新工科背景下有限元教学的多维度提升——以刚度矩阵的生成和组装为例

Multidimensional Enhancement of Finite Element Teaching in the Background of New Engineering—A Case Study on the Generation and Assembly of Stiffness Matrix

摘要: 新工科建设作为中国工程教育改革的重要方向，旨在培养适应新技术革命和产业变革的创新型复合型人才。有限元分析中的刚度矩阵生成与组装是工程力学课程的核心知识点，但传统教学模式存在理论与实践脱节、内容抽象、学生参与度低等问题。文章以刚度矩阵的生成和组装为例，提出多维度教学提升策略：结合虚拟仿真软件实现理论实践融合，采用Hermite多项式单元简化计算，通过MATLAB和Mathematica通用函数强化计算能力训练，最终构建“理论–实践–计算”三位一体的教学体系。实践表明，该方法显著提升了学生对复杂力学概念的理解深度和工程应用能力，为新工科背景下工程力学教学改革提供了可借鉴的路径。

Abstract: As an important direction of China’s engineering education reform, the construction of New Engineering aims to cultivate innovative and composite talents to adapt to the new technological revolution and industrial transformation. The generation and assembly of the stiffness matrix in finite element analysis are core knowledge points in the engineering mechanics curriculum. However, the traditional teaching mode has problems such as the disconnection between theory and practice, the abstraction of content, and the low participation of students. Taking the generation and assembly of the stiffness matrix as an example, this paper proposes a multidimensional teaching improvement strategy: combining virtual simulation software to integrate theory and practice, using Hermite polynomial elements to simplify the calculation, and using MATLAB/Mathematica universal functions to strengthen the training of computational ability, and finally constructing a “theory-practice-calculation” integrated teaching system. Practice shows that this method has significantly improved students’ understanding of complex mechanical concepts and their ability to apply engineering, and has provided a reference for the reform of engineering mechanics teaching under the background of New Engineering.