Structural Engineering and Mechanics

  • 제81권3호
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  • Pages.335-348
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  • 2022
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Easy function for solving linear elasticity problems

  • Rezaiee-Pajand, Mohammad (Department of Civil Engineering, Ferdowsi University of Mashhad) ;
  • Karimipour, Arash (Department of Civil Engineering, Member of Center for Transportation Infrastructure System (CTIS), University of Texas at El Paso (UTEP))
  • 투고 : 2020.01.27
  • 심사 : 2021.11.17
  • 발행 : 2022.02.10
⟨ 이전 논문 다음 논문 ⟩

초록

It is well known that after finding the displacement in the structural mechanics, strain and stress can be obtained in the straight-forward process. The main purpose of this paper is to unify the displacement functions for solving the solid body. By performing mathematical operations, three sets of these key relationships are found in this paper. All of them are written in the Cartesian Coordinates and in terms of a simple function. Both analytical and numerical approaches are utilized to validate the correctness of the presented formulations. Since all required conditions for the bodies with self-equilibrated loadings are satisfied accurately, the authors' relations can solve these kinds of problems. This fact is studied in-depth by solving some numerical examples. It is found that a very simple function can be used for each formulation instead of ten different and complex displacement potentials defined by previous studies.

키워드

참고문헌

  1. Adamek, V. (2018), "The limits of Timoshenko beam theory applied to impact problems of layered beams", Int. J. Mech. Sci., 145, 128-137. https://doi.org/10.1016/j.ijmecsci.2018.07.001.
  2. Bhaskar, K. and Pydah, A. (2014) "An elasticity approach for simply-supported isotropic and orthotropic stiffened plates", Int. J. Mech. Sci., 89, 21-30. https://doi.org/10.1016/j.ijmecsci.2014.08.013
  3. Brischetto, S. (2016), "Exact and approximate shell geometry in the free vibration analysis of one-layered and multilayered structures", Int. J. Mech. Sci., 113, 81-93. https://doi.org/10.1016/j.ijmecsci.2016.04.010.
  4. Chen, Y.D., Pei, C.Y. and Chen, S.H. (2011), "Bifurcations of non-semi-simple eigenvalues and the zero-order approximations of responses at critical points of Hopf bifurcation in nonlinear systems", Struct. Eng. Mech., 40, 335-346. https://doi.org/10.12989/sem.2011.40.3.335.
  5. Daneshjou, K., Talebitooti, R. and Tarkashvand, A. (2016), "Analysis of sound transmission loss through the thick-walled cylindrical shell using three-dimensional elasticity theory", Int. J. Mech. Sci., 106, 286-296. https://doi.org/10.1016/j.ijmecsci.2015.12.019.
  6. Daneshjou, K., Talebitooti, R. and Tarkashvand, A. (2017), "An exact solution of three-dimensional elasticity for sound transmission loss through FG cylinder in presence of subsonic external flow", Int. J. Mech. Sci., 120, 105-119. https://doi.org/10.1016/j.ijmecsci.2016.10.008.
  7. Gallimard, L., Ladeveze. P. and Pelle. J.P. (2002), "Applications of an improved estimator of the constitutive relation error to plasticity problems", Struct. Eng. Mech., 14, 381-400. https://doi.org/10.12989/sem.2002.14.4.381.
  8. Gao, Y.C. and Gao, T.J. (2000), "Large deformation contact of a rubber notch with a rigid wedge", Int. J. Solid Mech., 37, 4319-4334. https://doi.org/10.1016/S0020-7683(99)00191-2.
  9. Kang, J.H. (2014) "Exact solutions for stresses, strains, and displacements of a rectangular plate with an arbitrarily located circular hole subjected to in-plane bending moment", Int. J. Mech. Sci., 89, 482-486. https://doi.org/10.1016/j.ijmecsci.2014.10.019.
  10. Karageorghis, A. and Lesnic, D. (2018) "Reconstruction of an elliptical inclusion in the inverse conductivity problem", Int. J. Mech. Sci., 142, 603-609. https://doi.org/10.1016/j.ijmecsci.2018.05.002
  11. Li, P.D., Li, X.Y., Kang, G.Z. and Muller, R. (2017), "Three-dimensional fundamental solution of a penny-shaped crack in an infinite thermo-magneto-electro-elastic medium with transverse isotropy", Int. J. Mech. Sci., 130, 203-220. https://doi.org/10.1016/j.ijmecsci.2017.05.052.
  12. Liang, L. and Dui, C.G. (2018), "Exact solutions for functionally graded micro-cylinders in first gradient elasticity", Int. J. Mech. Sci., 142, 49-54. https://doi.org/10.1016/j.ijmecsci.2018.09.011.
  13. Liew, K.M., Teo, T.M. and Han, J.B. (2001), "Three-dimensional static solutions of rectangular plates by variant differential quadrature method", Int. J. Mech. Sci., 43(7), 1611-1616. https://doi.org/10.1016/S0020-7403(00)00098-9
  14. Rezaiee-Pajand, M. and Karimipour, A. (2019b), "Stress analysis by two cuboid isoparametric elements", Eur. J. Comput. Mech., 28(5), 373-410. https://doi.org/10.13052/ejcm2642-2085.2851
  15. Rezaiee-Pajand, M. and Karimipour, A. (2019c), "Analytical Scheme for Solid Stress Analysis", Int. J. Appl. Mech., 12, 2050071. https://doi.org/10.1142/S1758825120500714
  16. Rezaiee-Pajand, M., Karimipour, A. and Ameli Basiri, M. (2020), "Study on the seismic behavior of steel shear plates", Proc. Inst. Civil Eng.-Struct. Build., 12, 1751-7702. https://doi.org/10.1680/jstbu.20.00019
  17. Rezaiee-Pajand, M., Rajabzadeh-Safaei, N. and Hozhabrossadati, S.M (2018), "Three-dimensional deformations of a curved circular beam subjected to thermo-mechanical loading using green's function method", Int. J. Mech. Sci., 142, 163-175. https://doi.org/10.1016/j.ijmecsci.2018.04.045.
  18. Rezaiee-Pajand. M. and Karimipour. A. (2019a), "Three stress-based triangular elements", Eng. Comput., 20, 1-12. https://doi.org/10.1007/s00366-019-00765-6.
  19. Sadds, M.H. (2005), Elasticity Theory, Elasticity Theory, Applications, and Numeric.
  20. Shaat, M. (2015) "Iterative nonlocal elasticity for Kirchhoff plates", Int. J. Mech. Sci., 90, 162-170. https://doi.org/10.1016/j.ijmecsci.2014.11.004
  21. Shaat, M. and Mohamed, S.A. (2014), "Nonlinear-electrostatic analysis of micro-actuated beams based on couple stress and surface elasticity theories", Int. J. Mech. Sci., 84, 208-217. https://doi.org/10.1016/j.ijmecsci.2014.04.020i.
  22. Tajed. V., Ohadi. A. and Sadighi. M. (2011), "Three-dimensional free vibration of variable thickness thick circular and annular isotropic and functionally graded plates on Pasternak foundation", Int. J. Mech. Sci., 53(4), 300-308. https://doi.org/10.1016/j.ijmecsci.2011.01.011.
  23. Waluyo, S. (2017), "Stress dependent relaxation time in large deformation", Struct. Eng. Mech., 61, 317-323. https://doi.org/10.12989/sem.2017.61.3.317.
  24. Yamada. T. (1998), "Finite element procedure of initial shape determination for hyperelasticity", Struct. Eng. Mech., 6, 173-183. https://doi.org/10.1007/978-3-642-79654-8_408
  25. Yan. G., Chuanzeng. Z., Wenzhen. Q. and Jieyu. D. (2018) "Investigation on near-boundary solutions for three-dimensional elasticity problems by an advanced BEM", Int. J. Mech. Sci., 142, 269-275. https://doi.org/10.1016/j.ijmecsci.2018.05.007.
  26. Yang. X., Chen. S. and Lian. H. (2001), "Interval finite element method based on the element method based on the element for eigenvalues analysis of structures with interval parameters", Struct. Eng. Mech., 12, 669-684. https://doi.org/10.12989/sem.2001.12.6.669.
  27. Zemanova. A., Zemana. J., Jandab. T. and Sejnohac. M. (2018), "Layer-wise numerical model for laminated glass plates with viscoelastic interlayer", Struct. Eng. Mech., 65, 639-380. https://doi.org/10.12989/sem.2018.65.4.369.
  28. Zhu. X. and Li. L (2017), "Longitudinal and torsional vibrations of size-dependent rods via nonlocal integral elasticity", Int. J. Mech. Sci., 133, 639-650. https://doi.org/10.1016/j.ijmecsci.2017.09.030.