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AutoFEM Analysis Deflection of a Plate under the Gravitation |  |
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AutoFEM Analysis Deflection of a Plate under the Gravitation | |
Deflection of a Plate under the Gravitational Load
Let us consider a beam under the gravitational load g. A length of the beam is L. The beam cross-section is a b x h rectangle.
Sought quantity is the maximum deflection of the beam.
Let us use the following initial data: L = 1 m, b = 0.5 m, h=1.5 mm.
Material characteristics: the Young's modulus E = 2.1E+011 Pa, Poisson's ratio ν = 0.28, ρ=7800 kg/m3.
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The finite element model with applied loads and restraints |
The analytical solution is calculated by the formula:
Thus, | z | = 2.428313E-001 m.
After carrying out calculation with the help of AutoFEM, the following results are obtained:
Table 1.Parameters of the finite element mesh
Finite Element Type |
Number of Nodes |
Number of Finite Elements |
linear triangle |
1326 |
2500 |
Table 2. Result "Displacement"
Numerical Solution |
Analytical Solution |
Error δ =100%* |z* - z | / | z | |
2.3290E-001 |
2.4283E-001 |
4.09 |
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*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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