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第5个Project是关于
钢制圆柱冷却过程的瞬态传热分析
对于一个直径为30mm,高度为60mm的钢制实心圆柱
它初始的温度是600度
假设它是均匀分布的
我们希望把它放置在一个温度为20度
换热系数是1200W每平方米度的介质中冷却
进行相应的热处理
我们来看一下
我们假设它的热传导系数随着温度变化
是这样的一个线性关系
比热的变化是这样的一个线性关系
圆柱冷却过程中
它随着时间变化，它的冷却情况、它的温度分布情况
是怎么样的一个形式
我们来进行有限元分析计算
对于这个问题它的要点也是
因为它属于一个轴对称问题
由于对称性的关系，我们就可以取1/4的横截面
作为计算模型，也就是这一部分
从这里可以看出来
下面这个面是绝热的
也就是我们所说的对称面
这个面和这个面是放置在冷却液中
也就是跟外界进行热交换的面
在建立相应的模型的时候
大家要注意统一对应的物理量的单位
这个模型我们采用的是PLANE77号传热单元
设置的时候注意
导热系数和热容是随温度线性变化的
在进行瞬态分析的时候
我们通过
可以设置初始温度为600度
再定义对应这个面的对流换热系数
因为我们希望获得冷却时间100秒以后
在整个时间分布上的温度变化情况
那么我们就可以通过
在后处理中
一般后处理的话
我们之前完成的是1/4的模型
我们就可以通过对称映射设置完成整个模型
也可以用矢量图来显示热流分布
然后在时间后处理中
我们还可以通过相应的命令得到
圆柱中心、侧表中间、端面的顶点上
它这个位置的温度随着时间变化情况
然后画出相应的温度变化曲线
我们先来看一下对应的命令流
命令流的关键主要在这
主要是要设置PLANE77号传热单元
然后在这是确定计算模型为瞬态分析
这个命令是设置圆柱的初始温度为600度
这个命令是设置换热边界条件
我们希望得到100秒内温度变化情况
所以这是时间的设置
这是我们设置计算子步的数目
这对应的是求解
求解完成了之后我们就进入后处理
对应的命令是
我们通过对称映射把1/4的模型
变成一个完整的模型
然后我们以矢量的方式来显示热流的分布情况
我们把之前的这部分命令拷到ANSYS平台
我们就可以看出来它热流的方向是怎样的形式
如果我们希望得到圆柱面和圆柱侧边
也就是我们所说的1号节点、2号节点
还有22号节点是圆柱侧边和端面的
随着时间的温度变化情况的变化的话
我们就要进入时序后处理模块
我们把这部分时序后处理模块的命令粘贴进去
从图中我们可以看出来
在圆柱中心内部
它开始的时候温度下降是比较慢的
随着时间的增加，到100秒的时候
它的内外温差相差不是很大了
-Finite element, infinite capabilities
--Video
-1.1 Classification of mechanics：particle、rigid body、deformed body mechanics
--1.1 Test
-1.2 Main points for deformed body mechanics
--1.2 Test
-1.3 Methods to solve differential equation solving method
--1.3 Test
-1.4 Function approximation
--1.4 Test
-1.5 Function approximation defined on complex domains
--1.5 Test
-1.6 The core of finite element: subdomain function approximation for complex domains
--1.6 Test
-1.7 History and software of FEM development
--1.7 Test
-Discussion
-Homework
-2.1 Principles of mechanic analysis of springs
--2.1 Test
-2.2 Comparison between spring element and bar element
--2.2 Test
-2.3 Coordinate transformation of bar element
--2.3 Test
-2.4 An example of a four-bar structure
--2.4 Test
-2.5 ANSYS case analysis of four-bar structure
--ANSYS
-Discussion
-3.1 Mechanical description and basic assumptions for deformed body
--3.1 Test
-3.2 Index notation
--3.2 Test
-3.3 Thoughts on three major variables and three major equations
--3.3 Test
-3.4 Test
-3.4 Construction of equilibrium Equation of Plane Problem
-3.5 Test
-3.5 Construction of strain-displacement relations for plane problems
-3.6 Test
-3.6 Construction of constitutive relations for plane problems
-3.7 Test
-3.7 Two kinds of boundary conditions
- Discussion
-- Discussion
-4.1 Test
-4.1 Discussion of several special cases
-4.2 Test
-4.2 A complete solution of a simple bar under uniaxial tension based on elastic mechanics
-4.3 Test
-4.3 The description and solution of plane beam under pure bending
-4.4 Test
-4.4 Complete description of 3D elastic problem
-4.5 Test
-4.5 Description and understanding of tensor
-Discussion
-5.1 Test
-5.1Main method classification and trial function method for solving deformed body mechanics equation
-5.2 Test
-5.2 Trial function method for solving pure bending beam: residual value method
-5.3 Test
-5.3How to reduce the order of the derivative of trial function
-5.4 Test
-5.4 The principle of virtual work for solving plane bending beam
-5.5 Test
-5.5 The variational basis of the principle of minimum potential energy for solving the plane bending
-5.6 Test
-5.6 The general energy principle of elastic problem
-Discussion
-6.1Test
-6.1 Classic method and finite element method based on trial function
-6.2 Test
-6.2 Natural discretization and approximated discretization in finite element method
-6.3 Test
-6.3 Basic steps in the finite element method
-6.4 Test
-6.4 Comparison of classic method and finite element method
-Discussion
-7.1 Test
-7.1 Construction and MATLAB programming of bar element in local coordinate system
-7.2 Test
-7.2 Construction and MATLAB programming of plane pure bending beam element in local coordinate syste
-7.3 Construction of three-dimensional beam element in local coordinate system
-7.4 Test
-7.4 Beam element coordinate transformation
-7.5 Test
-7.5 Treatment of distributed force
-7.6 Case Analysis and MATLAB programming of portal frame structure
-7.7 ANSYS case analysis of portal frame structure
-8.1 Test
-8.1 Two-dimensional 3-node triangular element and MATLAB programming
-8.2 Test
-8.2 Two-dimensional 4-node rectangular element and MATLAB programming
-8.3 Test
-8.3 Axisymmetric element
-8.4 Test
-8.4 Treatment of distributed force
-8.5 MATLAB programming of 2D plane rectangular thin plate
-8.6 Finite element GUI operation and command flow of a plane rectangular thin plate on ANSYS softwar
-Discussion
-9.1 Three-dimensional 4-node tetrahedral element and MATLAB programming
-9.2 Three-dimensional 8-node hexahedral element and MATLAB programming
-9.3 Principle of the isoparametric element
-9.4Test
-9.4Numerical integration
-9.5 MATLAB programming for typical 2D problems
-9.6 ANSYS analysis case of typical 3Dl problem
-Discussion
-10.1Test
-10.1Node number and storage bandwidth
-10.2Test
-10.2 Properties of shape function matrix and stiffness matrix
-10.3Test
-10.3 Treatment of boundary conditions and calculation of reaction forces
-10.4Test
-10.4 Requirements for construction and convergence of displacement function
-10.5Test
-10.5C0 element and C1 element
-10.6 Test
-10.6 Patch test of element
-10.7 Test
-10.7 Accuracy and property of numerical solutions of finite element analysis
-10.8Test
-10.8 Error and average processing of element stress calculation result
-10.9 Test
-10.9 Error control and the accuracy improving method of h method and p method
-Discussion
-11.1 Test
-11.1 1D high-order element
-11.2 Test
-11.2 2D high-order element
-11.3 Test
-11.3 3D high-order element
-11.4 Test
-11.4 Bending plate element based on thin plate theory
-11.5 Test
-11.5 Sub-structure and super-element
-12.1Test
-12.1 Finite element analysis for structural vibration: basic principle
-12.2 Test
-12.2 Case of finite element analysis for structural vibration
-12.3 Test
-12.3 Finite element analysis for elastic-plastic problems: basic principle
-12.4 Test
-12.4 Finite element analysis for elastic-plastic problems: solving non-linear equations
-Discussion
-13.1 Test
-13.1 Finite element analysis for heat transfer: basic principle
-13.2 Test
-13.2 Case of finite element analysis for heat transfer
-13.3 Test
-13.3 Finite element analysis for thermal stress problems: basic principle
-13.4 Test
-13.4 Finite element analysis for thermal stress problems: solving non-linear equation
-Discussion
-2D problem: finite element analysis of a 2D perforated plate
-3D problem: meshing control of a flower-shaped chuck
-Modal analysis of vibration: Modal analysis of a cable-stayed bridge
-Elastic-plastic analysis: elastic-plastic analysis of a thick-walled cylinder under internal pressur
-Heat transfer analysis: transient problem of temperature field during steel cylinder cooling process
-Thermal stress analysis: temperature and assembly stress analysis of truss structure
-Probability of structure: Probabilistic design analysis of large hydraulic press frame
-Modeling and application of methods: Modeling and analysis of p-type elements for plane problem
