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Free vibration of functionally graded sandwich shallow shells in thermal environments by a differential quadrature hierarchical finite element method

机译:功能梯度夹层浅壳在热环境中的自由振动,采用差分正交分层有限元方法

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摘要

This paper presents a differential quadrature hierarchical finite element method (DQHFEM) for dynamic analyses of functionally graded material (FGM) sandwich shallow shells in thermal and non-thermal environments. A layer-wise theory based on the first-order shear deformation theory (FSDT) for each layer was adopted. Effective material properties of the FGM are estimated according to Voigt's rule of mixture (ROM) and/or Mori-Tanaka (MT) scheme. For the shells in thermal environment, a nonlinear temperature distribution in thickness direction is considered and the elastic properties are assumed to be temperature dependent. The results obtained from the proposed formulation are validated with those available in literatures. Natural frequencies obtained from Sander's, Love's and Donnell's shell theories for different geometric and boundary conditions are compared with each other first to assess the performance of different shell theories for FGM sandwich shells under non-thermal environment. Then the effects of volume fraction index, core thickness and temperature gradient on natural frequencies of FGM sandwich shells are investigated. The presented DQHFEM is much like the fixed interface mode synthesis method but does not need modal analysis and is of high accuracy. This work is the first application of the method to functionally graded sandwich shells in thermal environments.
机译:本文提出了一种用于在热和非热环境中对功能梯度材料(FGM)夹层浅壳进行动力分析的差分正交分层有限元方法(DQHFEM)。每层均采用基于一阶剪切变形理论(FSDT)的分层理论。 FGM的有效材料性能是根据Voigt混合规则(ROM)和/或Mori-Tanaka(MT)方案估算的。对于热环境中的壳,考虑厚度方向上的非线性温度分布,并且假定弹性属性与温度有关。从提议的配方中获得的结果已得到文献中的验证。首先比较从桑德,洛夫和唐内尔的壳理论获得的不同几何和边界条件下的固有频率,以评估非热环境下FGM夹层壳的不同壳理论的性能。然后研究了体积分数指数,芯厚度和温度梯度对FGM夹层壳固有频率的影响。提出的DQHFEM与固定接口模式综合方法非常相似,但不需要模态分析并且具有很高的精度。这项工作是该方法在热环境中功能分级的三明治壳的首次应用。

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