基于里兹法研究复合材料层合板的动力屈曲问题

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Abstract Taking into account the effect of stress wave, the dynamic buckling of laminated composite plates under axial step loading has been researched theoretically using Ritz method. The trigonometric function including time items is used as the trial function and the effective dynamic buckling solution is deduced by analyzing the parity of the trial function. Based on Abraham de Moivre's formula, the governing equations of plates have been simplified and a differential equation has been obtained. Discussion of solutions to the differential equation, the critical buckling load has been gotten before the reflection of the stress wave. The influence of plies angle on the critical buckling load is discussed. Comparing the new Ritz Method with separation variable method, the critical buckling load curve of the new Ritz Method is coincidence with the curve of separation variable method. The dynamic buckling studying of laminated composite plates with different plies angles are simulated by ABAQUS. The maximum error is littler than 5 percent and it indicates that the theoretical values are consistent with the simulating ones. The results show that Ritz method combined with Abraham de Moivre's formula is effective and feasible.

Key words： Abraham de Moivre's formula Ritz method Stress wave the critical dynamic buckling load

Received: 27 March 2015 Published: 15 May 2016

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http://jvs.sjtu.edu.cn/EN/ OR http://jvs.sjtu.edu.cn/EN/Y2016/V35/I10/180

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