FEM with Floquet Theory for Non-slender Elastic Columns Subject to Harmonic Applied Axial Force Using 2D and 3D Solid Elements
FEM with Floquet Theory for Non-slender Elastic Columns Subject to Harmonic Applied Axial Force Using 2D and 3D Solid Elements
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DOI：
10.1007/978-3-030-13720-5_22
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
E. Clerkin;Markus Rieken
中科院分区：
文献类型：
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作者：
E. Clerkin;Markus Rieken
采用实体单元的Rayleigh-Ritz有限元列式，对受周期轴力作用的二维和三维固支柱进行了数值模拟。考虑了非线性应变。得到了一个质量单元矩阵和两个刚度矩阵。通过单元组装后，将计算出的固有频率和屈曲载荷与Euler-Bernoulli梁理论预测值进行比较。对于2D三角形和3D长方体单元，需要大量的自由度来充分收敛，这增加了应用Floquet理论来确定谐波受力柱的稳定性的特定计算成本。使用Hsu等人推广的方法来减少计算量并获得完整的单值矩阵。Floquet乘子的讨论与它们的分叉。通用的2D和3D元素允许讨论非细长柱。此外，还研究了由不纯材料组成的三维钢柱和高宽比变化的三维钢柱的稳定性。
The Rayleigh–Ritz formulation of finite element method using solid elements is implemented for a 2D and 3D clamped-clamped column which is subject to a periodically applied axial force. Non-linear strain is considered. A mass element matrix and two stiffness matrices are obtained. After assembly by elements, the calculated natural frequencies and buckling loads are compared to Euler–Bernoulli beam theory predictions. For 2D triangular and 3D cuboid elements, a large number of degrees of freedom are required for sufficient convergence which adds particular computational costs to applying Floquet theory to determine stability of the harmonically forced column. A method popularised by Hsu et al. is used to reduce the computational load and obtain the full monodromy matrix. The Floquet multipliers are discussed in relation to their bifurcations. The versatile 2D and 3D elements used allows for the discussion of non-slender columns. In addition, the stability of a 3D steel column comprised of impure materials or with changed aspect ratio are investigated.