材料力学中梁三点弯曲实验的教学探索全场变形可视化

EXPLORING THE TEACHING OF THREE-POINT BENDING EXPERIMENTS IN MECHANICS OF MATERIALS: VISUALIZATION OF FULL-FIELD DEFORMATION

  • 摘要: 在横力弯曲条件下,截面翘曲和纵向纤维间挤压可导致梁的弯曲正应力公式产生显著误差,但在跨高比大于5时误差可忽略不计。如何让学生理解梁横力弯曲的上述特点是材料力学教学中的难点之一。数字图像相关(digital image correlation, DIC)是一种先进的光学变形测量方法,具有非接触、全场、操作简单等优势。本文引入DIC方法开展了梁三点弯曲实验的教学改革探索,实现了横力弯曲变形特点的可视化测量与呈现。结合梁在不同跨高比下的应变场和广义胡克定律,获得了正应力沿截面高度的分布规律,探讨了梁弯曲正应力公式的内涵。实践表明,引入先进光学测量方法进行可视化表征和展示,加深了学生对不同关联知识点的理解,培养了融会贯通和实践能力,激发了学生的科技创新意识。

     

    Abstract: Although cross-sectional warping and compression between longitudinal fibers can cause significant errors in the beam bending normal stress calculation under transverse bending, these errors become negligible when the span-to-depth ratio of the beam exceeds 5. One of the key challenges in teaching mechanics of materials is helping students understand these specific characteristics of transverse bending. The digital image correlation (DIC) is an advanced optical deformation measurement technique that provides benefits like non-contact, full-field measurement, and simple operation. This paper explores teaching reform in three-point bending experiments by introducing the DIC method to achieve visual measurement and presentation of the deformation characteristics under transverse bending. By combining the strain field of beams with different span-to-depth ratios and generalized Hooke's law, the normal stress distribution along the cross-section height can be obtained, enabling a more comprehensive understanding of the beam bending normal stress formula. The practice shows that introducing advanced optical measurement methods to visualize key content enhances students' understanding of various related knowledge, cultivates integrative and practical skills, and stimulates their interest in scientific and technological innovation.

     

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