有限元总体刚度矩阵集成的教学  

Teaching Design of Global Stiffness Matrix Assembly in FEM

作　　者：胡圣荣 张巍[1] HU Shengrong;ZHANG Wei(College of Water Conservancy and Civil Engineering,South China)

机构地区：[1]华南农业大学水利与土木工程学院,广州510642

出　　处：《机械工程师》2024年第11期29-31,36,共4页Mechanical Engineer

摘　　要：单元刚度矩阵组装到总体刚度矩阵的原理和方法是有限元教学中基本而重要的内容,因涉及的节点平衡方程问题简单而讲解不够深入,容易导致留下认知隐患。文中介绍了有限元总体刚度矩阵集成的两种教学设计,一种涉及节点平衡方程,另一种不涉及节点平衡方程。针对由节点平衡方程引出的似是而非的认知问题展开教学。教学过程中采用提问、讨论、推导、动画演示等方式以加深学生的认知和理解。The principle and method of assembling element stiffness matrix into global stiffness matrix is an important content of finite element teaching.However,the node equilibrium equation involved is usually described less due to its simplicity,which leaves cognitive pitfalls.This paper introduces two teaching designs for the integration of finite element total stiffness matrix,one involving the nodal equilibrium equation and the other not involving the nodal equilibrium equation.The node equilibrium equation is discussed with specious problems.The teaching process includes questioning,discussion,deduction and animation demonstration to deepen students'cognition and understanding.

关 键 词：有限元 节点平衡方程 单元刚度矩阵 总体刚度矩阵 

分 类 号：TP391.7[自动化与计算机技术—计算机应用技术]