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梯度型非局部高阶梁理论与非局部弯曲新解法

陈玲 沈纪苹 李成 刘鑫培

陈玲, 沈纪苹, 李成, 刘鑫培. 梯度型非局部高阶梁理论与非局部弯曲新解法[J]. 力学学报, 2016, 48(1): 127-134. doi: 10.6052/0459-1879-15-170
引用本文: 陈玲, 沈纪苹, 李成, 刘鑫培. 梯度型非局部高阶梁理论与非局部弯曲新解法[J]. 力学学报, 2016, 48(1): 127-134. doi: 10.6052/0459-1879-15-170
Chen Ling, Shen Jiping, Li Cheng, Liu Xinpei. GRADIENT TYPE OF NONLOCAL HIGHER-ORDER BEAM THEORY AND NEW SOLUTION METHODOLOGY OF NONLOCAL BENDING DEFLECTION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(1): 127-134. doi: 10.6052/0459-1879-15-170
Citation: Chen Ling, Shen Jiping, Li Cheng, Liu Xinpei. GRADIENT TYPE OF NONLOCAL HIGHER-ORDER BEAM THEORY AND NEW SOLUTION METHODOLOGY OF NONLOCAL BENDING DEFLECTION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(1): 127-134. doi: 10.6052/0459-1879-15-170

梯度型非局部高阶梁理论与非局部弯曲新解法

doi: 10.6052/0459-1879-15-170
基金项目: 国家自然科学基金(11202145),苏州大学“车吴学者计划”项目和江苏省高校自然科学基金(14KJB460026)资助项目.
详细信息
    通讯作者:

    李成,副教授,主要研究方向:微纳米力学、复合材料力学.E-mail:licheng@suda.edu.cn

  • 中图分类号: O331

GRADIENT TYPE OF NONLOCAL HIGHER-ORDER BEAM THEORY AND NEW SOLUTION METHODOLOGY OF NONLOCAL BENDING DEFLECTION

  • 摘要: 针对文献中关于纳米结构刚度受非局部效应影响趋势的不一致预测,基于梯度型的非局部微分本构模型,利用迭代法及泰勒展开法求得了非局部高阶应力的无穷级数表达,非局部应力相当于经典弯曲应力与非局部挠度的逐阶梯度之和. 然后推导了梯度型非局部高阶梁弯曲的挠曲轴微分方程,并结合正则摄动思想,求解了非局部挠度的表达式. 最后给出数值算例,具体量化挠度受非局部尺度因子的影响大小. 研究表明:相比于其经典值,纳米结构的非局部弯曲挠度可呈现出或增大或减小或不变的趋势,考虑梯度型非局部高阶应力降低或提高或不影响纳米结构的刚度,具体结果依赖于外载和边界约束的类型. 算例显示外载形式和边界约束条件均各自独立地影响着纳米结构的非局部弯曲挠度,同时首次观察到非局部最大弯曲挠度的位置可能受非局部尺度因子的影响. 研究结论解决了非局部弹性力学应用于纳米结构的若干疑点,并为理论的发展和优化提供支持.

     

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出版历程
  • 收稿日期:  2015-05-12
  • 修回日期:  2015-08-17
  • 刊出日期:  2016-01-18

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