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TEST CASE 6.5 THERMAL EXPANSION AT THE PRESENCE OF THE GAP

Reference:

O. Harris, Introduction to Stress Analysis, The Macmillan Co., New York, NY, 1959, pg. 58, problem 8

 

Problem description:

Console bar is heating up. In order to restrict heat extension a gap at the bar end is applied. Determine axial load N in truss at the moment of gap disappearing.  

 

Problem sketch:

Type of created problem:

Flat frame (X, Z, UY).

 

Geometric characteristics:

L = 3 m; δ = 0.002 m.

 

Material properties:

Elastic modulus: E = 10.5·106 tf;

Thermal expansion coefficient: α = 12.5·10-6 °С-1.

 

Boundary conditions:

Left side of beam: X = Z = UY = 0.

 

Loads:

ΔТ = 100 °С.

 

Model description:

The system is modeled by 2 general finite elements of spatial bar (FE type is 10) and 1 physically nonlinear single-noded FE of one-sided inelastic links (FE type is 266). A gap is modelled via single-noded finite element with a large rigidity with a gap. A node, which contain single-noded element is linked at directions Z and UY. For nonlinear solution, iterative process is used (number of steps is 1, minimum number of iterations is 3000).

 

Calculation results:

Target value

Analytical solution

LIRA 10

Deviation, %

N, tf

6125

6125

0.00