华南理工大学有限元分析题库

三．推导题

1.推导三节点三角形平面单元的位移函数（16分）

2.推导三节点三角形平面单元的单元刚度矩阵。

3.试推导杆单元的形状函数、几何矩阵、应力矩阵及刚度矩阵。

四 跟据题意完成下列计算，填写空白处的命令： （25分）（除指定空外每空1分）.

梁承受均布载荷：1.0e5 Pa 10m

1.1Interactive →Run

1.2设置计算类型

ANSYS Main Menu: Preferences →select → OK 1.3选择单元类型

ANSYS Main Menu: Preprocessor →Element Type→Add/Edit/Delete… →Add… → select →OK (back to Element Types window) →Close (the Element Type window) 1.4定义材料参数

ANSYS Main Menu: Preprocessor →Material Props →Material Models →Structural →Linear →Elastic →Isotropic →input → OK。 1.6生成几何模型 ? 生成特征点

ANSYS Main Menu: Preprocessor →Modeling →Create →Keypoints →In Active CS →依次输入三个点的坐标：input: →OK

? 生成梁

ANSYS Main Menu: Preprocessor →Modeling →Create → →lines →Straight lines →连接两个特征点，1(0,0),2(10,0) →OK

1.7 网格划分（此问每空2分）

ANSYS Main Menu: Preprocessor →Meshing →Mesh Attributes →Picked lines →OK →选择: SECT:1（根据所计算的梁的截面选择编号）；Pick Orientation Keypoint(s):YES→拾取：3#特征点(5,1) →OK→Mesh Tool →Size Controls) lines: Set → (in Picking Menu) →input →OK (back to Mesh Tool window) → (in Picking Menu) → Close (the Mesh Tool window)

1.8 模型施加约束 ? 最左端节点加约束

→

change

the

working

directory

into

yours

→

input

ANSYS Main Menu: Solution →Define Loads →Apply →Structural →Displacement

→ On Nodes →pick the node at (0,0) → OK → select → OK

? 最右端节点加约束

ANSYS Main Menu: Solution →Define Loads →Apply →Structural →Displacement → On Nodes →pick the node at (10,0) → OK → select → OK

? 施加y方向的载荷

ANSYS Main Menu: Solution →Define Loads →Apply →Structural →Pressure → On Beams →Pick All → → OK

1.9 分析计算

ANSYS Main Menu: Solution →Solve → →OK(to close the solve Current Load Step window) →OK

1.10 结果显示（此问每空4分）

ANSYS Main Menu: General Postproc → → select Def + Undeformed →OK (back to Plot Results window) →Contour Plot →Nodal Solu →select:

→OK 1.11 退出系统

ANSYS Utility Menu: File→ Exit → →OK。