| 分数导数Kelvin型粘弹性厚壁筒平面应力问题分析 |
| Fractional derivative Kevlin model to plane stress problems of viscoelastic thickwalled cylinder |
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| DOI： |
| 中文关键词: 分数导数 Mittag-Leffler函数 粘弹性 厚壁筒 |
| 英文关键词: fractional derivative Mittag-Leffler function viscoelasticity thickwalled cylinder |
| 基金项目:广东省自然科学基金资助项目(E010428) |
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| 中文摘要: |
| 利用弹性-粘弹性对应原理及拉普拉斯变换，结合Mittag-Leffler函数，分析体积应变为弹性、畸变部分的流变性质符合分数导数Kelvin模型的粘弹性厚壁筒的平面应力问题，导出了相应的应变解析解。分数导数型粘弹性厚壁筒的位移随时间的变化与分数导数的阶数有关。该模型考虑了剪切弹性模量对位移的影响，更接近实际。 |
| 英文摘要: |
| Using the elasticity-viscoelasticity corresponding principle and Laplac transformation combined with Mittag-Leffler function，the plane stress problems of the viscoelastic thickwalled cylinder，whose volume strain was elastic and the rheological properties of whose distortion at constant volume were in accordance with the fractional derivative Kevlin model，were analysed，and the analystical solutions were obtained.The displacement of the fractional derivative viscoelastic thickwalled cylinder was a function of time and related to the order of fractional derivative.Considering the influence of the shearing modulus on the displacement，the model was closer to the reality. |
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