悬臂梁角点的应力非对称问题的实验研究

Experimental Study of Asymmetric Stress at the Corner of a Cantilever Beam

采用网格法研究弹性悬臂梁自由端角点在端部竖向均布荷载下的大变形,利用现代图像采集技术获得实验图像,借助MATLAB图像处理技术对图像数据进行处理,以应变与转动的S-R分解定理为理论基础,计算整旋角并绘制整旋角等高线分布图。等高线分布图显示越靠近角点处,整旋角的等值线越密集,即角点处的整旋角的梯度增大,从而证明体力矩的存在是引起悬臂梁自由端角点应力非对称现象的原因。

This article studies the large deformation in the free end corner of an elastic cantilever beam under vertical uniform distribution loading at the end point by grid method. Modern image capturing technology was utilized to obtain experimental images, which were inputted to a computer later. MATLAB software was utilized to process images. The mean rotation angle was calculated based on S -R strain and rotation decomposition theorem, the mean rotation angle contour was plotted. The contour shows that there is obvious stress asymmetry when an elastic cantilever beam is under vertical uniform distribution loading at the end point. Isolines of mean ;rotation angle become denser and denser and the gradient of mean rotation angle increases. It verified that the presence of body moment is the reason of asymmetric stress at the free end corner.