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基于非局部弹性应力场理论的纳米尺度效应研究:纳米梁的平衡条件、控制方程以及静态挠度

C·W·林

C·W·林. 基于非局部弹性应力场理论的纳米尺度效应研究:纳米梁的平衡条件、控制方程以及静态挠度[J]. 应用数学和力学, 2010, 31(1): 35-50. doi: 10.3879/j.issn.1000-0887.2010.01.005
引用本文: C·W·林. 基于非局部弹性应力场理论的纳米尺度效应研究:纳米梁的平衡条件、控制方程以及静态挠度[J]. 应用数学和力学, 2010, 31(1): 35-50. doi: 10.3879/j.issn.1000-0887.2010.01.005
C. W. Lim. On the Truth of Nanoscale for Nanobeams Based on Nonlocal Elastic Stress Field Theory: Equilibrium,Governing Equation and Static Deflection[J]. Applied Mathematics and Mechanics, 2010, 31(1): 35-50. doi: 10.3879/j.issn.1000-0887.2010.01.005
Citation: C. W. Lim. On the Truth of Nanoscale for Nanobeams Based on Nonlocal Elastic Stress Field Theory: Equilibrium,Governing Equation and Static Deflection[J]. Applied Mathematics and Mechanics, 2010, 31(1): 35-50. doi: 10.3879/j.issn.1000-0887.2010.01.005

基于非局部弹性应力场理论的纳米尺度效应研究:纳米梁的平衡条件、控制方程以及静态挠度

doi: 10.3879/j.issn.1000-0887.2010.01.005
基金项目: 香港特别行政区研究资助委员会资助项目(RGCHKSAR,CityU117406)
详细信息
  • 中图分类号: O343

On the Truth of Nanoscale for Nanobeams Based on Nonlocal Elastic Stress Field Theory: Equilibrium,Governing Equation and Static Deflection

  • 摘要: 该文成功地解答了3个关于非局部应力理论用于纳米梁的问题:(ⅰ) 在绝大多数研究中,非局部效应增加导致纳米结构体刚度下降,其现象表现为弯曲挠度增加,固有频率减少,屈曲载荷下降,但为什么Eringen 的非局部弹性理论给出了完全相反的结论;(ⅱ) 为什么在某些研究结果中,非局部效应消失或是对研究结果无影响,比如纳米悬臂梁在集中载荷作用下的弯曲挠度; (ⅲ) 在高阶控制方程中,为什么高阶边界条件不存在.通过应用非局部弹性理论和精确变分原理分析纳米梁的弯曲问题,推导出全新的平衡条件、控制方程、边界条件和静态响应.这些方程和条件包含了与之前的相关研究结果符号相反的高阶微分项,这一差别导致了纳米效应对结构体的影响结果完全相反. 还证明之前为大家所公认的纳米梁静态或动态平衡条件实际上没有达到平衡,只有用等效弯矩代替非局部弯矩时,才可达到平衡.这些结论通常是可以被其它方法,比如应变梯度理论、耦合应力模型以及相关实验所证明.
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出版历程
  • 收稿日期:  2009-09-29
  • 修回日期:  2009-11-19
  • 刊出日期:  2010-01-15

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