关于材料力学中弯曲内力表征问题的探讨

DISCUSSION ON THE CHARACTERIZATION OF BENDING INTERNAL FORCES IN MECHANICS OF MATERIALS

  • 摘要: 弯曲变形是工程构件最常产生的变形形式之一,亦是材料力学的学习重点。其中,弯曲内力是学习弯曲相关知识的基础。本文将分别从作图方法和实验测试两方面对弯曲内力的表征问题开展讨论。首先,以直梁和刚架为分析对象,针对现存作图方法中容易造成学生误解和困惑的问题,提出一种更为统一的弯曲内力图作法,打通教学堵点。其次,结合挠曲线近似微分方程和数字图像相关(DIC)技术,提出一种基于全场变形测量的内力表征方法,达成实验技术、变形理论和内力计算三者的有机融合,进而加深学生对弯曲变形相关知识点的理解,培养学生的创新思维和融会贯通能力。

     

    Abstract: Bending deformation constitutes one of the most prevalent forms of mechanical behavior in engineering structural components and serves as a foundational topic in mechanics of materials. The characterization of bending internal forces underpins the comprehension of bending-related principles. This study systematically investigates the representation of bending internal forces from both graphical analysis and experimental testing perspectives. First, employing straight beams and rigid frames as analytical models, a unified graphical methodology for constructing bending internal force diagrams is proposed to address pedagogical bottlenecks caused by ambiguities in existing approaches. Second, by integrating approximate differential equations of the elastic curve with Digital Image Correlation (DIC) technology, a novel full-field deformation-based characterization method is developed. This approach establishes an integrated framework combining experimental techniques, deformation theory, and internal force computation, thereby enhancing students' conceptual understanding of bending deformation mechanisms. The proposed methodology fosters innovative thinking and interdisciplinary synthesis capabilities, offering a robust pedagogical strategy for advancing structural mechanics education.

     

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