1. Reference problem#

1.1. Geometry#

Geometry of the four substructures (\(\mathrm{TRI1}\), \(\mathrm{TRI2}\),,, \(\mathrm{TRI3}\), \(\mathrm{TRI4}\)):

_images/100002000000022A0000018B208D3244A46E1CA3.png _images/1000000000000589000003900C18A21AECEFF724.jpg

Substructure meshing

Triangle geometry \((m)\):

\(C=1\)

thickness: \(e=0.01\)

Node coordinates:

\(\mathrm{NO1}=(1.0\mathrm{,0}.0)\)

\(\mathrm{NO43}=(0.687,0.108)\)

Mesh group:

\(\mathrm{BASE}\): set of nodes forming the base of the triangle

\(\mathrm{GAUCHE}\): set of nodes forming the right side of the triangle

\(\mathrm{DROITE}\): set of knots forming the left side of the triangle

\(\mathrm{TOUT}\): set of nodes forming the triangle

1.2. Elastic properties of materials#

  • Young’s modulus: \(E=2.1E11\mathrm{Pa}\)

  • Poisson’s ratio: \(\nu =0.3\)

  • volume density: \(\rho =7800.0{\mathrm{kg.m}}^{-3}\)

1.3. Boundary conditions and loads#

  • **Substructure:* \(\mathrm{TRI1}\):

    • Compulsory trips:

      • \(\mathrm{TOUT}\): \(\mathrm{DRZ}=0.0\)

      • \(\mathrm{BASE}\): \(\mathrm{DX}=\mathrm{DY}=\mathrm{DZ}=\mathrm{DRX}=\mathrm{DRY}=0.0\)

        • Interfaces:

          • \(\mathrm{BASE}\): type: CRAIGB, mask: \(\mathrm{DRZ}\)

    • **Substructure:* \(\mathrm{TRI2}\):

      • Nautical angles \((\alpha ,\beta ,\gamma )\): \((0.0\mathrm{,0}.0\mathrm{,180}.0)\)

        • Compulsory trips:

          • \(\mathrm{TOUT}\): \(\mathrm{DRZ}=0.0\)

          • \(\mathrm{BASE}\): \(\mathrm{DX}=\mathrm{DY}=\mathrm{DZ}=\mathrm{DRX}=\mathrm{DRY}=0.0\)

          • \(\mathrm{DROITE}\): \(\mathrm{DX}=\mathrm{DY}=\mathrm{DZ}=\mathrm{DRX}=\mathrm{DRY}=0.0\)

          • \(\mathrm{GAUCHE}\): \(\mathrm{DX}=\mathrm{DY}=\mathrm{DZ}=\mathrm{DRX}=\mathrm{DRY}=0.0\)

        • Interfaces:

          • \(\mathrm{BASE}\): type: CRAIGB, mask: \(\mathrm{DRZ}\)

          • \(\mathrm{GAUCHE}\): type: CRAIGB, mask: \(\mathrm{DRZ}\)

          • \(\mathrm{DROITE}\): type: CRAIGB, mask: \(\mathrm{DRZ}\)

    • **Substructure*: \(\mathrm{TRI3}\):

      • Compulsory trips:

        • \(\mathrm{TOUT}\): \(\mathrm{DRZ}=0.0\)

        • \(\mathrm{BASE}\): \(\mathrm{DX}=\mathrm{DY}=\mathrm{DZ}=\mathrm{DRX}=\mathrm{DRY}=0.0\)

        • \(\mathrm{DROITE}\): \(\mathrm{DX}=\mathrm{DY}=\mathrm{DZ}=\mathrm{DRX}=\mathrm{DRY}=0.0\)

        • Interfaces:

          • \(\mathrm{DROITE}\): type: CRAIGB, mask: \(\mathrm{DRZ}\)

    • **Substructure:* \(\mathrm{TRI4}\):

      • Nautical angles \((\alpha ,\beta ,\gamma )\): \((0.0\mathrm{,180}.0\mathrm{,0}.0)\)

        • Compulsory trips:

          • \(\mathrm{TOUT}\): \(\mathrm{DRZ}=0.0\)

          • \(\mathrm{BASE}\): \(\mathrm{DX}=\mathrm{DY}=\mathrm{DZ}=\mathrm{DRX}=\mathrm{DRY}=0.0\)

          • \(\mathrm{DROITE}\): \(\mathrm{DX}=\mathrm{DY}=\mathrm{DZ}=\mathrm{DRX}=\mathrm{DRY}=0.0\)

        • Interfaces:

          • \(\mathrm{DROITE}\): type: CRAIGB, mask: \(\mathrm{DRZ}\)