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所在平台: Udemy |
课程主页: https://www.udemy.com/course/basics-of-fea-i/
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**课程名称：** 有限元分析基础（一） **课程概述：** 本课程是有限元分析系列讲座的第一部分。课程内容涵盖了矩阵代数、微分方程及其求解方法，以及有限元加权残值法。通过讲解和演算各种数值例子，帮助学习者理解不同概念及其应用。这些知识对后续课程的学习以及理解ANSYS软件的应用至关重要。 **先修要求：** 掌握基础数学知识。 **课程内容：** 1. **有限元分析介绍：** 介绍有限元分析（FEA）的概念、优点、缺点及应用领域。 2. **矩阵代数基础：** 回顾矩阵代数的基本知识，重点学习高阶矩阵求逆的高斯消元法。 3. **线性微分方程基础与精确解法（Exact Method）：** 学习线性微分方程的基础知识，以及求解这些方程的精确方法。 4. **有限元加权残值法：** * 研究基于泰勒级数展开的有限差分法，并将其与精确解法进行比较。这对于验证ANSYS软件解的准确性非常重要。 * 学习用于求解线性微分方程的各种加权残值方法，包括弱形式和非弱形式方法，如子域法、加权平均法（Galerkin）、Petrov-Galerkin法、配置法、最小二乘法和Rayleigh Ritz法。
This course is the first part of the lecture series of Finite Element Analysis subject. It takes you through various topics like Matrix Algebra, Differential Equations and their solutions and FEM-Weighted Residue Approach. Various numerical are solved to explain different concepts and their applications. These topics help while solving of next course chapters and also help in understanding of ANSYS solutions. Basic Mathematics is the requirement for understanding of this subject.We start with Introduction to Finite Element Analysis, its advantages, disadvantages and applications. Then we brush up some basics of Matrix Algebra and learn the Gauss Elimination Method for finding inverse of a higher order matrix.Further, we move to the Basics of linear differential equations and the ways to calculate their solutions which is called the Exact Method.Then we study FEM-Weighted Residue Approaches and the 7 methods to find solution of Linear Differential Equations which is a Finite Difference Method based on Taylor's series method and compare the solution with exact method. This is very important as ANSYS solutions need to be checked by exact solution for their accuracy. We study the Weak and Non-Weak form type methods to find the solution namely Sub-domain, Galerkin, Petrov-Galerkin, Collocation, Least Square and Rayleigh Ritz methods.
