当前课程知识点:Finite Element Method (FEM) Analysis and Applications > 14、Project > Thermal stress analysis: temperature and assembly stress analysis of truss structure > Video I-6
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第6个Project是关于
桁架结构的温度及装配应力分析
我们可以看出来这样的一个桁架结构
如果杆件的1、3、7、8的温度升高50度
由于热胀冷缩的原因
它肯定会发生相应的热应力
肯定会有相应的变形
另外一个就是,如果我们由于制造的误差
使得杆件9和10短了0.63mm
而杆件6长了0.27mm
如果我们还是按照原来的方案强制装配的话
我们也可以想像它肯定会产生相应的应力情况
我们应该怎样来进行计算呢
我们来看一下
它的建模要点是
选择可以施加温度载荷的二维杆单元
也就是LINK1单元
对于第一个问题
我们是单纯的由于温度热胀冷缩引起的应力问题
而第二个问题是属于装配的应力问题
对于这样的一个问题我们应该怎么处理呢
对于第一个问题我们可以将参考温度变为20度
再对1、3、7、8号单元施加一个温度是70度
也就是说它的温度升了50度
这样我们就可以通过刚才输入的热胀冷缩力
可以得到由于温度变化引起的受力情况
对于第二个问题,我们可以看出来
因为对于6、9、10号单元
由于制造误差引起的长度方向的变化
我们也可以通过施加适当的一个温度变化
用来等效它对应的制造误差
等效温度的变化我们可以通过这个式子计算得到
也就是制造误差除以热膨胀系数
再除以原来的杆件的长度就可以计算得到
而根据它我们就可以得到
单元6比原来长了0.27mm
相当于在单元6温度升高24度
9、10号单元短了0.63mm
相当于把单元9、10的温度降低了39.6度
我们初始温度是20度
变化后的温度在6号单元对应的是44度
而9、10号单元对应的是-19.6度
我们来看一下对应的命令流
我们通过对应的这个命令施加热膨胀系数
这个命令是参考温度
也就是我们所说的环境温度,这里是20度
我们在1、3、7、8单元设置它温度升到70度
然后我们就可以进行相应的求解
对于杆单元我们可以用
这是由于温度引起的结构受力变化情况的命令流
我们来看另外一个命令流
由于制造误差引起的装配产生的应力
根据前面的分析我们也可以把它等效成温度变化的形式
等效的温度我们可以看出来
第一个温度是我们刚刚说的44度
变化温度变到44度
第二个温度是-19.6度
对应的是在6、9、10号单元上施加相应的温度
后处理也是跟刚才前面一样
也就是可以通过
显示出线单元的轴力
我们进入ANSYS平台
由于温度变化引起的轴力变化情况
这就是我们对应的计算结果
我们先把这个Clear掉
就是把这个模型清除掉
我们来看一下由于计算误差而引起的应力情况
也就是我们刚才所说的Project61的这个命令流
我们可以看出来
因为这根杆是伸长了
而另外这两根杆收缩了
所以我们看到它的变形情况是这样的一个情形
-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