Abstract
This paper is concerned with the study of size effects over elastic response due to strain gradient elasticity (SGE). The general form of SGE with higher order gradients is simplified and either modified couple stress theory (MCST) or modified strain gradient theory (MSGT) models the size effects. An element-free Galerkin (EFG) model of the SGE response is obtained, and the algebraic governing equations of motion are derived here from the variational principles. Following validation, a comparison of the size effects exhibited by MCST and MSGT is carried out. The effect of each component of the higher gradients over the stiffness of the beam is also studied.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Mindlin RD, Eshel NN (1968) On first strain-gradient theories in linear elasticity. Int J Solids Struct 4(1):109–124
Yang FACM, Chong ACM, Lam DCC, Tong P (2002) Couple stress based strain gradient theory for elasticity. Int J Solids Struct 39(10):2731–2743
Lam DCC, Yang F, Chong ACM, Wang J, Tong P (2003) Experiments and theory in strain gradient elasticity. J Mech Phys Solids 51(8):1477–1508
Akgoz B, Civalek O (2013) A size-dependent shear deformation beam model based on the strain gradient elasticity theory. Int J Eng Sci 70:1–14
Ghiba I-D, Neff P, Madeo A, Munch I (2017) A variant of the linear isotropic indeterminate couple-stress model with symmetric local force-stress, symmetric nonlocal force-stress, symmetric couple-stresses and orthogonal boundary conditions. Math Mech Solids 22(6):1221–1266
Paolucci S (2016) Continuum mechanics and thermodynamics of matter. Cambridge University Press
Belytschko T, Lu YY, Gu L (1994) Element-free galerkin methods. Int J Numer Meth Eng 37(2):229–256
Sidhardh S, Ray MC (2018) Element-free galerkin model of nano-beams considering strain gradient elasticity. Acta Mech 229(2765). https://doi.org/10.1007/s00707-018-2139-x
Liu GR (2009) Meshfree methods: moving beyond the finite element method. CRC Press
Ma HM, Gao X-L, Reddy JN (2008) A microstructure-dependent timoshenko beam model based on a modified couple stress theory. J Mech Phys Solids 56(12):3379–3391
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Sidhardh, S. (2020). Size-Dependent Responses of Timoshenko Beam Incorporating the Strain Gradient Theories of Elasticity. In: Maity, D., Siddheshwar, P., Saha, S. (eds) Advances in Fluid Mechanics and Solid Mechanics. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-0772-4_16
Download citation
DOI: https://doi.org/10.1007/978-981-15-0772-4_16
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-0771-7
Online ISBN: 978-981-15-0772-4
eBook Packages: EngineeringEngineering (R0)