Node

Background

The Node class defines a point in a finite element mesh. This class provides with member functions that allow

• Node::Coordinates : to obtain the coordinates of the node
• Node::TotalDegreeOfFreedom : to obtain the numbering for total degrees of freedom (without restrain and constraint)
• Node::FreeDegreeOfFreedom : to obtain the numbering for free degrees of freedom (with restrain and constraint).

This class also provided with private member variables that stores information regarding

• Node::Displacements displacements of the node at each degree of freedom,
• Node::Velocities velocities of the node at each degree of freedom,
• Node::Accelerations accelerations of the node at each degree of freedom.

The Figure below shows a schematic representation of a node in 1 dimension, 2 dimensions and 3 dimensions, respectively. The single arrows represent the translational degree-of-freedom, while the triple arrows represent the rotational degree-of-freedom.

REFERENCE:

• Forde, B. W. R., Foschi, R. O., & Stiemer, S. F. (1990). "Object-oriented finite element analysis". Computers & Structures, 34(3), 355–374.
• Mackie, R. I. (1992). "Object oriented programming of the finite element method". International Journal for Numerical Methods in Engineering, 35(2), 425–436.

Pre-Analysis

The python 01-Pre_Process/Method/Attach.py file provides with an interface to populate the Entities dictionary. A Node can be created using the addNode() function. This function will transform the provided information into json format to be parse in the Run-Analysis.

• addNode(tag, ndof, coords, freedof, totaldof):

  • tag : The identifier of this node, i.e., tag > -1
  • ndof : Number of degree of freedom, i.e., ndof > 0
  • coords : Coordinates of the node, i.e., (x,y) or (x,y,z)
  • freedof : The free (with restrain/constraint) degree of freedom numbering of this node
  • totaldof : The total (without restrain/constraint) degree of freedom numbering of this node

  Example

  A NODE can be defined using the python interface as follows:
  SVL.addNode(tag=6, ndof=3, coords=[1.00, 0.00, 0.00])

  Application
  Please refer to the D05-ST_Lin_2DBernoulliArc_Elastic_Frame2.py file located at 03-Validations/01-Debugging/ to see an example on how to define nodes using the addNode function.

On the contrary, the 01-Pre_Process/Method/Remove.py file provides with an interface to depopulate the Entities dictionary. For example, to remove an already define Node, use:

• delNode(tag):
  • tag : The identifier of the node to be removed, i.e., tag > -1

Run-Analysis

The C++ 02-Run_Process/01-Node/Node.cpp file provides with the Node class implementation. A Node is created using the built-in json parse-structure provided in the Driver.hpp. A Node is defined inside the "Nodes" json field indicating its "Tag" as follows,

• {
      "Nodes": {
          "Tag": {
              "ndof" : int,
              "totaldof": [ ],
              "freedof" : [ ],
              "coords"  : [ ]
          }
      }
  }
  

  Variable	Description
  Tag	A unique node number identifier.
  ndof	Number of degree-of-freedom in the node.
  totaldof	List of total degree-of-freedom identifiers.
  freedof	List of free degree-of-freedom identifiers, ( \(= -1\)) is restrain, ( \(\leq -2\)) is constraint, and and ( \(\geq 0\)) is free.
  coords	The coordinates in 1-, 2-, and 3-dimensions of the node.

  
  

  Attention

  The node identifier number must be unique and positive ( \(\geq0\)).

  The numbering in totaldof and freedof defines the sparse matrix pattern.

  The node object handles the domain-reduction motion used in Load.

  It is worth mentioning that the number of degree of freedom ndof at each node is defined by the user, and such number should be consistent with the element that will be connected to that node. Defining the number of degree of freedom in this manner allows to add explicitly internal degree of freedom that can be used to formulate elements, see for instance PML2DQuad4.

  Example

  A fixed tri-dimensional NODE with 3 degree of freedom and coordinate (0.0, 0.0, 10.5)
  { "Nodes": { "4": { "ndof" : 3, "totaldof": [12, 13, 14], "freedof" : [-1, -1, -1], "coords" : [0.0, 0.00, 10.50] } } }

  A free two-dimensional NODE with 3 degree of freedom and coordinate (0.20, 0.50)
  { "Nodes": { "48": { "ndof" : 3, "totaldof": [345, 346, 347], "freedof" : [327, 328, 329], "coords" : [0.20, 0.50] } } }