FiberSection
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This material is not yet available
The fiber section model implements a complex cross section built from multiple FiberMaterial material class instances
\[\varepsilon(z) = \varepsilon_0 - z \,\phi\]
\[f = \int_A \sigma(z)\, dA
\qquad \qquad
M = -\int_A z\sigma(z)\, dA\]
\[df = \int_A \mathcal{C}(z)\, dA \, d\varepsilon_0
-\int_A z\mathcal{C}(z)\, dA \, d\phi
=: \mathbb{D} \, d\varepsilon_0
+\mathbb{C} d\phi\]
\[dM = -\int_A z\mathcal{C}(z)\, dA \, d\varepsilon_0
+\int_A z^2\mathcal{C}(z)\, dA \, d\phi
=: \mathbb{C} \, d\varepsilon_0
+ \mathbb{B} \, d\phi\]
where
\(\varepsilon_0\) |
axial strain (input) |
\(\phi\) |
curvature change (input) |
\(f\) |
resulting axial force (output) |
\(M\) |
resulting moment (output) |
\(\mathcal{C}(z)\) |
material tangent stiffness of a fiber-material at distance z |
\(\mathbb{D}\) |
axial stiffness |
\(\mathbb{B}\) |
flexural stiffness |
\(\mathbb{C}\) |
coupling stiffness |