ruptura de su estructura en pedazos pequeños que ANSYS puede reconocer y entonces "encolando" estos pedazos de su modelo juntos. Una vez esto está completo es difícil de tirarlo aparte  para que usted debe salvar a su modelo AHORA (ve Apéndice página 5-1 si usted ya no sabe hacer esto). 1. vaya a Preprocessor>Meshing>Mesh Attributes>Picked Línes. La Línea pico Atributos ventana sale automáticamente. EstéseguroqueEscoge y Solo se selecciona. ,

,

,

Figure 2-22 Pick Line Attributes 2. en el workspace nota que el ratón será un negro pequeño que apunta la flecha hacia arriba. 3. selecto linea 1 3 5 y 7 (todas las diagonales) cada uno con un solo clic izquierdo. ,

,

,

,

La nota: Usted puede querer volverse línea que numera bajo PlotCtrls>Numbering  para ver la línea que numera si esto ya no se hace. 4. OK selectcione en la Línea Atribuye la ventana.la ventana que define los Atributos de Línea sale automáticamente. 2-12

Figure 2-23 Define Line Attributes window for material 1 (aluminum) 5. En esta ventana usted puede poner el Número Material número constante Real y tipo del Elemento para las líneas que usted seleccionó. Desde que usted seleccionó a todos los miembros aluminios defina estas líneas de acuerdo con: ,

,

a. el Número Material = 1  b. el Número Constante Real = 1 c. el tipo del Elemento = 1 d. esta no necesita de definir la Sección del Elemento. e. Seleccione Aplica para que usted vuelva a la Ventana de Línea de Pico. 6. seleccione con un clic del ratón izquierdo todos los miembros de acero (2 4 y 6). Ahora usted está listo definir las propiedades materiales para los miembros de acero. ,

,

7. OK seleccione en la Línea Atribuye la ventana. la ventana que define los Atributos de Línea sale automáticamente.

Figure 2-24 Define Line Attribute window for material 2 (steel)

2-13

8. Defina estas propiedades para los miembros de acero: a. el Número Material = 2  b. la Constante Constante Real = 2 c. el Tipo del Elemento = 1 d. OK Seleccione. Esto cerrará esta ventana y la la ventana de la Línea Attributes Attributes (si usted ya lo ha hecho no es necesario). 9. vaya a Preprocessor>Meshing>Size Controls>ManualSize>Lines> All lines. La ventana de Tamaño de Elemento sale automáticamente.

Figure 2-25 Element Size window 10. Ponga el número de divisiones por línea (NDIV) a 1. Las otras cajas deben  permanecer pálidas. 11. OK seleccione esto cerrará la ventana. Note que las líneas de su braguero aparecerán más corto que antes (vea debajo): ,

Figure 2-26 Truss after number of divisions per element are set to 1

2-14

 La nota: Este completamente seguro que su modelo es correcto ANTES DE QUE  usted lo enrede juntos (los pró ximos pasos ). Usted no puede poner las cargas e n  su modelo o desplazamie desplazamientos del hallazgo de nodos hasta que se e nrede. Este  paso es el corazó corazó n de ANSY ANS YS . Podría ser u na idea buena para guardar su braguero ahora. 12. Vaya a Preprocessor>Meshi n g>Mesh>L  g>Mesh>Liines. La ventana Pick MeshLines sale automáticame nte. Estéseguroqueescoge y solo se seleccio na.

Figure 2-27 Pick Mesh Lines window 13. Seleccione cada línea individualmente con un solo clic izquierdo. Su ratón debe  parecerse una flecha apuntando apuntando ascendente. ascendente. 14. Una vez su braguero entero este completamente resaltado seleccione OK en la ventana Meshlines. ,

15. Su braguero parecerá ser un color ahora y conectará gusta antes. ¡Ésta es una indicación que su Malla tuvo el éxito.

Figure 2-28 Fullymeshedtruss Esto completa la fase de Preprocessing. Su modelo está ahora completo y está listo ser  cargado. AhoravayaEscalonar 2 la Fase de la Solución. ,

2-15

II. La Fase de la solución - aquí usted estará aplicando cargas y constreñimiento a su  braguero. A. tipo de Análisis 1. vaya a Solution>Analysis Type>New Analysis in the Main Menu. La ventana de Tipo de Análisis sale automáticamente.

Figure 2-29 Analysis Type window 2. Seleccione Static and OK. B. Aplicando los Constreñimientos 1. usted puede querer encender su elemento numerando a través de PlotCtrls>Numbering y  poniendo Elem. Attrib. Numerando a los Números del Elemento. Luego vaya a Solution> Define Loads >Apply> Structural> Displacement>On Keypoints.Aplique U en la ventana de KP sale automáticamente. EstéseguroqueEscoge y Solo se enciende. ,

Figure 2-30 Apply U on KP¶s window

2-16

2. Select node 1 (coincident with the origin) with a left click near or on the point. Doing so will highlight the point with a small yellow box. 3. In the Apply U on KP¶s window select Apply. The Define Constraints window will pop-up. ,

Figure 2-31 Define Constraints window 4. Set the following: a. UY  b. Apply as a constant value c. Displacement value = 0 d. Leave KEXPND option as default. e. Select Apply this will close the Define Constraints window (Figure 2-31).  Note there is now a small triangle under node 1. 5. The Apply U on KP¶s window (Figure 2-30) should still be available. Now select node 5 (far right and bottom of truss). Doing so will highlight the point with a small yellow box. 6. Select Apply. The Define Constraints window (Figure 2-31) will pop-up. 7. Select the following: a. UX and UY  b. Apply as a constant value c. Displacement = 0 d. Leave KEXPND option as default. e. Select OK  this will close the Define Constraints window and the Apply U on KP¶s window. Note there are two small triangles (one horizontal and another vertical) under node 5. ,

,

C. Apply Loads 1. Go to Solution>Define Loads>Apply>Structural>Force/Moment>On Keypoints in the Main Menu. The Apply F/M on KP¶s window will pop-up. Be sure that Pick and Single are selected.

2-17

Figure 2-32 Apply F/M on KP¶s window 2. Select node 2; it will be highlighted by a small yellow box as before. 3. Select Apply in the Apply F/M window. The Define F/M on KP¶s window will  pop-up.

Figure 2-33 Define F/M on KP¶s window 4. Select the following: a. FX  b. Apply as constant c. Magnitude = -400 [units of lb ]. f 

d. Select Apply. This will close the Define F/M window (Figure 2-33) but will leave the Apply F/M window open. 5. Now select node 2 again and Apply in the Apply F/M window (Figure 2-32). The Define F/M window (Figure 2-33) will pop-up. 6. Select the following: a. FY  b. Apply as a constant c. Magnitude = -300 [units of lb ]. f  d. Select OK. This will close both the Define F/M and Apply F/M windows.

2-18

7. Repeat this process (steps 5 and 6) for node 3 (load = -1000) [units of lb ]. After  f  doing so your truss should look like the one below. ,

Figure 2-34 Fully constrained and loaded truss D. Apply Solution 1. Now your truss is fully constrained and loaded. You are now ready to have ANSYS actually solve the truss. Go to Solution>Solve>Current LS in the Main Menu. The Solve Current Load Step window will appear. Select OK.

Figure 2-35 Solve Current Load Step window

2. Then ANSYS will solve the truss. It may take a few seconds before both of the following windows appear. You may close them both.

Figure 2-36 Solution windows.

2-19

This completes the Solution Phase. You are now ready for the final step Post-processing. ,

III. Post-processing - this is the last step of the three major analysis steps in ANSYS. In this section we will order ANSYS to output internal member forces member axial stresses and node displacements. ,

,

A. Reaction Forces 1. Go to General Postprocessor>List Results>Reaction Solution. In the pop-up window select All items and OK. The Reaction Solution window will pop-up.

2-37 Reaction Solution Table 2. Note that the reaction solution results are listed by node number. You can see the node numbering on your truss by going to Plot Controls>Numbering>Nodes (this may not be necessarily the same as the Keypoint numbers). B. Member Forces and Axial Stresses 1. Go to General Postproc>Element Table>Define Table. The Define Element Table window will pop-up.

Figure 2-37 Define Element Table window 2. Select ³Add...´. The Define Additional Element Table Items window will pop-up.

2-20

Figure 2-38 Define Additional Element Table window 3. Set the following a. In the ³User Label for item´ box type ³Axial Stress´.  b. In the left hand box scroll to the bottom and select ³By sequence num´. c. In the right hand box select LS. d. Place a ³1´ after the comma in the Selection box in the lower right. e. Select OK. You will return to the Element Table Data Window. 4. Select ³Add...´ this will launch the Additional Elements window again. ,

,

Figure 2-39 Define Additional Element Table window 5. Set the following: a. In the User label item set the name to ³member forces´.  b. Set ³By sequence num´ in the left hand box (may already be done). c. Select SMISC in the right hand box. d. Place a 1 next to SMISC in the selection box after the comma. e. Select OK. This will close the window. 6. Close element Data Table.

2-21

7. Go to General Postproc>Elem Table> List Elem Table. The List Element Data windowwills pop-up.

Figure 2-40 List Element Data 8. Select Member Forces and Axial stresses by left clicking on each - the two quantities you defined. They should be at the top of the listing. 9. Select OK. This will close the window. Your element table will appear. Note how the values are listed. The element numbers are in the first column followed by the Member Forces and Axial Stresses.

Figure 2-41 Element Table 10. To output this data go to the File at the top of the window. You can save it to your EWS account or print the data (if you do not know how to do this see Appendix page 5-2). ,

,

11. You can also get a visual representation of your truss using some of the graphical results options. Go to General Postproc>Element Table>Plot Elem Table. The Contour Plot of Element Table window will pop-up.

2-22

Figure 2-42 Contour Plot of Element Table window 12. In the ³Item to be plotted´ box (Fig. 2-42) you can choose what you would like to output. For this example we will plot member forces. Leave the lower box as ³No - do not average´. 13. Click OK. This will close the window.

Figure 2-43 Contour Plot of Truss 14. You should now be able to see a deformed truss with the member forces plotted.  Note that along the bottom you can see that the element forces correspond to the certain colors of the plot. C. Displacements 1. General Postproc>Plot Results>Deformed shape. The Plot Nodal Solution windows will pop-up.

Figure 2-44 Plot Nodal Solution window

2-23

2. Choose your plot preference; for this example plot ³deformed and undeformed.´ 3. Click OK. This will close the window.

Figure 2-45 Deformed and undeformed truss 4. To see the values of the deformations go to General Postproc>List Results>Nodal Solution. The Nodal Solution window will pop up.

Figure 2-46 Nodal Solution window 5. Set DOF solution in the left box and ³All dofs´ in the right box 6. Click OK. This will close the window and create a table of displacement results.

Figure 2-47 Displacement Table This completes the Post-processing. You should now move on to the FRAME example. 2-24

3. FRAME EXAMPLE

As you should already know the major difference between trusses and frames is that members are beams and thus can have a reaction moment. The following frame will be constructed: ,

Figure 3-1 Given Frame Once again a complete finite element analysis in ANSYS has three components: Preprocessing, Solution, and Post-processing. This tutorial assumes that you have already worked through the truss tutorial. Consequently procedures that are the same or very similar to those in the truss example will not be outlined in much detail. ,

,

The greatest differences between the frame and truss examples occur in defining and assigning member properties and applying loads (in this case a distributed load). You will find that many of the steps in this tutorial are similar to those in the truss. I. Preprocessing A. Introduction ± think about the steps that you will complete in this section of the tutorial and how they are similar or different from the truss tutorial. The steps to be completed in this phase are listed below. 1. Modeling (similar) 2. Element Type (different - beam) 3. Real Constants (similar - cross sectional area) 4. Material Properties (similar) 5. Sections (new) 6. Meshing (similar) B. Modeling ± none of the principles used in this example are different from the truss. Try to complete this without help of the tutorial. 1. Go to Preprocessor>Modeling>Create>Keypoints>Active CS. The coordinates for the Keypoints are:

3-1

2. Connect the Keypoints with lines from Preprecessor>Modeling>Create> Lines>Lines>Straight lines. C. Define the Element Type ± this frame is composed of beams. 1. Go to Preprocessor>Element Type>Add/Edit/Delete on the Main Menu. The Define Element type window will appear. 2. Click Add... the Library of Element Types window will pop-up.

Figure 3-2 Library of Element Types Window 3. Select Beam in the left-hand box and 2D Elastic in the right. 4. Select OK. This will close the window and return you to the Element Types window. Close this window as well. D. Define Real Constants 1. Go to Preprocessor>Real Constants>Add/Edit/Delete in the Main Menu. The Real Constants window will pop-up. 2. Select Add. Another window will appear prompting for which beam to select. You will only have one choice since you have only defined one type of beam. 3. Select OK. The Real Constants for a Beam window will appear.

3-2

Figure 3-3 Define Real Constants

for a Beam

4. In this window you define all of the constants for members 1 and 5. Real Constant set number 1 will correspond to the W8x42 beam used for members 1 and 5. Define this beam: a. Real Constant Set No. = 1  b. Cross-sectional area = 20 c. Moment of Inertia = 8000 d. Height = 8 e. Shear deflection constant = 0 f. Initial strain = 0 g. Added mass/unit length = 42 lb /ft. = 3.5 lb ./in. m m ( I n British units, lb and lb have the same numerical value.)  f  m h. Select Apply. Just like entering in Keypoint coordinates ANSYS is now ready to accept the constants for the second and third types of beams. ,

 Note: Remember that you are workin g this problem in lb and INCHES . Often tables will   f 

report these values i n other unit sets such as ³Added mass/u nit len gth´ in lb  /ft . Pay close m

attention to your units! Also, in the British system, u nits of force are i n lb and units of mass  f 

are in lb . m

5. Repeat step 4 for the other two beam types with values from the following table. Once you are complete select OK and close out of the Real Constants boxes.

3-3

E. Define Material Properties 1. Go to Preprocessor>Material Props>Material Models in the Main Menu. The Define Material Properties window will appear. 2. Define the material just as you defined steel or aluminum in the truss example. Double click in right hand box Structural>Linear> Elastic>Isotropic. Enter E (EX=30000000) and Poisson's Ratio (PRXY=0.3) and Exit. F. Define Sections ± this section tells ANSYS what sort of beam you are using. In this example we will use traditional I beams. 1. Go to Preprocessor>Sections>Beam>Common Sectns. The Beam Tool window will appear.

Figure 3-4 Beam Tool

3-4

2. For clarity let us have the dimensions of each beam correspond with the same Real Constant Set. For the W 8x42 beam (Real Constant set 1) enter the following: a. ID = 1  b. Name = W8x42 c. Sub Type = I (from drop-down menu) d. Offset to centroid e. W1 = W2 = W3 = 8 f. T1 = T2 = T3 = 1 g. Select Apply. This will save the information for the W 8x42 beam. ,

 Note: all of these dimen sion values are e x pressed in units of inches.

3. Repeat step 4 for the other two beam types with values from the following table. Once you are complete select OK.

G. Meshing 1. Go to Preprocessor>Meshing>Size Cntrls>ManualSize>Lines>All lines in the Main Menu. The Element Size box will appear. Set the number of divisions (ndiv) to 25. Leave the other boxes blank and select OK. Your frame will now appear to be of dashed lines.  Note: The ndiv function divides the eleme nt into small pieces, ³fi nite elements´. For the truss, we set the number of division s per element to 1. It was not necessary for a n y further  division s because in a truss there are no inter nal moments or rotation s that need to be calculated . For this frame e xample (and for all structures that have members with i nter nal   forces that vary with position , such as beams ) we need to be able to calculate i nter nal  moments, rotation s, and other structural properties so we need several eleme nts per part to  get accurate results. Thus we have selected 25 divisio n s per element as a good ma nageable value.  Also note that you could choose a differe nt number of divisio n s per element . Just remember  that your results may be less accurate with fewer fi nite elements. However, do not create too man y elements as your analysis will become computatio nally more e x pen sive possibly causin g the program to crash or freeze. This is also why it is so importa nt to save ofte n while conductin g your analysis and especially before Meshi n g !

3-5

2. Go to Preprocessing>Meshing>Mesh Attributes>Picked lines a select lines box will appear. Select lines 1 and 5 with a single left click. The members will be highlighted. 3. Select Apply in the pick lines box. The Line Attributes box will appear. ,

Figure 3-5 Line Attributes window 4. Set the following: a. Material number = 1  b. Real Constant number = 1 c. Element type number = 1 d. Element section = W8x42 e. Select Apply. This will close the Line Attributes window. 5. Repeat this process for the other members in the frame assigning the following constants:

6. It is always a good idea to save your project before meshing ± do this now. 7. Go to Preprocessor>Meshing>Mesh>Lines. Select all of the lines and OK. If the mesh was successful the frame will made of blue-green solid lines.

3-6

II. Solution A. Introduction ± the most significant change from the truss tutorial is the presence of  the distributed load. 1. Analysis Type (similar - static) 2. Define Frame Constraints (different - three fixed ends) 3. Define Frame Loads (different - distributed) 4. Apply Solution (similar) B. Analysis Type ± just like in the truss tutorial this is a static analysis. 1. Go to Solution>Analysis Type>New Analysis in the Main Menu. The Analysis Type window will appear. 2. Select the first option Static and OK. C. Define Frame Constraints ± we will fix the three bottom ends of the frame. 1. Go to Solution>Define Loads>Apply>Structural>Displacement>On Keypoints in the Main Menu. Just as with the truss tutorial a selection box will appear. 2. Single left click on all three bottom nodes; each will be highlighted by small yellow boxes. Select OK in the selection box. The Apply Constraints box will appear. ,

,

,

,

Figure 3-6 Apply Constraints window 3. Select All Degrees of Freedom (All DOF) since all of the free ends are fixed and constrained in the x y and rotational directions. 4. Apply as a constant value of 0. 5. Select OK. You should see two small green triangles and little red crosses indicating these are constrained in all three directions at each end. ,

D. Define Frame Loads ± unlike in the truss that contained all point loads you will need to apply a distributed load to the frame. This will be simulated by applying a load to each node. ,

1. Go to Solution>Define Loads>Apply>Structural>Pressure>On Beams. The Apply Pressure on Beams selection window will appear.

3-7

Figure 3-7 Apply Pressure on Beams selection window 2. In this case change the select style option to BOX (not Single). 3. In the workspace highlight all of the nodes on the top of the frame where the distributed load will be applied by enclosing this area in a box. You make the  box by holding down the left mouse button and dragging. ,

Figure 3-8 ANSYS workspace window after the top of the frame is selected for application of a distributed load 4. Undoubtedly you will select some of the vertical supports where you do not want to apply the distributed load thus you must deselect these locations. In the Apply Pressure on Beams selection window (Figure 3-7) change the Pick  option (at the top) to Unpick and the Box option to Single. Then individually left click on the each small yellow box on the vertical supports where no load should be applied. 5. Once you are certain that only the nodes where the load should be applied are highlighted select OK in the Apply F/M on Nodes window. The define pressure on beams window will appear. ,

,

,

,

3-8

Beams window

Figure 3-9 Apply Pressure on

6. Set the pressure value to 100. The other boxes may remain blank. Select OK.  Remember this load was given in 100 lb/in. , but you would need to convert this value if this were given in lb/ft . or other set of u nits!

E. Apply the Solution 1. Go to Solution>Solve>Current LS. Select Solve in the pop-up window. 2. Just as with the truss close all of the pop-up boxes. 3. It would be a good idea to ³Save As«´ before Post-processing. ,

III. Post-processing A. Introduction ± as discussed in the notes of section I.G.1 (page 3-5) recall that by setting the number of divisions per node (ndiv = 25) we broke the beams into small  pieces or ³finite elements´. For most of the Post-processing functions we will use in this section ANSYS will return data tabulated for these small pieces (finite elements) that ANSYS calls nodes. THESE NODES ARE DIFFERENT FROM KEYPOINTS. ANSYS assigns a number to each node and reports Post-processing information according to this nodal number. Before beginning your Post-processing it is good to see the numbers assigned to each of your nodes so you can make a meaningful interpretation of this data. 1. To see you nodal numbering go to PlotCntrls>Numbering. In the numbering window turn node numbers to ON. Select OK. ,

,

 For this e xample, the nodes at the fi xed points (bottom of vertical members ) are 1, 52, a nd  102 (from left to right respectively ). You numberin g might be different and is dependent  upon the precise order you created li nes, Keypoi nts, etc.  Also, if you have trouble seein g your nodal numbers, you ca n zoom in on your model  display by PlotC ntrls>Pan Zoom Rotate. A tool bo x will appear .

3-9

2. Take note of the nodal numbers in significant places such as those at the ends of  each beam. Note that the nodal numbering will increase or decrease linearly from one end of a beam to another. B. Reaction Forces 1. Go to General Postproc>List Results>Reaction Solution. In the pop-up window select All items and OK. The Reaction Solution window will pop-up.

Figure 3-10 Reaction Solution window 2. You can see that the forces at node 1 (which in this example are coincident with Keypoint number 1) are 2025.4 lb . in the x direction and 8807.9 lb in the y f  f  direction and a moment of ±76121 lb -in. Similarly the forces at node 102 f  (which corresponds to Keypoint number 5) are ±2025.4 lb in the x direction f  8807.9 lb in the y directions and a moment of 76121 lb-in. Your solution may f   be somewhat different from the one given here. ,

,

3. Also note that the sum of all the reaction forces are listed at the bottom under  total values. This is a good fast way to check that your model is correct. Note that the x forces sum to 0 lbs. (since none were applied) the y forces sum to 36 000 lb (since 100lb /in. * (180in.+180in.) = 36 000 lb were applied) and the f  f  f  moments sum to 0 lb -in. ,

,

,

f 

4. If you desire you should print these results now. See the printing section (near  the end of this booklet) on how to do this. ,

C. Member Forces and Stresses ± reporting this data is no different from the truss tutorial. See section III.B (in the Post-processing section) in the truss tutorial while keeping in mind that the output will be listed by NODE and not Keypoint as explained previously in the Reaction Forces section. D. Member Displacements and Rotations 1. Go to General Post-processing>List Results>Nodal Solution>DOF Soln. The List  Nodal Solution window will pop-up.

3-10

Figure 3-11 List Nodal Solution window 2. In this window select All DOFs (degrees of freedom) and OK. The solution will appear in tabular form.

Figure 3-12 Nodal Solution Table 3. In this window the displacement in the x and y direction and the rotation of each node is listed. At the bottom of the list maximum values for each parameter are reported. With your nodal numbering turned on you should be able to find the corresponding node to the Keypoint or other member location of interest. ,

,

This concludes the frame tutorial. Proceed to Chapter 4 the plate tutorial. 3-11 ,

4.

PLATE EXAMPLE

For this example we will model the plate below. Although it has a thickness ANSYS allows us to model it as a two dimensional representation. 20´ steel square plate with 4´ diameter hole Thickness = .1´ Uniform tensile loading of 8 psi ,

Figure 4-1 Steel plate with hole in center  When we model this plate we will take advantage of its SYMMETRY. We can see symmetry by dividing the plate into 4 parts about the center of the hole and then apply constraints to edges of this divided part. As a rule of thumb it is always good to take advantage of symmetry because it allows for your analysis to be smaller and subsequently more specific. Below is the geometry that we will define in ANSYS: ,

,

Figure 4-2 Model of plate that takes advantage of symmetry

I. Preprocessing A. Introduction ± below is an overview of the steps we will complete in this example and how those steps compare to the previous examples:

4-1

1. Modeling (different ± defining areas and using Boolean operations) 2. Element Type (different ± plate with thickness) 3. Real Constants (similar - define element thickness) 4. Material Properties (no changes here) 5. Meshing (different ± mesh areas and refine mesh) B. Modeling 1. Begin by going to: Preprocessor>Modeling>Create>Areas>Rectangle>By 2 Corners the Create Rectangle by 2 corners window will appear. ,

Figure 4-3 Create Rectangle by 2 Corners window 2. The boxes WX and WY specify the coordinates of one corner of the rectangle. Enter 0 in both boxes and width and length of 10 (we will be working this  problem in inches and pounds). 3. Now we must create the hole in the rectangle. Go to Preprocessor> Modeling>Create>Areas>Circle>Solid Circle. The Create Solid Circular Area window will pop up.

4-2

Figure 4-4 Create Solid Circular Area window 4. The WP X and WP Y boxes specify the center point of the circle. Our circle will  be centered at (0 0) and has a radius of 2. Your model should be as below: ,

Figure 4-5 Model after defining both rectangular and circular areas. 5. Just like when using a CAD program you must perform a Boolean operation to remove the circle from the rectangle. Go to Preprocessor> Modeling>Operate>Booleans>Subtract>Areas. The Subtract Area selection window will appear. ,

4-3

Figure 4-6 Subtract Area selection window 6. Single left click on the rectangle in the workspace. Be sure that you click on the area that is occupied ONLY BY THE RECTANGLE. Do not click on the area occupied by both the rectangle and the circle. The rectangle should now appear   pink or purple. 7. Select OK in the Subtract Area window (Figure 4-6). You have now defined the area that we will be subtracting from. 8. Single left click on the circle in the workspace. Be sure that you click on the area occupied ONLY BY THE CIRCLE. Do not click on the area occupied by both the circle and the rectangle. The circle should now be highlighted. 9. Select OK in the Subtract Area selection window. You have now defined all of  your geometry. C. Element Type 1. Go to Preprocessor>Element Type>Add/Edit/Delete. The Define Element Type window will appear just as in the previous tutorials (Figure 2-17). Select Add... The Element Type Library window will appear. 2. In the left hand box select Structural Solid. In the right hand box select Quad 4 node (42). This will define the elements to be small quadrilaterals each with 4 nodes from which the location of each square will be calculated. 3. Select OK. Note that the Element Types window will still be open. Be sure that the element type is highlighted and select Options. The Element Type Options window will appear:

4-4

Figure 4-7 Element Type Options 4. In the Element Behavior box select ³Plane Stress with Thk´. The other options may remain as default. Select OK and Close the Element Type window. D. Real Constants 1. Go to Preprocessor>Real Constants>Add/Edit/Delete. The Real Constants window will appear  select Add. A new window will appear - be sure that the correct (and only) element type is highlighted (Type 1 Plane 42) and select OK. The Define Real Constants Set window will appear. ,

Figure 4-8 Define Real Constants Set window 2. Keep the type number as the default (1). Set the thickness to .1. Select OK. Close out of the Real Constants windows.

4-5

E. Material Properties - note nothing in this section has changed from previous tutorials  ± try doing this on your own! 1. Go to Preprocessor>Material Props>Material Models. In the Define Material Properties window select Structural>Linear>Elastic>Isotropic. 2. In the pop up window set the modulus of elasticity (EX) to 290000000 (remember we are working in pounds and inches so this number is in psi!) and Poisson's ratio (PRXY) to 0.3. F. Meshing ± be sure to save right now! 1. Go to Preprocessor>Meshing>MeshTool. The MeshTool box will appear.

Figure 4-9 MeshToolwindow

2. The MeshTool is a convenient and quick way to mesh an object and refine an object that is already meshed. Turn on the Smart Size option at the top of the MeshTool. 3. On the Fine to Coarse bar directly below the Smart Size box controls the size of  your finite elements. Left click and hold down on the control bar and slide it to the right to level 8 (the level is denoted above the bar). This will make fairly large finite elements. 4. Then select Mesh (towards the bottom of the window). A Mesh Selection box will appear. Left click once on the plate geometry so that it is highlighted.

4-6

5. Select OK in the Mesh Selection window. Now your element has been meshed and should appear to be divided into quadrilaterals.  However, we k now that the most important stresses in this plate are near the hole. Con sequently, we should Refineour mesh in this area. There is no need to Refi nethe mesh elsewhere si nce other stresses i n the plate are not as important .

6. On the MeshTool select Refine (near the bottom of the MeshTool). Note that the MeshTool is already set to refine at elements (directly above the refine button). A Refine Selection box will appear just like the Mesh Selection box. 7. Single left click on all of the finite elements adjacent to the hole (see below).

Figure 4-10 Refining the mesh near the hole 8. Then select OK in the Refine Selection box. The Refine Mesh at Element window will pop up.

4-7

Figure 4-11 Refine Mesh at Element 9. It is usually good to have your mesh change gradually so that you do not have disjointed elements. You can select the defaults (minimal refinement) in this window. Select OK.  Note: now the elements near the hole, where the most importa nt and interestin g stresses are located, are very small a nd will give a better appro ximation of the plate¶s behavior there . The elements elsewhere i n the plate are large, thus the appro ximation in that region will not  be as accurate. However this is not cause for co ncer n since the stresses there are unimportant and uninterestin g . You might be thi nkin g, ³Why don¶t I use the most accurate mesh everywhere i n the element?´ This is generally not a good idea because when ANSYS tries to solve the plate, it  will require a large amou nt of memory etc . from the computer . If ANSYS requires more memory than the computer ca n give, then ANSYS may crash or give i ncomplete results .

10. Once you are satisfied with your mesh move on to the Solution Phase. ,

 Note that you can refine your mesh several times u ntil you have fi nite elements in your  region of interest that are small enough to your satisfactio n. You can even REFINE your  mesh after you ru n the solution and look at post-processi n g output .

II. Solution Phase A. Introduction ± no radically new concepts are employed in this section that were not used in previous examples. 1. Analysis Type (no changes ± static) 2. Apply Constraints (similar ± X and Y direction on lines) 3. Apply Pressure (similar ± pressure on lines) B. Analysis Type ± go to Solution>Analysis Type>New Analysis. The New Analysis window will appear. Select Static and OK. C. Apply Constraints 1. Go to: Solution>Define Loads>Apply>Structural>Displacement>On Lines. The Apply Constraints window will appear. Select the bottom edge only and OK in the pick box. The Define Constraints window will appear.

4-8

Figure 4-12 Apply Constraints window 2. Set the following: a. UY  b. Apply as constant c. Displacement value = 0. d. Click on OK. 3. Repeat Steps 1 and 2 for the left edge with a zero-displacement constraint in the X direction. D. Apply Loads 1. Go to Solution>Define Loads>Apply>Structural>Pressure>On Lines. Another   pick box will appear. Select the right hand vertical line and OK. The Define Pressure on Lines box will appear.

4-9

Figure 4-13 Apply Pressure on Lines 2. Set a constant value pressure of -8 and select OK (since negative pressure points AWAY from its application point). E. Apply Solution - now all the loads are applied and you are ready to solve. Go to Solution>Solve>Current LS. Select OK in the series of boxes that appear just as in the other tutorials. You are now ready for post-processing. III. Post-processing ± The major difference between post-processing with the plate and with the other examples is that you will probably find the graphical outputs most helpful. As you might guess tabular output will list far too many nodes to be helpful. The graphical output will likely be the easiest and most meaningful for your analysis. All graphical outputs that you will need can be accessed from: ,

General Postproc> Plot Results>Contour Plot>Nodal Solu. This set of commands will output the stress displacement rotation energy or any other  relevant outputs. Results will be generated in the workspace. If you desire you can refer  to the Truss E  xample tutorial Post-processing section to review this process. ,

,

,

,

4-10

5. APPENDIX

Some common tasks such as saving opening and printing files may be different from working in other operating systems that may already be more familiar to you. The purpose of the section is to outline these tasks to make using ANSYS easier for you. The second section outlines how to access and manipulate files on your EWS account. ,

I. Working with ANSYS and Unix

A. Saving an ANSYS file ± ANSYS is set to save files automatically to your EWS (Engineering WorkStation) account. This is ideal for your finite element analyses  because several files are created throughout the analysis including the main database file (.db) a backup database file (.dbb) and various solution and results files. In order for you analysis to operate properly it is important that all of these files be in the same location so that ANSYS can access them when necessary. The EWS account is especially convenient because you can access it from any EWS computer and you do not have the worries that are associated with using a disk  (such as it being damaged or lost). ,

,

,

Below are a few steps to follow to save your project: 1. From the top menu bar  go to File>Save As. The Save window will appear. You should include the file type extension which is .db. If you want to call your file ³truss1´ then in the box enter: truss1.db 2. Note that you are already set to save in your EWS account. This directory is listed in the bottom box of the Save As window. For this example let us name our file truss1.db You must include the file type extension (.db) otherwise you will not  be able to see it when you want to reopen your project. 3. At the end of the account name enter and select OK. You can confirm your save was successful by going to ³File>Save As´ again and noting the name in the right hand box. ,

,

,

 Note: You may also notice (especially if you have already saved projects before ) that there is a file called  file.dbon your account . This is a default ANSYS file . If you do not specify a name for your project, all of your data will be saved i nto this file. It is a good idea to depend on this function only for backup purposes .

B. Open a previously saved ANSYS file 1. ANSYS uses the work ³Resume´ instead of ³Open´. Let us say that you want to open truss1.db. Go to File>Resume From. The Resume From window will appear. 2. You will already be in your EWS account where all of your ANSYS files should  be located. Highlight truss1.db and select OK. Your project will launch. 3. If you have been saving to the default file (file.db) you can open this by simply choosing: File>Resume Jobname.db.

5-1

C. Printing result tables 1. When you have a table window open you can choose File>Copy to Output. This will copy the table to your project output file. 2. To view your project output file open another xterm window and type lsat the  prompt (meaning ³list´). This will list all of the files on your account. Find the file ending in .out this is the ANSYS output file and can be opened or printed using a text editor. There are several text editors available on the Unix systems. If you are unfamiliar with using a text editor you should ask the EWS site consultant on duty how to launch and use one. D. Printing graphical outputs ,

1. Go to PlotCntrls>Capture Image. The ³Capture Image´ box will appear. 2. Select ³Print to´ towards the bottom of the screen. This will activate the ³Printer   Name´ box. 3. In the ³Printer Name´ box you will need to type in a Unix command to send the  job to the printer. This process may change from year to year. However at the time this tutorial was created you would type: th for the 4 floor Engineering Hall lab and for the lab in MEL.. As a general rule you should type . II. Managing Files on your EWS Account

A. How to access all of your EWS files from a Unix machine 1. Open an xterm window. 2. At the prompt type lsthis command will ³list´ all of the files currently saved on your EWS account. B. Deleting files quickly ± sometimes when working in ANSYS you will get a message that there was an error saving or ANSYS could not properly execute a save command. This is probably because you do not have enough room on your EWS account to save your project. You must remove files from your account to make room for your analysis. 1. For this case let us say that we want to remove the file paper1.doc from our  EWS account. Type rmfor remove followed by the file name and its extension. For our example we would type rm paper1.doc ,

2. We will then be prompted if we really want to remove the file. Type y for yes. 3. Let us say that you wanted to remove all files that end with the extension .doc. Instead of removing each file individually as outlined above type: rm *.doc The* is a ³wild card´ command. So after typing this you will be prompted ³ if   you are sure you want to remove´ for each file ending in .doc individually. You can use the wildcard anywhere in the command line so you could also type: rm paper* and this would remove anything that begins with ³paper´ regardless of  extension. When using the wildcard command you will be prompted to remove each file individually. ,

,

5-2

III.Creating Axisymmetric Models

When using ANSYS you may be asked to create an axisymmetric model. Just as mentioned in the introduction to the plate tutorial it is always a good analysis technique to take advantage of symmetry in design. You can define geometry to be rotated about an axis thereby taking advantage of axial symmetry. Consider the part below: ,

,

Figure 5-1 Axisymmetric bar. The y-axis is that of axial symmetry. Note the bar is also symmetric with respect to the x-axis. You can take advantage of this symmetry in ANSYS. It was already outlined how to model traditional symmetry (which for this example is the bar¶s symmetry with respect to the x axis) in the plate tutorial. To take advantage of the axial (about the y-axis) symmetry you must first model the section that is to be rotated about the y axis. Look at the wire-frame representation below:

5-3

Figure 5-2 Wireframe representation of axisymmetric bar. Note that the section to be modeled (highlighted in gray) is entirely in quadrant I of the modeling plane (all values are non-negative). For ANSYS to properly define your geometry you must define the section (highlighted in gray) entirely in quadrant I; you cannot allow any of this two-dimensional geometry to have negative coordinates. ,

Also ANSYS is programmed to rotate your element about the y axis in the workplane. Thus if you want a solid bar (not hollow) you must align one side of your geometry on the y axis. ,

,

Once your geometry is sufficiently defined then you must tell ANSYS that the problem is axisymmetric. This is done in Preprocessing>Real Constants. See section I.C of the Plate tutorial (pg. 4-4). Follow this section as written except for steps 4 and 5. From the options window (Figure 4-7) set the Element Behavior to ³Axisymmetric´ (instead of ³Plate with Thickness´). Then you can skip step 5 since there will be no need to define Real Constants. ,

Be sure to constrain properly your sketch in the Solution phase. For this example displacement will be constrained to zero in the y direction on the z axis. By specifying the elements to be ³axisymmetric ´ you have implicitly constrained all points on the y axis from moving in the x direction so no explicit constraint needs to be applied. ,

,

,

5-4