有限元分析与应用

你将学到什么

Basic equations of mechanics

Mathematical principles of Finite Element Method (FEM)

Realizations in discrete and continuum structures

Basics of MATLAB and ANSYS

课程概况

Do you want to become an expert at structural analysis?

Finite Element Method (FEM) is a powerful tool. FEM is an effective numerical technique for partial differential equations (PDEs) in engineering. The fact that modern engineers can obtain detailed information for structural, thermal, electromagnetic problems with virtual experiments largely gives credit to FEM. The finite element method provides infinite possibilities for engineering, and this course provides a detailed introduction of FEM and its applications in engineering and beyond.

This course is divided into 15 lessons, which introduce basic equations of mechanics, mathematical principles of FEM, realizations in both discrete and continuum structures, various applications in engineering and skills at modeling with FEM software. Examples are demonstrated with MATLAB and ANSYS.

有限元方法(finite element method)：基于数学力学原理，采用计算机信息化分析手段，完整获取复杂工程问题及科学研究中的定量化结果，也被称为一种基于计算机信息化处理的“虚拟实验”，在数学上它是求取复杂微分方程近似解的有效工具，是现代仿真技术的重要基础原理。有限元分析的力学基础是弹性力学，方程求解的数学原理是加权残值法和泛函极值原理，实现的方法是数值化离散技术，最终的载体是有限元分析软件。有限元方法已成为机械、航空航天、土木、力学等专业学生的必备知识。

这门课程的主要内容包括：基本变量和力学方程、数学求解原理、离散结构和连续体的有限元分析实现、各种应用领域、有限元分析的软件平台和建模技巧等。在强调有限元理论的工程背景和物理概念的同时，通过一些典型的实例来深入浅出地系统阐述有限元分析的基本原理。此外，课程基于MATLAB演示基于有限元原理的编程方法，通过ANSYS来展示应用有限元方法的具体建模过程。