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首页> 外文期刊>Applied Mechanics and Engineering >LARGE DEFLECTION ANALYSIS OF CANTILEVER BEAMS WITH AN OPENING
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LARGE DEFLECTION ANALYSIS OF CANTILEVER BEAMS WITH AN OPENING

机译：开孔悬臂梁的大挠度分析

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摘要

Numerical solutions have been obtained for analyzing the elastic deflection and stresses of a cantilever beam with a variable cross-sectional area. The variable cross-section was due to a circular, an elliptical and a square opening/hole/slot having the same cross- sectional area placed at different positions of the beam's span. An extensive numerical simulation was carried out using both the small and large deflection theories to calculate the stresses and the deflections of the same beam. A computer code in "C" has been developed using the Runge-Kutta technique for the purpose of simulation. The position of the opening over the beam's span is found to have significant effect on the beam's response under a tip load. Results show the linear theory fails to account for the change in curvature at high intensity loadings and underestimates the deflections. If same amount of material is removed considering different cross-sectional area (square, circle and ellipse), it is found that the maximum deflection is developed for the circular holes and the square slots, while the circular holes cause to develop the maximum stress. The discrepancy between the linear and nonlinear solutions is the maximum if the hollow section is near the fixed end. Among the three types of openings, the elliptic slots develop the minimum stress and tip deflections.
机译：已经获得了数值解来分析具有可变横截面面积的悬臂梁的弹性挠度和应力。可变的横截面归因于圆形，椭圆形和正方形的开口/孔/槽，它们具有相同的横截面面积，放置在光束跨度的不同位置。使用小和大挠度理论进行了广泛的数值模拟，以计算同一梁的应力和挠度。为了进行模拟，已使用Runge-Kutta技术开发了“ C”计算机代码。发现在尖端载荷下，梁跨度上开口的位置会对梁的响应产生重大影响。结果表明，线性理论未能说明高强度载荷下曲率的变化，并且低估了挠度。如果考虑到不同的横截面面积（正方形，圆形和椭圆形）去除了相同数量的材料，则会发现圆形孔和方形槽口出现了最大挠度，而圆形孔会产生最大应力。如果中空部分靠近固定端，则线性和非线性解之间的差异最大。在这三种类型的开口中，椭圆形缝隙会产生最小的应力和尖端变形。

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