ProductsAbaqus/Standard Elements testedC3D8HT C3D8RT C3D8RHT C3D8T C3D10MT C3D10MHT CAX4RHT CAX4RT CAX6MHT CAX6MT CGAX3HT CGAX3T CGAX4HT CGAX4RT CGAX4RHT CGAX4T CGAX6MHT CGAX6MT CGAX8HT CGAX8RT CGAX8RHT CGAX8T CPE4RT CPE4RHT CPE4T CPE6MHT CPE6MT CPEG3HT CPEG3T CPEG4HT CPEG4RT CPEG4RHT CPEG4T CPEG6MHT CPEG6MT CPEG8HT CPEG8RHT CPEG8T CPS4RT CPS4T CPS6MT CPS8RT CPS8T Features testedContinuum coupled temperature-displacement elements are removed and added during a steady-state analysis. Problem descriptionModel:The models have dimensions 5.0 × 2.0 in the x–y plane with an out-of-plane dimension of 1.0. In the axisymmetric case the models have dimensions 2.0 × 5.0 in the r–z plane, and the inner radius, Ri, equals 105. The inner radius is large to ensure that the strains in the circumferential direction are approximately uniform, which allows a comparison of the results obtained in this analysis with those obtained analytically. Material:
Loading and boundary conditionsThe left side of the model is held at θ=0.0. There is a film condition on the right side of the model. The sink temperature is θ0=100.0, and the film coefficient, h, is 1.0. After a steady-state solution is obtained, some of the elements in the model are removed. The temperatures along the new external boundary are held fixed. The removed elements are added back into the model in the last step, and a new film condition is applied on the right side. The new sink temperature is θ0=200.0, and the same h is used. During all three steps the following mechanical boundary conditions are maintained: uy=0.0 at all points along y=0; ux=0.0 at the point (0,0). Reference solutionThe solution for the one-dimensional steady-state heat transfer problem is given in Heat transfer model change: steady state. The solution for the mechanical response of the model is ϵx=∂u∂x=ϵthex=αθ(x)=αxL+k/hθ0.
The expression for ϵx is integrated to give u=12αx2L+k/hθ0+f(y).
The y-component of strain is given as ϵy=∂v∂y=αxL+k/hθ0.
Integrating for v gives v=αxyL+k/hθ0,
where the boundary condition that v=0 at y=0 is used to eliminate the terms that are only functions of x. The condition that γxy=∂u∂y+∂v∂x=0
is used to find f(y), and the x-displacement is given as u=α2(x2-y2)L+k/hθ0.
These expressions are used to calculate the displacements in the model. The temperature distribution can be calculated with the expression from Heat transfer model change: steady state. The results for the axisymmetric case are obtained by replacing x with z and y with (r-Ri) in the relations for temperature and displacements. In addition, the displacements are multiplied by a factor of (1+ν), where ν is the Poisson's ratio. This takes into account the contribution from the approximately constant strain in the circumferential direction. Results and discussionThe model produces the theoretical results in both the first and third steps for the element temperatures and for the quadratic element displacements. The displacements obtained using the model with linear elements do not match the theoretical results but are still reasonable. Input files
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