Class TriangularElement2D

java.lang.Object
org.episteme.core.mathematics.analysis.fem.TriangularElement2D
All Implemented Interfaces:
Element
public class TriangularElement2D extends Object implements Element
A 2D linear triangular finite element with 3 nodes.

Local coordinates (xi, eta) range from 0 to 1, with xi + eta invalid input: '<'= 1. Shape functions: N1 = 1 - xi - eta N2 = xi N3 = eta

Since:
1.0
Author:
Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

  • Constructor Details

    • TriangularElement2D

      public TriangularElement2D(Node n1, Node n2, Node n3)

  • Method Details

    • getNodes

      public List<Node> getNodes()
      Description copied from interface: Element
      Returns the nodes associated with this element.
      Specified by:
      getNodes in interface Element
      Returns:
      the list of nodes

    • getShapeFunctions

      public List<ShapeFunction> getShapeFunctions()
      Description copied from interface: Element
      Returns the shape functions associated with this element.
      Specified by:
      getShapeFunctions in interface Element
      Returns:
      the list of shape functions

    • computeJacobian

      public Matrix<Real> computeJacobian(Vector<Real> localCoords)
      Description copied from interface: Element
      Computes the Jacobian matrix at the given local coordinates.

      J = d(x,y,z)/d(xi,eta,zeta)

      Specified by:
      computeJacobian in interface Element
      Parameters:
      localCoords - the local coordinates
      Returns:
      the Jacobian matrix

    • getQuadraturePoints

      public List<QuadraturePoint> getQuadraturePoints()
      Description copied from interface: Element
      Returns the quadrature points and weights for numerical integration over this element.
      Specified by:
      getQuadraturePoints in interface Element
      Returns:
      a list of quadrature points (local coords + weight)