1. Reference problem

1.1. Geometry

Beam length: \(L=0.6m\)

Consistent thickness: \(h=0.01m\)

Rectangular section:

Initial right section:		Section variation:
width:	\({b}_{0}=0.03m\)	\(b={b}_{0}{e}^{-2\alpha x}\) with \(\alpha =1.\)
do:	\({A}_{0}={3.10}^{-4}{m}^{2}\)	\(A={A}_{0}{e}^{-2\alpha x}\)
moment of inertia:	\({\mathrm{Iz}}_{0}=0.25{10}^{-8}{m}^{4}\)	\(\mathrm{Iz}={\mathrm{Iz}}_{0}{e}^{-2\alpha x}\)

Point coordinates ( \(m\) ) :

	\(A\)	\(B\)
\(x\)		0.6
\(y\)

1.2. Material properties

\(E={2.10}^{11}\mathrm{Pa}\)

\(\nu =0.3\)

\(\rho =7800.\mathrm{kg}/{m}^{3}\)

1.3. Boundary conditions and loads

Points \(A\) and \(B\): embedded, \(u=v=0.\), \(\theta =0\).