Class LinearElement1D

java.lang.Object
org.episteme.core.mathematics.analysis.fem.LinearElement1D
All Implemented Interfaces:
Element
public class LinearElement1D extends Object implements Element
A 1D linear finite element with 2 nodes.

Local coordinate xi ranges from -1 to 1. Shape functions: N1 = 0.5 * (1 - xi) N2 = 0.5 * (1 + xi)

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

  • Constructor Details

    • LinearElement1D

      public LinearElement1D(Node n1, Node n2)

  • 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)