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固体力学与流体力学有限元分析

一、课程介绍

有限元方法是一个在机械、土木、海洋、船舶、汽车和航空等工业中得到广泛应用的现代计算技术。目前，此方法也在基于仿真模拟的计算机辅助设计中开始得到应用。本课程的主要教学目的不仅要让学生了解和掌握这一现代计算技术的基础知识，而且让学生熟悉一个基于有限元方法的解决传热，固体力学和流体力学等问题的数值工具的开发和研究。本课程能够用来更好地培养学生，掌握必要的技能，从而能够使用有限元方法解决复杂的科学和工程实际问题。

本课程以统一的方式介绍固体、结构、流体和传热问题的有限元分析的基础知识和现代技术。课程内容包括：介绍有关传热、固体和流体力学问题的控制方程；介绍相应的有限元模型方程的推导和求解方法；讨论如何正确合理地使用有限元方法来解决各类实际问题，其中包括怎样建立合适的有限元模型、解释和分析结果、了解和评估误差等。

The finite element methods studied in this course are practical procedures that are employed extensively in the mechanical, civil, ocean, shipbuilding, automobile and aeronautical industries. The finite element methods are also becoming popular in simulation-based computer-aided designs. In addition to providing students with the basics of the finite element technique, this course also provides a numerical tool for the solution of different classes of problems in heat transfer, solid mechanics and fluid mechanics. This course will prepare students with a necessary skill to solve complex real world problems in science and engineering using finite element methods.

This course Introduces the fundamentals of finite element analysis of solid, structural, fluid, and heat transfer problems in a unified manner. Topics of the course include governing equations for heat transfer, solid and fluid mechanics; their finite element formulations and solution procedures; appropriate use of finite element methods including setting up an appropriate model, interpreting the results, and assessing the solution error.

二、教学大纲

（1）课程基本信息

课程代码 Course Code	NA26018	*学时 Teaching Hours		32		*学分 Credits		2
*课程名称 Course Name	（中文）固体力学与流体力学的有限元分析
	（English）Finite Element Analysis of Solids and Fluids
*授课语言 Instruction Language	英文 English
*开课院系 School	船舶海洋与建筑工程学院 School of Naval Architecture, Ocean and Civil Engineering
先修课程 Prerequisite	流体力学，结构力学，计算方法，程序语言 Fluid Dynamics, Solid Mechanics, Numerical Method, Programming Language
授课教师 Instructors	姓名Name		职称Title		单位Department		联系方式E-mail
	万德成 Decheng Wan		教授 Professor		船舶与海洋工程系 Naval Architecture and Ocean Engineering		dcwan@sjtu.edu.cn
	刘成 Cheng Liu		副教授 Associate Professor		船舶与海洋工程系 Naval Architecture and Ocean Engineering		chengliu@sjtu.edu.cn
	邹璐Lu Zou		副教授Associate Prof.		船舶与海洋工程系Naval Architecture and Ocean Engineering		luzou@sjtu.edu.cn
	王建华Jianhua Wang		助理研究员 Assistant Prof.		船舶与海洋工程系Naval Architecture and Ocean Engineering		jianhuawang@sjtu.edu.cn

（2）课程内容及基本要求

*教学安排 Schedules	教学内容Content	授课学时 Hours	教学方式 Format	授课教师 Instructor
	概述：有限元分析的基本概念和应用 Introduction: Basic Concept of the Finite Element Analysis and Applications 有限元分析：数学基础、积分表达和变分方法 Mathematical Preliminaries, Integral Formulations, and Variational Methods	3	讲授 Lecture	刘成 Cheng Liu
	有限元基本程序架构和组成，一维问题的计算机程序的开发 Architecture of FE code, computer Implementation One-Dimensional Problems	3	讲授 Lecture	刘成 Cheng Liu
	杆/梁单元、绗架结构问题中的有限元方法和应用 FE method/applications of FEM in large deformation of frames with beam/rod element	3	讲授 Lecture	刘成 Cheng Liu
	特征值问题和瞬态问题方面的有限元方法和应用 FE method/applications of FEM in Eigenvalue and Time-Dependent Problems	3	讲授 Lecture	刘成 Cheng Liu
	二维问题的计算机程序的开发 Computer Implementation of two-dimensional Problems	3	讲授 Lecture	刘成 Cheng Liu
	单元插值函数、等参变换方法 Interpolating functions, isoparametric element	3	讲授 Lecture	刘成 Cheng Liu
	有限元线性方程组的数值求解方法 Numerical solution of linear systems of FEM	3	讲授 Lecture	刘成 Cheng Liu
	有限单元法程序FEM1D、FEM2D、OOFEM介绍 Brief introduction for open source code: FEM1D、FEM2D、OOFEM	3	讲授 Lecture	刘成 Cheng Liu
	流体力学中的有限元方法和应用 FE method/applications in fluid mechanics	3	讲授 Lecture	刘成 Cheng Liu
	分析不连续物理场的扩展有限元方法理论及应用 extended FE method/applications in analysis of discontinuous physical field	3	讲授 Lecture	刘成 Cheng Liu
	专题交流汇报讨论： Computer Project Presentations and Discussions	2	汇报与讨论 Presentations and discussions	刘成 Cheng Liu
机动内容1：	网格类方法程序实现中的若干实际问题 Practical considerations for mesh-based numerical method	2-3	讲授 Lecture	刘成 Cheng Liu
机动内容2：	并行程序设计概述 Brief introduction for programing with parallel computation support	2-3	讲授 Lecture	刘成 Cheng Liu

（3）考核方式
完成实际编程计算练习，以小论文的形式撰写计算结果分析报告，并在课堂上交流讨论。

Develop finite element codes to complete two projects for given problems, write the reports in the form of a mini scientific paper and present the results in the class.

（4）参考资料
1. Singiresu S. Rao “The Finite Element Method in Engineering,” Fifth Edition, Butterworth-Heinemann, 2011, ISBN: 978-1-85617-661-3. Sixth Edition, Butterworth-Heinemann, Nov. 2017, ISBN-10: 0128117680; ISBN-13: 978-0128117682.
2. J. N. Reddy "An Introduction to the Finite Element Method," Forth Edition, McGraw Hill,2018
3. D.V. Hutton "Fundamentals of Finite Element Analysis," McGraw Hill, 2004.
4. J. Fish and T. Belytschko "A First Course in Finite Elements," J. Wiley, 2007.
5. K.-J. Bathe "Finite Element Procedures, Prentice-Hall," 1996.
6. E. Madenci and I. Guven "The Finite Element Method and Applications in Engineering Using ANSYS," Springer, 2015.
7. Klaus-Jürgen Bathe. 2.092 Finite Element Analysis of Solids and Fluids I. Fall 2009. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu. License: Creative Commons BY-NC-SA.
8. Klaus-Jürgen Bathe. 2.094 Finite Element Analysis of Solids and Fluids II. Spring 2011. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu. License: Creative Commons BY-NC-SA.

三、课件下载
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