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

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Journal of Vibration and Shock ›› 2019, Vol. 38 ›› Issue (15) : 157-162.

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

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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.

Key words

structural dynamic analysis / step-by-step method / finite element method / geometric nonlinearity / Euler-Bernoulli beam

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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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