YUE Ying;ZHAO Xia;ZHAO Wei;WEI Xiantao;WANG Zhongping;ZHANG Zengming;

• 1:National Physical Experiment Teaching Demonstration Center
• 2:University of Science and Technology of China

Abstract：

Elasticity is an important interface between physics and engineering, encompassing a wealth of mathematical tools and physical concepts, which is of great significance for students to solidify their theoretical foundation and enhance their practical abilities. This paper focuses on the bending problem of beams and elaborates on the construction of Timoshenko beam theory from the perspective of the basic equations of elasticity. The deflection equation is solved by combining the Green's function method and the Laplace transform. A cantilever beam teaching model constructed with dry spaghetti and a 3D-printed support is used. By calculating the deflection curve and simulating the strain field, and comparing the results with experimental measurements, the effectiveness of the theoretical model and numerical methods is verified. This study integrates theoretical models, numerical calculations, simulation modeling, and experimental measurements deeply, and can provide an inspiring teaching case for experimental teaching in physics and engineering courses in colleges and universities.

Key Words： elasticity mechanics;Timoshenko beam theory;3D printing;deflection

Abstract:

Keywords:

Foundation: 中国科学技术大学教育教学改革研究项目（2025xjyxm054）

Authors: YUE Ying;ZHAO Xia;ZHAO Wei;WEI Xiantao;WANG Zhongping;ZHANG Zengming;

References：

• [1]TIMOSHENKO S P. Theory of Elasticity[M]. New York:Mc Garw-Hill, 1970.
• [2]CHEN T, SU G Y, SHEN Y S, et al. Unified Green's functions of forced vibration of axially loaded Timoshenko beam:Transition parameter[J]. International Journal of Mechanical Sciences, 2016, 113:211-20.
• [3]王续宏,李翔宇.轴向受载铁木辛柯梁的弯曲研究[J].成都大学学报(自然科学版), 2019, 38(2):187-9,205.WANG X H, LI X Y. Bending study of Timoshenko beams under axial load[J]. Journal of Chengdu University(Natural Science Edition), 2019, 38(2):187-189, 205.(in Chinese)
• [4]KREYSZIG E. Advanced engineering mathematics[M].Hoboken:John Wiley&Sons, 2011.
• [5]GOODNO J M G B J. Mechanics of materials[M]. Cengage Learning, 2009.
• [6]张增明.大学物理实验[M].北京:高等教育出版社,2024.ZHANG Z M. University physics experiments[M]. Beijing:Higher Education Press, 2024.(in Chinese)
• [7]付宝连.弹性力学中的能量原理及其应用[M].北京:科学出版社, 2004.FU B L. Energy principles in elasticity and their applications[M]. Beijing:Science Press, 2004.(in Chinese)
• [8]ZHANG Y, LI X, DAI Y, et al. On the number of fractured segments of spaghetti breaking dynamics[J]. Theoretical and Applied Mechanics Letters, 2022, 12(4).
• [9]HEISSER R H, PATIL V P, STOOP N, et al. Controlling fracture cascades through twisting and quenching[J]. Proceedings of the National Academy of Sciences of the United States of America, 2018, 115(35):8665-70.