从正问题到反问题:梁弯曲教学中工程思维能力的培养与实践

FROM FORWARD TO INVERSE PROBLEMS: CULTIVATING AND PRACTICE OF ENGINEERING THINKING IN BEAM BENDING TEACHING

  • 摘要: 均质纯弯梁的弯曲正应力和变形分析是材料力学课程中的学习重点。本文依托固体力学核心课程体系的贯通性改革,将现有材料力学课程中的均质梁纯弯教学内容拓展到非均质组合梁弯曲分析。通过引入相当截面变换思想,将矩形截面双层组合梁转化为T型截面均质梁,建立了相当截面等效惯性矩与组合梁跨中挠度之间的显式函数关系。在此基础上,进一步提出“相对法”,阐明了采用三点弯曲试验测定功能梯度涂层弹性模量的实验原理,明确了其相比于“直接法”的优势。教学实施上,设置了自主实验设计模块,引导学生设计与开展三点弯试验,实际测量功能梯度涂层的等效弹性模量。数值仿真模块,指导学生采用虚拟实验,明确了组合梁弯曲问题理论模型及涂层等效模量测定实验方案的合理可行性。该教学方案有助于学生理解梁弯曲理论、力学实验与数值仿真在工程问题中的综合应用,并深化对等效变换、相当截面、惯性矩、挠度及三点弯曲实验等材料力学核心概念的理解与实际运用。

     

    Abstract: The analysis of bending normal stress and deformation of homogeneous beams under pure bending is a core topic in Mechanics of Materials. Leveraging the comprehensive reform of the solid mechanics curriculum, this paper extends the teaching of homogeneous beams to the bending analysis of heterogeneous composite beams. By applying the equivalent section transformation principle, a rectangular double-layer composite beam is transformed into a T-section homogeneous beam, establishing an explicit relationship between the equivalent moment of inertia and the mid-span deflection. On this basis, a "relative method" is introduced to clarify the experimental principle for determining the equivalent elastic modulus of functionally graded coatings via three-point bending tests, highlighting its advantages over the "direct method." The teaching implementation features an autonomous experimental module where students design and conduct tests to measure the coating's modulus. Additionally, a numerical simulation module guides students through virtual experiments to verify the feasibility of the theoretical model and the experimental scheme. This integrated approach helps students understand the comprehensive application of theory, experiment, and simulation in engineering, deepening their mastery of key concepts such as equivalent transformation, moment of inertia, deflection, and three-point bending.

     

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