Skip to main content
SpringerLink
Log in

Nonlocal Beam Equations

  • Chapter
  • First Online:
Nonlocal Euler–Bernoulli Beam Theories

Part of the book series: SpringerBriefs in Applied Sciences and Technology ((BRIEFSCONTINU))

  • 367 Accesses

Abstract

This chapter derives Euler–Bernoulli beam equations based on classical nonlocal theories, including the Eringen’s stress-gradient beam equation, the Mindlin’s strain-gradient beam equation, and the higher-order beam equation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Mindlin RD, Tiersten HF (1961) Effects of couple-stresses in linear elasticity. Arch Ration Mech Anal 11(1):415–448

    Article  MathSciNet  Google Scholar 

  2. Mindlin RD (1963) Micro-structure in linear elasticity. Arch Ration Mech Anal 16(1):51–78

    Article  MathSciNet  Google Scholar 

  3. Mindlin RD (1965) Second gradient of strain and surface-tension in linear elasticity. Int J Solids Struct 1:417–438

    Article  Google Scholar 

  4. Kroner E (1967) Elasticity theory of materials with long range cohesive forces. Int J Solids Struct 3:731–742

    Article  Google Scholar 

  5. Eringen AC (1972) Linear theory of nonlocal elasticity and dispersion of plane waves. Int J Eng Sci 10:425–435

    Article  Google Scholar 

  6. Eringen AC (1972) Nonlocal polar elastic continua. Int J Eng Sci 10:1–16

    Article  MathSciNet  Google Scholar 

  7. Eringen AC (1983) On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J Appl Phys 54(9):4703–4710

    Article  Google Scholar 

  8. Eringen AC, Edelen DGB (1972) On Nonlocal Elasticity. Int J Eng Sci 10:233–248

    Article  MathSciNet  Google Scholar 

  9. Peddieson J, Buchanan GR, McNitt RP (2003) Application of nonlocal continuum models to nanotechnology. Int J Eng Sci 41:305–312

    Article  Google Scholar 

  10. Lim CW, Zhang G, Reddy JN (2015) A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. J Mech Phys Solids 78:298–313

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Mechanical and Electronic Engineering, China University of Petroleum, Qingdao, China

    Dr. Jingkai Chen

Authors
  1. Dr. Jingkai Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jingkai Chen .

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Chen, J. (2021). Nonlocal Beam Equations. In: Nonlocal Euler–Bernoulli Beam Theories. SpringerBriefs in Applied Sciences and Technology(). Springer, Cham. https://doi.org/10.1007/978-3-030-69788-4_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-69788-4_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-69787-7

  • Online ISBN: 978-3-030-69788-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation