1. Reference problem#
1.1. Geometry#
Or a plate whose characteristics are as follows:
length: \(a=1.5m\) |
width: \(b=1m\) |
thickness: \(t=0.01m\) |
The characteristic points of the plate have the following coordinates:
\(A\) |
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\(x\) |
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\(y\) |
1.5 |
1.5 |
1.5 |
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\(z\) |
1.2. Material properties#
The parameters characterizing the properties of the material are:
\(E=2.1{10}^{\mathrm{11 }}\mathrm{Pa}\) |
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1.3. Boundary conditions and loads#
1.3.1. Flexion problem#
The plate is easily supported on all sides: for any point \(P\) on the edge we have: \(w=0\).
1.3.2. Membrane problem#
For all points on the plate, we block the movement in \(z\) and the three degrees of rotation, that is to say:
\(w=0.\) \({\theta }_{x}={\theta }_{y}={\theta }_{z}=0.\)
On the sides \(\mathrm{AD}\) and \(\mathrm{BC}\) we block the movement in \(y\): for \(y=0.\) or \(y=a\) we have \(v=0\).
At points \(A,B,C,D\), springs with a stiffness of \(k\) are attached. The axis of these springs is the \(x\) direction.
The numeric value for \(k\) is \(k=25N/m\).