Documentation
The aim of this test case is to validate the following functions:
The simulation results of SimScale were compared to the analytical results derived from [Roark]. The mesh used was created locally consisting of quadratic hexahedral elements and uploaded to the SimScale platform.
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Geometry of the bimetallic strip
The bimetallic strip has a length of l=10m, width of w=1m and the total height of h=0.1m with each strip thickness of ta=tb=0.05m.
Tool Type : CalculiX
Analysis Type : Thermomechanical
Mesh and Element types :
Mesh type | Number of nodes | Number of 3D elements | Element type |
---|---|---|---|
quadratic hexahedral | 3652 | 600 | 3D isoparametric |
Mesh used for the SimScale
Material:
Upper strip:
Lower strip:
Initial Conditions:
Constraints:
Temperature:
Contact:
(1)\[K_1 = 4 + 6 \frac {t_a}{t_b} + 4 \left(\frac {t_a}{t_b}\right)^2 + \frac {E_a}{E_b} \left(\frac {t_a}{t_b}\right)^3 + \frac {E_a}{E_b} \frac {t_a}{t_b} = 16\] (2)\[d_x = \frac {6 l (\gamma_b – \gamma_a) (T – T_o) (t_a + t_b)}{(t_b)^2 K_1} = 0.0015 \ m\] (3)\[d_z = \frac {3 (l)^2 (\gamma_b – \gamma_a) (T – T_o) (t_a + t_b)}{(t_b)^2 K_1} = 0.075 \ m\] (4)\[\sigma = \frac {(\gamma_b – \gamma_a) (T – T_o) E_a}{K_1} \left[3 \frac {t_a}{t_b} + 2 – \frac {E_a}{E_b} \left(\frac {t_a}{t_b}\right)^3\right] = 50 \ MPa\]
The equation (1), (2), (3) and (4) used to solve the problem is derived in [Roark]. Equations (2) and (3) are the displacements of the bimetallic strip in x and z direction respectively. Whereas, equation (4) is the normal stress in x direction at the bottom surface.
Comparison of the x and z displacements computed on node N3 and σxx computed on node N2 with [Roark] formulations.
Quantity | [Roark] | SimScale | Error |
---|---|---|---|
dx (m) | 0.0015 | 0.0015 | 0% |
dz (m) | 0.075 | 0.074975 | 0.03% |
σ (Mpa) | 50 | 48.79 | 2.42% |
[Roark] | (1, 2, 3, 4) (2011)”Roark’s Formulas For Stress And Strain, Eighth Edition”, W. C. Young, R. G. Budynas, A. M. Sadegh |
Last updated: January 29th, 2019
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