《有限元基础理论》报告学院：班级：姓名：学号：任课老师：二〇一一年十二月题目一：三维托架实体受力分析题目：1、三维托架实体受力分析：托架顶面承受50psi的均匀分布载荷。

托架通过有孔的表面固定在墙上，托架是钢制的，弹性模量E=29×106psi，泊松比v=0.3.试通过ANSYS输出其变形图及其托架的von Mises应力分布。

题目1的分析：先进行建模，此建模的难点在对V3的构建（既图中的红色部分）。

要想构建V3，首先应将A15做出来，然后执行Main Menu>Preprocessor>Modeling>Operate>Booleans>Add>V olumes命令，将所有的实体合并为一个整体。

建模后，就对模型进行网格的划分，实行Main Menu>Preprocessor>Meshing>MeshTool,先对网格尺寸进行编辑，选0.1，然后点Meshing，Pick all进行网格划分，所得结果如图1.1。

划分网格后，就可以对模型施加约束并进行加载求解了。

施加约束时要注意，由于三维托架只是通过两个孔进行固定，故施加约束应该只是针对两孔的内表面，执行Main Menu>Solution>Define Loads>Apply>Structrual>Displacement>Symmetry B.C>On Areas命令，然后拾取两孔的内表面，单击OK就行了。

施加约束后，就可以对实体进行加载求解了，载荷是施加在三维托架的最顶上的表面的，加载后求解运算，托架的变形图如图1.2。

图1.1、托架网格图图1.2输出的是原型托架和施加载荷后托架变形图的对比，虚线部分即为托架的原型，从图1.2可看出，由于载荷的作用，托架上面板明显变形了，变形最严重的就是红色部分，这是因为其离托板就远，没有任何物体与其分担载荷，故其较容易变形甚至折断。

这是我们在应用托架的时候应当注意的。

图1.2、托架位移变形图图1.3为托架的应力分布图，由图可看出主要在两孔处出现应力集中，也就是说这些地方所受的应力的最大的，比较容易出现裂痕。

我们在应用托架的时候，应当注意采取一些设施，以便减缓其应力集中。

特别是在施加载荷时，绝对不能够超过托架所能承受的极限，否则必将导致事故的发生。

文后附上建模分析时所执行的命令流。

图1.3、托架应力分布图1.指定分析标题1．选取菜单路径Utility Menu | File | Change Jobname，将弹出Change Jobname (修改文件名)对话框。

2．在Enter new jobname (输入新文件名)文本框中输入文字“bracket”，为本分析实例的数据库文件名。

单击对话框中的“OK”按钮，完成文件名的修改。

3．选取菜单路径Utility Menu | File | Change Title，将弹出Change Title (修改标题)对话框。

4．在Enter new title (输入新标题)文本框中输入文字“press analysis of bracket structure”，为本分析实例的标题名。

单击对话框中的“OK”按钮，完成对标题名的指定。

2.定义单元类型1．选取菜单路径Main Menu | Preprocessor | Element Type | Add/Edit/Delete，将弹出Element Types (单元类型定义)对话框。

单击对话框中的按钮，将弹出Library ofElement Types (单元类型库)对话框。

2．在左边的滚动框中单击“Structural Solid”，选择结构壳单元类型。

在右边的滚动框中单击“Quad 10node 92”,在对话框中单击“OK”按钮，完成对这种单元的定义。

3.指定材料特性1．选取菜单路径Main Menu | Preprocessor | Material Props | Material Models，将弹出Define Material Model Behavior (材料模型定义)对话框。

2．依次双击Structural，Linear ，Elastic 和Isotropic，将弹出1 号材料的弹性模量EX 和泊松比PRXY 的定义对话框。

3．在EX文本框中输入2.9E11，PRXY文本框中输入0.3。

定义材料的弹性模量为2.9E6 N/m2，泊松比为0.3。

单击“OK”按钮，关闭对话框。

4．在Define Material Model Behavior (材料模型定义)对话框中，选取路径Material | Exit，完成对材料模型的定义。

5．单击ANSYS10.0 的ANSYS Toolbar (工具条)上的“SAVE”按钮，保存数据库文件4.建立托架的有限元模型1．选取路径Main Menu | Preprocessor | Modeling | Create | Volume|Block|By Dimensions，将弹出Create Block by Dimensions(根据坐标创建体)对话框。

在对话框输入：X1,X2 X-coordinates：-1,1Y1,Y2 Y-coordinates：-1.5，1.5Z1, Z2 Z-coordinates：0，1/8然后单击“APPLY”按钮，再次在对话框输入：X1,X2 X-coordinates：-1,1Y1,Y2 Y-coordinates：1.5，1.625Z1, Z2 Z-coordinates：0，32．选取路径Main Menu | Preprocessor | Modeling | Operate |Booleans|Add|Volumes将弹出Add Volumes(体相加)对话框，在对话框单击“PICK ALL”按钮完成体相加操作。

3．在执行显示keypoint的操作之后，执行显示line的操作，选取路径Main Menu | Preprocessor | Modeling | Create |Lines|Lines|StrainghtLine将弹出Create Straight Line对话框，然后选择关键点5、13生成L13直线，单击“OK”按钮完成操作。

4．选取路径Main Menu | Preprocessor | Modeling | Create |Area|Arbitrary|By Lines将弹出对话框Create Area By Lines然后选择直线L1,L9,L13,L20,L24,L25，单击“OK”即可生成面A4。

5．选取路径Main Menu | Preprocessor | Modeling |Operate|Extrude|Areas|Along Normal弹出对话框Extrude Area by…选择面A4单击“OK”按钮，将弹出另一个对话框，在Length extrusion 项输入“-1/8”，单击“OK”按钮。

然后再次如前做的将所有体相加的操作。

6．选取路径Main Menu | Preprocessor | Modeling |Create|Areas|Circle|Solid Circle将弹出Solid Circular Area对话框，在WP x,WPy,Radius项分别输入0，-0.5，0.25单击Apply,再次输入0，0.5，0.25然后单击“OK”按钮。

然后选取路径Main Menu | Preprocessor | Modeling |Operate|Extrude|Areas|Along Normal弹出对话框Extrude Area by…选择其中一个圆面单击“Apply”按钮，将弹出另一个对话框，在Length extrusion项输入“1”，单击“OK”按钮。

对另一个圆面做相同操作。

7．选取路径Main Menu | Preprocessor | Modeling | Operate |Booleans|Subtract|Volumes将弹出Subtract Volumes(体相减)对话框，选择两个圆柱体所在的体，单击“Apply”按钮，然后选择两个圆柱体，单击“OK”按钮，完成体相减操作。

5.网格划分1．选取路径Main Menu | Preprocessor | Modeling|Meshing|MeshTool将弹出MeshTool对话框，单击“Mesh”按钮，弹出另一对话框，再次单击“PICK ALL”按钮完成网格划分。

6.施加约束，载荷并求解1．选取菜单路径Main Menu | Preprocessor | Loads | Define Loads | Apply | Structural | Displacement | On Areas，将会弹出拾取对话框,选择两圆孔，单击对话框中的“OK”按钮。

完成施加约束操作。

2．选取菜单路径Main Menu | Solution | Define Loads | Apply | Structural |Pressure |On Areas将会弹出拾取对话框,选择面A10,A19单击“OK”按钮，弹出另一对话框，在Load PRES value 项输入“50”单击“OK”完成施加载荷操作。

3．选取菜单路径Main Menu | Solution |Solve|Current LS弹出Solve Current Load Step对话框，单击“OK”开始求解，求解结束后，关闭相应对话框。

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