1. Reference problem#

1.1. Geometry#

A discrete element of zero size with 2 knots.

Local coordinate system = global coordinate system.

A K_ TR_D_L stiffness matrix assigned by default:

\(1.6N/m\) in translation, \(1.9N/m\) in rotation.

The stiffness characteristics in the local direction \(y\) (here equal to the global axis \(Y\)) are modified by a behavior relationship of the type ARME in force-displacement introduced by a characteristic material.

1.2. Material properties#

Linked to an incremental behavior ARME with 5 parameters: \({d}_{e}\) (keyword DLE) = (keyword) = \(0.048m\), \({d}_{l}\) (keyword DLP) = \(0.7m\), \({K}_{\mathrm{el}}\) (keyword KYE) = \(1.67\mathit{E4}N/m\) \({K}_{\mathrm{pl}}\) KYP \(2.9\mathit{E3}N/m\), \({K}_{G}\) (key word KYG) = \(\mathrm{1 E6 }N/m\).

  • \({d}_{e}\) limiting displacement of the elastic domain,

  • \({d}_{l}\) limiting displacement of the plastic domain,

  • \({K}_{\mathrm{el}}\) slope of the elastic domain,

  • \({K}_{\mathrm{pl}}\) slope of the plastic domain,

  • \({K}_{G}\) ultimate slope,

Behaviour of a cocking arm under longitudinal stress

_images/1000104E00001F510000112816547A497DB92680.svg

\({d}_{e}=0.048m\), \({d}_{l}=0.7m\), \({L}_{e}=\mathrm{800 }N\), \({F}_{m}=\mathrm{2800 }N\)

Unidirectional force-displacement behavior with 1 internal variable: \({d}_{p}–{d}_{e}\) defined by 5 parameters: \({d}_{e}\), \({d}_{l}\), \({K}_{\mathrm{el}}\), \({K}_{\mathrm{pl}}\) and \({K}_{G}\), assigned to a discrete element with 2 nodes.

1.3. Boundary conditions and loads#

Embedding in one of the 2 knots.

Force imposed in the local direction \(y\) (identical to global \(Y\)) on the second node, in load increments. A unit increment equal to \(\mathrm{500 }N\).

1.4. Initial conditions#

Zero displacements, efforts, and internal variables.