Lamb波在复合材料板中传播的谱有限元模拟

Modeling of Lamb Wave Propagations in Composite Plates by Spectral Element Method

众所周知Lamb波在复合材料中的传播呈各向异性的特点,经典有限元法模拟这类问题效率不高,所以,本文采用谱有限元法进行研究。先建立了一种新的谱有限板单元,该单元以Gauss-Lobatto-Legendre点作为节点,使质量矩阵是对角矩阵;另外,该单元采用了扩展的位移场,能够较好地模拟板结构的三维特性。然后,对复合材料板结构中Lamb波在对称模式与反对称模式下的传播速度进行了求解,将计算结果与Mindlin板谱单元的结果以及三维弹性理论的结果进行了比较,并讨论了Lamb波在反对称层合板中的传播特点。最后,模拟了Lamb波在含和不含损伤复合材料层合板中的传播,数值结果表明所建立的谱有限板单元可以较好地模拟出Lamb波在复合材料板结构中的传播特性。

It is well known that the propagation of Lamb waves in composite materials exhibits anisotropic characteristics,and that the conventional finite element method is inefficient for modeling such problems.Therefore,the spectral finite element method was used in the present investigations.A new spectral plate element was established.The Gauss-Lobatto-Legendre points were taken as the nodes,thus the mass matrix was in diagonal form.The extended form of the displacement fields was employed,thus the two dimensional element can be used to model three dimensional behavior of plate structures.The velocity of symmetric and anti-symmetric modes of Lamb wave propagating in composite plates was then computed.The results were compared to the data obtained by spectral finite element method based on Mindlin＇s theory and analytical solutions of three dimensional elasticity.In addition,the characteristics of Lamb wave propagating in anti-symmetric laminated plates were discussed.Finally,Lamb wave propagating in composite laminated plates with and without damage was simulated.Numerical results indicate that the proposed spectral element can be modeled the characteristics of Lamb wave propagating in laminated composite plates.