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AutoFEM Analysis Beam under the Action of Two Tensile Forces |  |
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AutoFEM Analysis Beam under the Action of Two Tensile Forces | |
Beam under the action of two tensile forces
Let us consider a beam of length L, loaded with two forces F, applied by normal to either of the ends. The cross-section of the beam is a rectangle of width b and height h.
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Sought quantity is the maximum beam extension.
Assume F = 1000 N, L = 0.5 m, b = 0.05 m, h = 0.02 m.
Characteristics of material have values: Young's modulus E = 2.1E+011 Pa, Poisson's ratio ν = 0.28.
Both ends of the beam are assumed free and subjected to the load F, directed normally to their faces.
To solve this study in AutoFEM Analysis, it is necessary to turn on the option "Stabilize the unfixed model" with additional stiffness equal 1.
You should check this box at the Properties dialog of Static Analysis on the page "Solving".
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The finite element model with applied loads and restraints |
The analytical solution appears as:
w = ( F . L ) / ( A . E ) = 2.381E-006 m
where P – is the force, L – the beam length, E – the material Young's modulus, A = b . h - the area of the beam section.
After carrying out calculation with the help of AutoFEM, the following results are obtained:
(extension of the beam is equal to (1.1892E-006)+(1.1918E-006)=2.3810E-006 m)
Table 1.Parameters of the finite element mesh
Finite Element Type |
Number of Nodes |
Number of Finite Elements |
quadratic tetrahedron |
923 |
2445 |
Table 2. Result "Displacement, 0X"*
Numerical Solution |
Analytical Solution |
Error δ =100%* |0X* - 0X| / |0X| |
2.3810E-004 |
2.381E-004 |
0.001 |
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Conclusions:
The relative error of the numerical solution compared to the analytical solution is equal to 0.01% for quadratic finite elements.
*The results of numerical tests depend on the finite element mesh and may differ slightly from those given in the table.
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