Refined mechanical and mathematical model of an elastic half-plane
DOI:
https://doi.org/10.54355/tbus/2.1.2022.0014Keywords:
elastic foundation, half-plane, displacements, stresses, deformation, distribution functionAbstract
Loads cause vertical movements of the foundations of all the structures. Their magnitude determines the building safe operation. A closed analytical solution to the problem of the linear elastic theory for the distribution of stresses and strains in a homogeneous isotropic elastic foundation has been presented. The article considers the calculation of the stress-strain state of an elastic half-plane by the method in displacement functions. The theory of calculating an elastic half-plane has been built. New formulas have been are found that determine displacements and stresses at any points of an elastic foundation. An example of calculating an elastic half-plane under the action of a normal and tangential loads has been given.
Downloads
Metrics
References
Mehanika gruntov, osnovaniya i fundamenty / B.I. Dalmatov. — Leningrad: Stroiizdat, 1988. — 415 p.
Mehanika gruntov / N.A. Tsytovich. — Moscow: Gosstroiizdat, 1963. — 636 p.
Raschet deformacij osnovanij zdanij i sooruzhenij / S.G. Kushner. — Zaporozh'e: PLC «IPOZaporozh'e», 2008. — 496 p.
Complex variable methods in plane elasticity / Lu Jian-ke. — Singapore: World Scientific Pub Co Inc, 1995. — 240 p.
On complex variable method in finite elasticity / A. Akinola // Applied Math. — 2009. — Vol. 1. — P. 1–16.
Analytical Methods in Geomechanics / K.T. Chau. — Florida, USA: CRC Press, 2012. — 424 p.
Methods of the theory of functions of a complex variable in problems of geomechanics / A.N. Bogomolov, A.N. Ushakov. — Volgograd: Peremena, 2014. — 227 p.
A complex variable solutions for a deforming circular tunnel in an elastic half-plane / A. Verruijt // Numerical and Analytical Methods in Geomechanics. — 1997. — Vol. 21, No. 2. — P. 77-89. https://doi.org/10.1002/(SICI)1096-9853(199702)21:2<77::AID-NAG857>3.0.CO;2-M DOI: https://doi.org/10.1002/(SICI)1096-9853(199702)21:2<77::AID-NAG857>3.0.CO;2-M
Stress-strain state of an elastic half-plane at a linear shift of a part of its boundary / A.N. Bogomolov, A.N. Ushakov // Vestnik MGSU. — 2017. — Vol. 12, No. 2. — P. 184-192. https://doi.org/10.22227/1997-0935.2017.2.184-192 DOI: https://doi.org/10.22227/1997-0935.2017.2.184-192
Representation of incomplete contact problems by half-planes / H. Andresen, D. Hills, M. Moore // Eur. J. Mech. A Solids. — 2020. — Vol. 85. — P. 104138. https://doi.org/10.1016/j.euromechsol.2020.104138 DOI: https://doi.org/10.1016/j.euromechsol.2020.104138
Closed-form solutions for tilted three-part piecewise-quadratic half-plane contacts / H. Andresen, D.A. Hills, J. Vazquez // Int. J. Mech. Sci. — 2019. — Vol. 150. — P. 127-134. https://doi.org/10.48550/arXiv.1902.08044 DOI: https://doi.org/10.1016/j.ijmecsci.2018.09.024
Half-plane partial slip contact problems with a constant normal load subject to a shear force and differential bulk tension / M. Moore, R. Ramesh, D. Hills, et al. // J. Mech. Phys. Solids. — 2018. — Vol. 118. — P. 245-253. https://doi.org/10.1016/j.jmps.2018.05.017 DOI: https://doi.org/10.1016/j.jmps.2018.05.017
Explicit equations for the half-plane sub-surface stress field under a flat rounded contact / J. Vazquez, C. Navarro, J. Domınguez // J. Strain Anal. Eng. Des. — 2014. — Vol. 49, No. 8. — P. 562-570. https://doi.org/10.1177/0309324714545665 DOI: https://doi.org/10.1177/0309324714545665
Asymptotic analysis of stresses in an isotropic linear elastic plane or half-plane weakened by a finite number of holes / J. Kratochvil, W. Becker // Arch. Appl. Mech. — 2012. — Vol. 82. — P. 743-754. https://doi.org/10.1007/S00419-011-0587-Z DOI: https://doi.org/10.1007/s00419-011-0587-z
Development of a distributed dislocation dipole technique for the analysis of multiple straight, kinked and branched cracks in an elastic half plane / M.W. Hallback, N. Tofique // Int. J. Solids Struct. — 2014. — Vol. 51. — P. 2878-2892. https://doi.org/10.1016/j.ijsolstr.2014.04.011 DOI: https://doi.org/10.1016/j.ijsolstr.2014.04.011
Stress intensity factor for the interaction between a straight crack and a curved crack in plane elasticity / M.R. Aridi, N.M.A. Nik Long, Z.K. Eshkuvatov / Acta Mech. Solida Sin. — 2016. — Vol. 29. — P. 407-41. https://doi.org/10.1016/S0894-9166(16)30243-9 DOI: https://doi.org/10.1016/S0894-9166(16)30243-9
Evaluation of the T-stress for multiple cracks in an elastic half-plane using singular integral equation and Green’s function method / Y.Z. Chen // Appl. Math. Comput. — 2014. — Vol. 228. — P. 17-30. https://doi.org/10.1016/j.amc.2013.11.094 DOI: https://doi.org/10.1016/j.amc.2013.11.094
Osnovy teorii uprugosti i plastichnosti / A.V. Alexandrov, V.D. Potapov. — Moscow: Vysshaya shkola, 1990. — 400 p.
Mehanika ploskih i prostranstvennyh konstrukcij / K.A. Tursunov. — Karaganda: KTU Publishing House, 2010. — 130 p.
Downloads
Published
How to Cite
License
Copyright (c) 2022 Technobius
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
