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对于复杂的几何形状
我们采取分段、分片或者分块的方式
也就是子域的方式来构造相应的简单函数
然后再拼出一个全域的拼接的试函数
这种方式是比较容易做得到
那么我们简单地看一看
对于1D问题
比如一条线
我们把它分成很多段，我们叫分段
那么我们把每一个分段分出来
这就作为基本的要件，我们叫基本构件
对于2D问题，这个复杂的几何域
同样地我们把它分成很多子域
当然分法有很多了
你可以分成矩形
也可以分成三角形
可以分成多边形
假定我们就把它分成三角形
那么这个里面基本的构件
就是一个三节点的三角形
对于3D问题
同样我们也可以把它进行分块
那这里的分块呢
比如也可以分成四面体
也可以分成六面体
也可以分成多面体
那么这些所有的1D、2D、3D问题的核心
就是要从里面分出基本构件
那么为了规范，为了标准
我们把里面分出来的这些基本构件
比如一维问题的两个节点的杆
二维问题里面三节点的三角形
三维问题里面八节点的六面体
像这些规范化的子域，我们就把它叫做单元
既然是规范化、参数化
我们做好一系列的之后
就可以用它对复杂的几何域
来拼出我们想要的形状
那么为了方法的规范和标准
我们分别把1D问题、2D问题、3D问题常用的
分成子域的这些基本构件，我们叫做单元
把它做成标准化的单元库
比如1D问题梁单元、杆单元
这些常用的单元 我们构造出来
事先把它的数学描述都做好，放到一个库里面
2D单元呢，二维问题
同样我们有四节点的四边形单元
当然它可以退化为三节点的三角形单元
那么还有六节点的曲边的曲边三角形单元
还有八节点的四边形单元等等
我们把这些做成标准化的单元库，叫基本构件
3D单元，同样我们有八节点的六面体单元
同样也是多节点的曲边的单元
这样的话，我们把这些都做成标准的基本构件的库
还有板壳单元
我们同样也是做成四节点的，还有八节点的
把它做成相应的单元库
这样的话，我们在使用的时候就不用重新去构造
把已经有的标准化的规范化的单元
需要什么就可以调用什么
根据复杂几何形状的状态
再把这些标准化的单元库调出来
这样的话就可以拼出复杂域的试函数
那么在建筑结构里面
这种思想，就叫做单元加组装的方式
建筑用的基本构件就是杆单元、梁单元，还有板
那么我们用这些基本构件
可以根据实际的需要搭建出
相应的土木建筑中的屋顶结构
不同的屋顶结构，简单的，复杂的
只要你按照真实的情况你都可以搭建出来
这样的话，我们基于几个简单的标准化的基本构件
也就是单元
可以根据需要任意组合出
满足我们实际复杂几何形状要求的试函数
这样的话就可以对2D问题3D问题任意几何复杂的情况
进行试函数的描述
这就是我们有限元非常重要的基础
就是由基本构件来构建复杂的对象
-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
