1. Reference problem#

1.1. Geometry#

_images/10000CD80000284F000012EABCD9F9D362A9C8AE.svg

Flat structure symmetric with respect to the line \(y=4.\)

Section beams

circular

outside diameter

\(\mathrm{de}=0.04m\)

inner diameter

\(\mathrm{di}=0.01m\)

Elbow

center

(\(y=4\) \(z=0\))

and radius = \(2\sqrt{2}m\)

Node-node link

\(\mathrm{Kx}=\mathrm{Kz}={10}^{5}N/m\)

in the local coordinate system

Point coordinates (in \(m\) ) :

\(A\)

\(B\)

\(C\)

\(D\)

\(E\)

\(F\)

G

\(x\)

\(y\)

—2.

\(z\)

—2.

\(2\sqrt{2}\)

—2.

1.2. Material properties#

Young’s module: \(E=2.1{10}^{11}\mathrm{Pa}\)

Poisson’s ratio: \(\nu =0.3\)

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

Coefficient of thermal expansion: \(\alpha ={10}^{-6}m/°C\)

1.3. Boundary conditions and loads#

Points \(A\) and \(G\) embedded

(\(v=w=0\))

(except for load case 2)

Loading:

  1. load concentrated in \(C\) and \(E\)

\(F=1000N\)

  1. displacement imposed in \(A\) and \(G\)

\(\mathrm{Dx}=\sqrt{2}\) as a local coordinate system for links \(\mathrm{AB}\) and \(\mathrm{GF}\)

  1. thermal expansion at \(t=100°C\)

  1. own weight

  1. material dependent on T