Structural Engineering and Mechanics

  • 제15권4호
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  • Pages.395-414
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  • 2003
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

On an improved numerical method to solve the equilibrium problems of solids with bounded tensile strength that are subjected to thermal strain

  • 투고 : 2002.06.08
  • 심사 : 2003.03.06
  • 발행 : 2003.04.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper we recall briefly the constitutive equations for solids subjected to thermal strain taking in account the bounded tensile stress of the material. In view to solve the equilibrium problem via the finite element method using the Newton Raphson procedure, we show that the tangent elasticity tensor is semi-definite positive. Therefore, in order to obtain a convergent numerical method, the constitutive equation needs to be modified. Specifically, the dependency of the stress by the anelastic deformation is made explicit by means of a parameter ${\delta}$, varying from 0 to 1, that factorizes the elastic tensor. This parameterization, for ${\delta}$ near to 0, assures the positiveness of the tangent elasticity tensor and enforces the convergence of the numerical method. Some numerical examples are illustrated.

키워드

참고문헌

  1. Alfano, G., Rosati, L. and Valoroso, N. (2000), "A numerical strategy for finite element analysis of no-tension materials", Int. J. Numer. Meth. Eng., 48, 317-350. https://doi.org/10.1002/(SICI)1097-0207(20000530)48:3<317::AID-NME868>3.0.CO;2-C
  2. Del Piero, G. (1989), "Constitutive equation and compatibility of the external loads for linear elastic masonrylike materials", Meccanica, 24, 150-162. https://doi.org/10.1007/BF01559418
  3. Lucchesi, M., Padovani, C. and Pagni, A. (1994), "A numerical method for solving equilibrium problems of masonry-like solids", Meccanica, 29, 109-123. https://doi.org/10.1007/BF01007496
  4. Lucchesi, M., Padovani, C. and Pasquinelli, G. (1995), "On the numerical solution of equilibrium problems for elastic solids with bounded tensile strength", Comput. Method Appl. Mech. Eng., 127, 37-56. https://doi.org/10.1016/0045-7825(95)00816-4
  5. Lucchesi, M., Padovani, C. and Pasquinelli, G. (2000), "Thermodynamics of no-tension materials", Int. J. Solids Struct., 37, 6581-6604. https://doi.org/10.1016/S0020-7683(99)00204-8
  6. Ogden, R.W. (1997), Non-linear Elastic Deformations, Dover Publications, Inc., Mineola, New York.
  7. Padovani, C., Pasquinelli, G. and Zani, N. (2000), "A numerical method for solving equilibrium problems of notension solids subjected to thermal loads", Comput. Method Appl. Mech. Eng., 190, 55-73. https://doi.org/10.1016/S0045-7825(99)00346-1
  8. Padovani, C. (2000), "On a class of non-linear elastic materials", Int. J. Solids Struct., 37, 7787-7807. https://doi.org/10.1016/S0020-7683(99)00307-8
  9. Simo, J.C. and Rifai, M.S. (1990), "A class of mixed assumed strain methods and the method of incompatible modes", Int. J. Numer. Meth. Eng., 29, 1595-1638. https://doi.org/10.1002/nme.1620290802

피인용 문헌

  1. Solids 3-D with bounded tensile strength under the action of thermal strains. Theoretical aspects and numerical procedures vol.18, pp.1, 2004, https://doi.org/10.12989/sem.2004.18.1.059
  2. An assumed strain quadrilateral element with drilling degrees of freedom vol.41, pp.3, 2004, https://doi.org/10.1016/j.finel.2004.05.004
  3. An Approach to Masonry Structural Analysis by the No-Tension Assumption—Part I: Material Modeling, Theoretical Setup, and Closed Form Solutions vol.63, pp.4, 2010, https://doi.org/10.1115/1.4002790