基于三次样条插值法的三点弯梁光弹实验应力求解

STRESS SOLUTION IN PHOTOELASTIC EXPERIMENTS OF THREE-POINT BENDING BEAMS ON THE CUBIC SPLINE INTERPOLATION METHOD

  • 摘要: 三点弯梁平面光弹应力求解是公认的实验力学课程教学难点。为解决此问题,本文引入三次样条插值方法,对梁内计算面及辅助面的等差线和等倾线进行全场数据插值,并基于切应力差法计算出截面应力的实验解。通过将所得结果与数值解、理论解进行对比,发现面内应力分布规律基本一致,从而验证了三次样条插值法在三点弯梁应力实验求解中的有效性。该方法的应用不仅有助于教学难点的高效突破,也提升了学生处理多学科交叉难题的创新思维与实践能力。

     

    Abstract: The determination of plane photoelastic stress for three-point bending beams is widely recognized as a difficult teaching topic in the experimental mechanics curriculum. To address this, this paper introduced the cubic spline interpolation method and obtained the full-field data of the arithmetic lines and inclination lines on the computational surface and auxiliary surfaces within the beam. Furthermore, the shear stress difference method was adpoted to determine the experimental solution of sectional stress. By comparing the results with numerical and theoretical solutions, the stress distribution laws were in good agreement, which verified the effectiveness of the cubic spline interpolation method in solving the stress of three-point bending beams. The introduction of this method had facilitated the efficient resolution of teaching challenges, fostering students' innovative thinking and practical skills in addressing interdisciplinary problems.

     

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