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This work highlights the existing contradictions in satisfying boundary conditions while modeling nanobeams in cantilevered configurations. Various analytical and numerical models can analyze it. Depending on the configuration, these models behave differently. Hence, it is difficult for an engineer to select the method to design the component/structure. Cantilevered nanobeams under point and uniformly distributed load (UDL) are investigated. Different methods’ results are contrasted. Inconsistencies found while satisfying essential and natural boundary criteria are examined. The nonlocal moment-curvature relationship and its effect on the solution are also discussed. All fundamental quantities are compared. While some methods anticipate cantilever hardening, others predict softening. The results show technique flaws. A unified and consistent approach to problem-solving is needed.

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On the Satisfaction of Natural and Essential Boundary Conditions for Bending in Nanobeams Within the Framework of Eringen’s Nonlocal Elasticity Theory

  • 会议论文

  • 发表日期：

    2025年

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  • Gaurab Kumar Khanra,
  • I. R. Praveen Krishna,
  • P. Raveendranath

摘要

This work highlights the existing contradictions in satisfying boundary conditions while modeling nanobeams in cantilevered configurations. Various analytical and numerical models can analyze it. Depending on the configuration, these models behave differently. Hence, it is difficult for an engineer to select the method to design the component/structure. Cantilevered nanobeams under point and uniformly distributed load (UDL) are investigated. Different methods’ results are contrasted. Inconsistencies found while satisfying essential and natural boundary criteria are examined. The nonlocal moment-curvature relationship and its effect on the solution are also discussed. All fundamental quantities are compared. While some methods anticipate cantilever hardening, others predict softening. The results show technique flaws. A unified and consistent approach to problem-solving is needed.