《桥梁结构电算》是桥梁工程专业大四的一门重要专业拓展课程，对学生解决复杂工程问题能力的培养具有重要意义。对边界条件的理解一直是困扰有限元初学者的重点难点问题，然而在当前越来越重视实践和思政教学的大背景下，专业理论课的学时被大大压缩，使得该课程存在学时少，内容多、学生缺乏兴趣、力学基础薄弱、未学习过有限元理论等诸多挑战。为帮助学生迅速入门并理解边界条件，基于近年来提出的最优学习的85%规则，开展与《结构力学》相融合的教学探索。从一座实际连续梁桥施工图出发，通过设置四组问题，将杆系结构边界条件与机动分析、链杆等学生已经掌握的既有知识相结合，循序渐进，由浅及深的引出对边界条件四层理解。让学生以辩证的眼光理解边界条件的分类、施加（解除）约束与链杆的关系、边界条件与杆系结构几何模型和单元划分之间的关系。利用不止一切边界是“连接”，一切结点（截面）都是“连接”的思想，将MIDAS/Civil中的一般支撑和各类连接统一用链杆表示，给出6个自由度约束方向与6根链杆的关系，为后续在软件中施加边界条件的具体操作打下基础。5年来的教学实践表明，基于85%规则的《桥梁结构电算》问题式教学方式具有很好的效果，学生在后续上机建模中很少出现之前的混淆不同类型边界条件的错误。

“Computation of Bridge Structures” is an important specialized course for senior students majoring in bridge engineering, which is of great significance to the cultivation of students' ability to solve complex engineering problems. Understanding boundary conditions has always been a key and difficult problem for finite element beginners. However, under the background of paying more and more attention to practice and ideological and political education, the class hours of professional theory courses have been greatly reduced, which makes the course have many challenges, such as fewer class hours, more content, students' lack of interest, weak mechanical foundation, and never learned the theory of finite element method. In order to help students to understand boundary conditions quickly and deeply, the teaching exploration of integration with “Structural Mechanics” is carried out based on the “Eighty Five Percent Rule” proposed in recent years for optimal learning. Four groups of questions are set up based on the construction drawing of an actual continuous beam bridge. The boundary conditions are combined with the known knowledge of kinematic analysis and rod, leading to four gradually deepened levels of understanding about boundary conditions. These explorations enable students to dialectically understand the classification of boundary conditions, the relationship between imposing (removing) constraints and rods, the relationship between boundary conditions and geometric models, and the meshing of the finite element model. Using the idea that not only all boundaries are "connections", but also all nodes (sections) are "connections", the supports and all kinds of connections in MIDAS/Civil are represented by chain bars. The relationship between six degrees of freedom constraint directions and six chain bars is given, which lays the foundation for the specific operation of applying boundary conditions in the software in the future. The teaching practice in the past five years shows that the problem-oriented teaching method of “Computation of Bridge Structures” based on the “Eighty Five Percent Rule” has a good effect, and students rarely make mistakes in confusing different types of boundary conditions in the subsequent computer modeling.

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重庆交通大学2019年教育教学改革研究资助项目（1903049）