基于能量守恒的平面大变形欧拉梁逐步积分算法

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振动与冲击 ›› 2019, Vol. 38 ›› Issue (15) : 157-162.

论文

谢金哲1，吴斌2,1，杨浩文1

作者信息 +

Step by step integration method in time domain for planar Euler-Bernoulli beams with large deformation based on energy conservation

XIE Jinzhe1, WU Bin1,2, YANG Haowen1

Author information +

文章历史 +

摘要

建立了用于描述平面欧拉梁大变形状态的形函数，并在动力响应数值分析中通过运用能量方法实现了算法的无条件稳定。空间离散采用对水平位移和竖向位移独立插值的方法，使其能够描述欧拉梁大变形状态。在时间离散上采用单参数修正方法对速度-加速度关系进行修正，实现了保守荷载作用下的结构能量守恒，同时该算法具有二阶局部精度。最后，通过三个数值模拟算例验证了算法的有效性。

Abstract

Here, a shape function to describe a planar Euler beam’s large deformation state was built, and the principle of energy conservation was employed to realize the used algorithm’s unconditionally stable in its dynamic response numerical analysis.The beam’s horizontal displacement and vertical one were discretized in space using the independent interpolation method to be able to describe its large deformation state.A single-parameter correction method was utilized to modify the relation between velocity and acceleration to realize the beam’s energy conservation under the action of conservative loads for time discretizing and the algorithm having local second-order accuracy.Finally, the effectiveness of the proposed algorithm was verified with three numerical simulation examples.

导出引用

谢金哲1，吴斌2,1，杨浩文1. 基于能量守恒的平面大变形欧拉梁逐步积分算法[J]. 振动与冲击, 2019, 38(15): 157-162

XIE Jinzhe1, WU Bin1,2, YANG Haowen1. Step by step integration method in time domain for planar Euler-Bernoulli beams with large deformation based on energy conservation[J]. Journal of Vibration and Shock, 2019, 38(15): 157-162

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