The main content of this course includes: fundamental mathematics and mechanics method, basic properties of the finite element method
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The main content of this course includes: fundamental mathematics and mechanics method, basic properties of the finite element method
--Finite element, infinite capabilities
--1.1 Classification of mechanics:particle、rigid body、deformed body mechanics
--1.2 Main points for deformed body mechanics
--1.3 Methods to solve differential equation solving method
--1.5 Function approximation defined on complex domains
--1.6 The core of finite element: subdomain function approximation for complex domains
--1.7 History and software of FEM development
--2.1 Principles of mechanic analysis of springs
--2.2 Comparison between spring element and bar element
--2.3 Coordinate transformation of bar element
--2.4 An example of a four-bar structure
--2.5 ANSYS case analysis of four-bar structure
--3.1 Mechanical description and basic assumptions for deformed body
--3.3 Thoughts on three major variables and three major equations
--3.4 Construction of equilibrium Equation of Plane Problem
--3.5 Construction of strain-displacement relations for plane problems
--3.6 Construction of constitutive relations for plane problems
--3.7 Two kinds of boundary conditions
--4.1 Discussion of several special cases
--4.2 A complete solution of a simple bar under uniaxial tension based on elastic mechanics
--4.3 The description and solution of plane beam under pure bending
--4.4 Complete description of 3D elastic problem
--4.5 Description and understanding of tensor
--5.2 Trial function method for solving pure bending beam: residual value method
--5.3How to reduce the order of the derivative of trial function
--5.4 The principle of virtual work for solving plane bending beam
--5.6 The general energy principle of elastic problem
--6.1 Classic method and finite element method based on trial function
--6.2 Natural discretization and approximated discretization in finite element method
--6.3 Basic steps in the finite element method
--6.4 Comparison of classic method and finite element method
--7.1 Construction and MATLAB programming of bar element in local coordinate system
--7.3 Construction of three-dimensional beam element in local coordinate system
--7.4 Beam element coordinate transformation
--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 Two-dimensional 3-node triangular element and MATLAB programming
--8.2 Two-dimensional 4-node rectangular element and MATLAB programming
--8.4 Treatment of distributed force
--8.5 MATLAB programming of 2D plane rectangular thin plate
--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
--9.5 MATLAB programming for typical 2D problems
--9.6 ANSYS analysis case of typical 3Dl problem
--10.1Node number and storage bandwidth
--10.2 Properties of shape function matrix and stiffness matrix
--10.3 Treatment of boundary conditions and calculation of reaction forces
--10.4 Requirements for construction and convergence of displacement function
--10.5C0 element and C1 element
--10.7 Accuracy and property of numerical solutions of finite element analysis
--10.8 Error and average processing of element stress calculation result
--10.9 Error control and the accuracy improving method of h method and p method
--11.4 Bending plate element based on thin plate theory
--11.5 Sub-structure and super-element
--12.1 Finite element analysis for structural vibration: basic principle
--12.2 Case of finite element analysis for structural vibration
--12.3 Finite element analysis for elastic-plastic problems: basic principle
--12.4 Finite element analysis for elastic-plastic problems: solving non-linear equations
--13.1 Finite element analysis for heat transfer: basic principle
--13.2 Case of finite element analysis for heat transfer
--13.3 Finite element analysis for thermal stress problems: basic principle
--13.4 Finite element analysis for thermal stress problems: solving non-linear equation
--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
--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
曾攀,清华大学机械工程系教授,博导
雷丽萍,清华大学机械工程系,副研究员。主要从事材料加工中的数值模拟、塑性微成形、大型装备结构设计与分析等方面的研究。