基于里兹法研究复合材料层合板的动力屈曲问题

摘要

考虑应力波效应，引用棣莫弗公式与里兹法结合来研究复合材料板的动力屈曲问题。设板的试函数为含有时间项的三角函数形式，通过对试函数奇偶性的判断得出有效的动力屈曲解。应用棣莫弗公式对控制方程进行化简，通过对化简所得的微分方程解的讨论，得出了应力波反射前复合材料层合板的临界动力屈曲载荷表达式，并探讨了不同铺层角度对于临界动力屈曲的影响。将里兹法获得的屈曲载荷值曲线与分离变量法所得的曲线进行对比，两条曲线几乎完全重合，同时应用 ABAQUS 有限元软件对不同角度下复合材料层合板进行动力屈曲模拟，将临界屈曲载荷模拟值与里兹法得出的理论值进行对比，二者误差不超过百分之五，说明棣莫弗公式与里兹法结合可有效应用于复合材料板动力屈曲的研究。%Taking into account the effect of stress wave,the dynamic buckling of laminated composite plates under axial step loading was analysed theoretically by using Ritz method.The trigonometric function including time items was used as a trial function and the effective dynamic buckling solution was deduced by analyzing the parity of trial function. Based on the Abraham de Moivre's formula,the governing equations of plates were simplified and a differential equation was obtained.Through the discussion of solutions to the differential equation,the critical buckling load can be got and will be reached before the reflection of the stress wave.The influence of plies angle on the critical buckling load was discussed.Comparing the new Ritz method with variable separation method,the critical buckling load curves of both methods are in good coincidence.The dynamic buckling of laminated composite plates with different plies angles were simulated and analysed by using ABAQUS.The maximum error is less than 5 percent and it indicates that the theoretical values are consistent with the simulated ones.The results show that the Ritz method combined with Abraham de Moivre's formula is effective and feasible.