弹性力学基础及有限元法-2

Non-Newtonian fluids
Rheology The study of materials with both solid and fluid characteristics.
Fluid mechanics The study of the physics of continuous materials which take the shape of their container.
Elasticity: unknown values
位移/displacements u, v, w 应力/stress x , y , z , xy , yz , zx
x , y , z , xy , yz , zx
Elemental volume
应变/strains
Newtonian fluids
(满足牛顿粘性定律的流体，比如水和空气)
The analysis Model

Under what conditions? The steady loads The fixed displacements

The object to be studied: elastic body
Stress-strain relationship
物理方程（广义胡克定律）
x
x
E

x
E
y
E
y
E



z
E
z
E
E
yz
xz
yz
G
xz
G
y
z

x
E

y
E
z
xy
xy
G
How to get the solution?
u , x x v , y y w , z z v w zy , z y u w zx , z x u v xy y x
Strain-Displacement Relation (几何方程)
a1b2 ab x ab
(u
u dx dx u ) dx u x dx x
y
v w ; z y z
Strain-Displacement Relation 几何方程
Topics suggested of the reports

1. 2. 3. 4.

有限元法在本专业中的应用（综述） 有限元法在本专业中的一个案例分析 该案例的改进 自创案例：
工程问题-数学模型-有限元模型-FEM求解讨论-结论
Introduction：简要日程
内容 弹性力学 有限元法 概念、方程组、 解法 概念、方法、 细节 静态分析：桁 架、平面、轴 对称； 动态分析 方式 授课 授课 授课 上机 学时 6 10 12 14-16 10 2 总学时 56(-4)
The equilibrium equations : Stress & loads

The equilibrium

X direction Y direction Z direction
The equilibrium equations :
Stress & loads

The equilibrium equations
△
Continuum mechanics The study of the physics of continuous materials
Plasticity Describes materials that permanently deform after a sufficient applied stress.

① Attendance of lecture and recitation 10%； ② Homework assignments, Lab practice and test 20%； ③ 70%


Study reports Or Final exam 。

4. 要求

认真做笔记、复习、作业、练习； 掌握基本概念、总体思路、基本方法； 掌握ANSYS的基本操作； 努力创作优质学习报告和案例报告。

1) the combination of theoretical study with the operations of ANSYS 2）Case study（案例教学） 3) Partial Bilingual (部分双语）
Introduction: the course

3. Grading（考核）
The set of equations
x
x
E

x
E
y
E
y
E



z
E
z
E
x xy xz fx 0 x y z xy y yz fy 0 x y z xz yz z fz 0 x y z
ANSYS
讨论、报告、 总复习、考试
Continuum mechanics
Elasticity Describes materials that return to their rest shape after an applied stress.
Solid mechanics The study of the physics of continuous materials with a defined rest shape.
u , x x v , y y w , z z v w zy , z y u w zx , z x u v xy y x
Elemental volume
1. Elasticity

2. FEM – theoretical method
3. FEM -- ANSYS
The concerted items The displacements: u, v, w The highest stress and stress distribution The largest strain and strain distribution
y
z

x
E

y
E
z
E
yz
xz
yz
G
xz
G
xy
xy
G
Question1: How about the loading & constrains ？
位移/displacements u, v, w 应力/stress x , y , z , xy , yz , zx
x xy xz fx 0 x y z xy y yz fy 0 x y z xz yz z fz 0 x y z
Strain-Displacement Relation (几何方程)
u u dy u d1d 2 y y tan xy a1d 2 v v dy dy v 1 v y y u xy y u
yx
v x
xy yx
u v xy yx y x
Strain-Displacement Relation (几何方程)
应力/stress x ( x, y, z ), y ( x, y, z ), z ( x, y, z ), xy ( x, y, z ), yz ( x, y, z ), zx ( x, y, z ) 应变/strains x ( x, y, z ), y ( x, y, z ), z ( x, y, z ),
u , x x v , y y w , z z v w zy , z y u w zx , z x u v xy y x
▽
Which mechanics do include in the continuum mechanics?
▽
▽
Introduction: the course

1. Goal（目的）:




2. Teaching method（教学方法）

1）To build a theoretical basis for students to learn FEM software; 2) To let students master the basic operations of ANSYS 3）to enable students to create own works
Elemental volume
xy ( x, y, z ), yz ( x, y, z ), zx ( x, y, z )
How to get the solution?

The solution of the equations：
1. The required known values (what must to be known?)



Review

The course Mechanics:


Elasticity

The object studied:


The objective: to describes materials that return to their rest shape after an applied stress The basic hypothesis: …… The methodology: …… The unknown values and a set of equations ……