Structural Engineering and Mechanics

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

  • Received : 2002.06.08
  • Accepted : 2003.03.06
  • Published : 2003.04.25
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Abstract

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.

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References

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  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