Sensitivity of the eigenvalues to the ply angles for composite plate
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摘要: 研究了层合板特征值对铺层角的灵敏度, 从经典层合板理论出发, 结合有限元方法, 通过虚功原理, 推导了层合板的刚度矩阵和质量矩阵, 并且导出了质量、刚度矩阵和铺层角、铺层厚度之间的显式关系; 利用摄动方法, 推导了层合板各阶特征值对各个铺层角灵敏度的显式表达式。通过数值算例, 对比了本文方法与有限差分法得到的结果, 表明差分法只有当增量步很小时才能够达到本文方法的精度。Abstract: This paper studies the sensitivity of eigenvalues to ply angles for composite plates. Based on the classicaltheory of the laminated composite plate , the mass mat rix and stiffness mat rix were obtained by using thefinite-element-method and principle of virtual work. The equation between ply angles and stiffness mat rix was determined and by using the perturbation method in dynamic equation , the sensitivities of the eigenvalues to the ply angles were obtained explicitly. Through the numerical example given in the paper , the conclusion was demonst ratedthat the present method has superiority in accuracy compared with the finite difference method.
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Key words:
- laminated plate /
- eigenvalues /
- ply angles /
- sensitivity analysis
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