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。
